ecomorphological structure of bat communities: a …

ECOMORPHOLOGICAL STRUCTURE OF BAT COMMUNITIES:

ALTERNATIVE MODELS AND ENVIRONMENTAL GRADIENTS

by

RICHARD D. STEVENS, B.S.

A THESIS

IN

ZOOLOGY

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

Approved

May, 1996

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ACKNOWLEDGMENTS

This thesis represents the culmination of effort of many people. In fact, if one

were to tabulate all of the contributions towards its completion, mine would, by far, be

in the minority compared to those of others.

I would like to fu-st thank my major professor. Dr. Michael Willig, for his

friendship, criticism, enthusiasm, encouragement, emotional and financial support, and

direction. I specifically thank Mike for instilling in me the desire to improve upon my

weaker idiosyncrasies and to capitalize on the stronger ones. Moreover, I am greatly

indebted to him for constant funding, which allowed me teaching-free support

throughout the entire time I pursued my master's.

I would like to thank Dr. Clyde Jones, Dr. Daryl Moorhead, and Dr. Robert

Owen for serving on my committee as well as for their interaction and direction. I

would especially like to thank Dr. Jones for allowing me to be a not-so-honorary

member of his lab, and for ensuring that I truly appreciate what it means to be a

mammalogist. I certainly gained a lot from interaction with and stimulation by him and

his students.

Many fellow graduate students have aided in the conceptual and methodological

development of this thesis. First, and certainly foremost, is the contribution of Alec B.

Shaner. Without Big Al's computer wizardry and mathematical adroitness, my ideas

would have simply remained questions. Maryann Lynch and Kate Lyons provided

much criticism when I lacked forethought, and much support and encouragement

during times of self-doubt. Dianne Hall was exceedingly helpful not only through her

editorial reviews, but also through sharing her wisdom during the latter stages of this

thesis and reassuring me that many of the emotions I was experiencing were quite

normal. Pragna Patel, Maryann Lynch, Kate Lyons, and Dianne Hall were invaluable

in proofing of data and tables. Dr. Charles Werth, Dr. Robert Hollander, Dr. Gerardo

ii

Camilo, Dr. Michael Gannon, Dr. Rick Manning, Brian Croyle, Javier Alvarez,

Elizabeth Sandlin, Steven Cox, Steven Presley, Michael Cramer, Michele Secrest,

Franklin Delano Yancey, II, Michelle Wallace, Burhan Gharaibeh, Johnny Peppers,

Celia Lopez-Gonzales, Justin Jones, Jeff McMillen, Cakky Brawley, and Gary

Greenstreet, all provided much appreciated direction, friendship, and support.

I owe thanks to many faculty members from Texas Tech, as well as other

institutions. Dr. Mark McGinely provided me with much direction in my early pursuit

of community ecology. Dr. Richard Strauss provided statistical expertise regarding

PCA and simulation analyses. Dr. Elgene Box, from the University of Georgia, and

Dr. Michael Rosenzweig, from the University of Arizona, provided direction regarding

primary productivity and evapotranspiration.

Various people and agencies have paid my salary during the time I pursued my

master's degree. Dr. John Zak as director of The Institute for Environmental Sciences

at Texas Tech University provided funding from 1992-1994. Dr. Jorge Saliva and the

U.S. Fish and Wildlife Service provided funds for two summers studying bats in

Puerto Rico. Finally, Dr. Tony Krzysik and the U. S. Army Corps of Engineers

provided funding during the latter stages of this thesis, not to mention insight as to

statistical methods for achieving more accurate density estimates, an appreciation of

ecological phenomena at landscape scales, and many good times in the Mojave Desert.

Several museums have provided specimens for examination. These include:

the Field Museum of Natural History; museums at the University of Kansas and

Louisiana State University; the Smithsonian Institution and United States National

Museum; the American Museum of Natural History; the Carnegie Museum of Natural

History; and The Museum, Texas Tech University. I especially want to thank the

curatorial staff at each of these institutions for their hospitality and patience during my

visits. More specifically, I want to thank Thor Holmes from the University of Kansas

m

for not forgetting his humble beginnings and providing shelter, food, and hospitality to

a poor traveling graduate student.

I would like to state my appreciation to the late Dr. J. Knox Jones, Jr. It was

unfortunate that Dr. Jones was unable to directiy influence a majority of my graduate

career. Nonetheless, Drs. Knox and Clyde Jones are responsible for my initial

involvement in mammalogy, and my subsequent development certainly will be lessened

by the absence of Dr. J. Knox Jones, Jr.

This thesis has probably been my most selfish undertaking, and I would like to

end by thanking my family. Not only has my family been very patient regarding my

lack of interaction, but they have always provided unconditional support and

encouragement. For this I am most thankful. I especially want to thank my mother and

father for their bravery in allowing me the freedom to pursue what I wanted regardless

of the avenue, and can only hope that my winding road will lead to something

comparable to their expectations.

IV

TABLE OF CONTENTS

ACKNOWLEDGMENTS ii

LIST OF TABLES viii

LIST OF FIGURES x

CHAPTER

I. INTRODUCTION 1

Objectives 5

Methodological Considerations 5

Literature Cited 8

II. THE RELATIONSHIP BETWEEN ABUNDANCE AND MORPHOLOGICAL DISSIMILARITY: A MODEL OF COMMUNITY STRUCTURE 12

Abstract 12

Introduction 13

The Model 15

Competitive Scenarios 17

The Community 18

Results 20

Discussion 20

Literature Cited 26

III. COMMUNITIES, INTERACTIONS, AND COMPETITIVE EXCLUSION: A SYNOPTIC EVALUATION OF SIZE ASSORTMENT 37

Abstract 37

Introduction 37

Methods 39

Feeding Guilds 39

Morphological Structure 40 V

Species Pools 41

Results 43

Principal Components Analyses 43

Minimum Spanning Trees 44

Discussion 44

Literature Cited 49

IV. COMMUNITIES, INTERACTIONS, AND THE LACK OF COMPETITIVE EXCLUSION: A SYNOPTIC EVALUATION OF DENSITY COMPENSATION 76

Abstract 76

Introduction 78

Methods 80

Communities 80

Feeding Guilds 80

Morphological Structure 81

Null Hypotheses 83

Results 85

Discussion 86

Literature Cited 90

V. GRADIENTS IN THE STRUCTURE OF NEW WORLD

BAT COMMUNITIES 100

Abstract 100

Introduction 101

Metiiods 104

Selection of Communities 104

Characterization of Community Structure 104

Morphological Structure 105

Numerical Structure 106 vi

Environmental Characterization 108

Principal Components Analysis 109

Multiple Regression and Correlation Analyses 110

Results 114

Environmental Axes 110

Principal Components Analyses I l l

Axes of Structure 112

Multiple Regression Analyses 113

Correlation Analyses 114

Discussion 115

Literature Cited 120

VL SYNTHESIS 148

Literature Cited 151

APPENDICES

A. LOCATION AND ANNOTATED DESCRIPTION OF

BAT COMMUNITIES 152

B. DESCRIPTION OF FEEDING GUILDS 157

C. DESCRIPTION OF MORPHOLOGICAL CHARACTERS 159

D. STRUCTURE OF FIFTEEN BAT COMMUNITIES 160

E. SIMULATION PROGRAM TO EVALUATE DENSITY COMPENSATION 203

F. SIMULATION PROGRAM TO EVALUATE SIZE ASSORTMENT 209

vu

LIST OF TABLES

2.1 Structure of the nocturnal granivore guild from the Sonoran Desert community 31

3.1 Eigenvalues and percent variation accounted for by the fu-st two principal components (PC) in analyses conducted on morphological characters of species in each guild, separately 53

3.2 Factor loadings for the first and second principal components for each of the five feeding guilds 54

3.3 Pearson product-moment correlations of each of seven ecomorphological characters with the first and second principal components derived for each of the feeding guilds 55

3.4 Results from simulation analyses evaluating whether the mean MST segment length from an actual feeding guild was indistinguishable from those under the null hypothesis of stochastic guild assembly 56

3.5 Results from simulation analyses evaluating whether the variance of MST segment lengths from an actual feeding guild was indistinguishable from those under the null hypothesis of stochastic guild assembly 61

3.6 Results of Fisher's test of combined probability for overall significance regarding mean MST lengths from each of fifteen bat communities 66

3.7 Results of Fisher's test of combined probability for overall significance of variance of MST lengths from each of fifteen bat communities 68

3.8 Results of Fisher's test of combined probability determining overall significance of mean MST lengths from each of five feeding guilds 70

3.9 Results of Fisher's test of combined probability determining overall significance of variance of MST lengths from each of five feeding guilds 71

4.1 Results from simulation analyses evaluating nonrandom patterns in abundance within fifteen bat communities 95

4.2 Results of Fisher's test assessing overall deterministic structure of bat communities when probabilities from all feeding guilds are combined 98

4.3 Results from Fisher's test assessing overall, deterministic structure of each of five feeding guilds when probabilities are combined for all locations 99

5.1 Bat communities used to evaluate gradients of structure 125

viii

5.2 Environmental parameters and their associated acronyms in parentheses ..126

5.3 Latitudinal (" N or S) and precipitation (mm/mo-^ attributes of nine locations of New World bat communities 128

5.4 Attributes of temperature (° C) of each of nine locations of New World bat communities 129

5.5 Attributes of productivity (g/m ) of each of nine locations of New World bat communities 130

5.6 Eigenvalues and percent variation explained by principal components used to characterize environmental gradients 131

5.7 Factor loadings for all climatic variables on the first four environmental principal component axes 132

5.8 Pearson product-moment correlations of each climatic variable with four environmental principal component axes 133

5.9 Eigenvalues (Eigen) and percent variation (%Var) accounted for by significant principal components characterizing the relationship among eleven measures of structure for communities and each guild, separately.. 134

5.10 Factor loadings (Eigen) and degree of association as determined by Pearson product-moment correlation coefficients between each of the measures of structure and each principal component (CPC) 135

5.11 Results from stepwise multiple regression analysis determining the degree to which measures of structure are a linear function of environmental gradients 140

5.12 Results from Kendall rank correlation analyses evaluating the degree of association between environmental variables and measures of structure 141

D. 1 Species composition, abundance, and morphological attributes of bat communities 161

ix

LIST OF FIGURES

2.1 Theoretical expectations of the relationship between morphological distance and abundance 32

2.2 Graphical representation of the distribution of r-values generated by chance (Ho) and the location of the rejection region dictated by the alternate hypothesis of deterministic structure 33

2.3 Three competitive scenarios based on considerations of morphology and abundance 34

2.4 Results from simulation analyses that evaluate each of three competitive scenarios for deterministic structure 35

3.1 Graphical representation of a minimum spanning tree (MST) 72

3.2 Graphical representation of faunal pools 73

3.3 Graphical representation of the null hypothesis regarding mean minimum spanning (MST) tree segment lengths 74

3.4 Graphical representation of the null hypothesis regarding the variance of the minimum spanning tree (MST) lengths 75

5.1 Scattergram of the relationship (r = 0.761) between numerical structure for frugivores (CPC 3) and variability of temperature (EPC 2) 143

5.2 Scattergram of the relationship (r = 0.782) between morphological structure characterized by mean interspecific distance (CPCl) within the gleaning animalivore guild and the relative variabiUty of productivity (EPC4) 144

5.3 Scattergram of the relationship (r = 0.766) between numerical structure (CPC 3) of the gleaning animalivore guild and the absolute variabihty in precipitation and productivity (EPC 1) 145

5.4 Scattergram of the relationship (r = -0.908) between numerical structure (CPC 2) of the nectarivore guild and variability in temperature (EPC2)....146

5.5 Scattergram of the relationship (r ndaii = -0.674) between morphological structure characterized by the mean interspecific distance within the aerial insectivore guild and relative variability in precipitation and productivity.. 147

A. 1 Graphical representation of the approximate location of each bat community evaluated 159

CHAPTER I

INTRODUCTION

The morphological, biogeographic, and taxonomic radiation of the Chiroptera

is one of the most conspicuous characteristics of the class Mammalia. Bats are the

second largest order of mammals, and include two suborders, 18 families, 186 genera,

and 986 species (Nowak, 1991). Chiropteran diversity is organized into a well-

documented latitudinal gradient, whereby species richness increases with decreasing

latitude (Findley, 1993; Lyons, 1995; Willig and Lyons, in lit.; Willig and Sandlin,

1991; Willig and Selcer, 1989; Wilson, 1974). Furthermore, the latitudinal gradient

in bat species richness is so strong that it is the principal component inducing the

latitudinal gradient in species richness for mammals as a whole (Findley, 1993;

Wilson, 1974; however, see Kaufman, 1995). A considerable effort over the last 50

years has focused on distinguishing and understanding causal factors of the latitudinal

gradient. Increases in species richness with decreasing latitude are facilitated by an

increase in the number of species within ecological communities in tropical areas

(Begon et al., 1990). Thus, understanding the factors that affect community

composition are of interest from a biogeographical, as well as ecological, perspecitve.

A community is defined as a group of species that co-occur in space and time

(Begon et al., 1990). Entire communities often represent hundreds if not thousands of

species, and as such, may be complex from an ecological perspective (Simberloff and

Day an, 1991). Communities commonly are categorized into feeding guilds, which

often represent more germane study units than do entire communities (Bonaccorso,

1975; Findley, 1993; Hawkins and MacMahon, 1989; Simberloff and Dayan, 1991;

Willig, 1982; Willig and Moulton, 1989). Feeding guilds are groups of potentially

interacting species that consume similar resources in a similar fashion (Root, 1967).

1

Traditionally, it was believed that biotic interactions, primarily competition, mediate

the co-existence of species within feeding guilds and ultimately structure

communities (Robinson et al., 1993; Brown, 1989; Davidson et al., 1984; Fleming,

1984). As a result, competition theory provides much of the historical foundation of

contemporary animal community ecology.

An important assumption in community ecology is that the consumption of

resources is dependent on the size and shape of trophic apparati, and thus, the ecology

of an organism is reflected in its morphology (Bonaccorso, 1975; Brown and

Lieberman, 1973; Findley and Black, 1983; Findley and Wilson, 1982; Freeman,

1981, 1984, 1988, 1992; Hespenheide, 1973; Mares, 1976; Smartt, 1978). If

morphology reflects ecology, and competition mediates the structure of feeding

guilds, then there must be a limit to how similar two species can be and still coexist in

the same community (Abrams, 1983; MacArthur and Levins, 1967). If two species

are too similar, then they will experience such intense interspecific competition that

either one or both will diverge morphologically or be driven to extinction at the local

level. Thus, character displacement and competitive exclusion within feeding guilds

should produce patterns of morphology that are more overdispersed than would be

expected due to chance alone (Brown and Wilson, 1956; Gause, 1934; Hardin, 1960).

Indeed, this has been widely documented, not only for mammals, but for a number of

other vertebrate taxa as well (Simberloff and Boeklen, 1981).

Hyperdispersion of morphologies within feeding guilds alternately could be

the result of stochastic processes. Throughout the 1980s, community ecologists

employed null models to demonstrate the artifactual nature of many morphological

patterns (Bowers and Brown, 1982; Connor and Simberioff, 1979; Simberloff, 1984;

Simberloff and Boeklen, 1981; Strong and Simberioff, 1981; Willig and Moulton,

1989). As a result, evidence regarding competition and its influence on the

ecomorphological structure of communities is equivocal.

Two important oversights potentially obscure the role of competition in

structuring communities. First, patterns of morphology may not be the only

indicators of deterministic structure. Nonetheless, contemporary null models,

designed to detect hyperdispersed morphologies within communities, are incapable of

evaluating other manifestations of competitive interactions. For example, if resource

consumption is determined by morphology, then pairs of morphologically similar

species should exhibit more intense competition than do pairs of species that are less

similar. As a result, a negative correlation should exist between morphological

similarity and abundance within feeding guilds; the ultimate local extinction of a

species is but a consequence of this process.

Second, competition need not structure all communities in all situations to be

important. In fact, competitive interactions should not be expected to manifest in all

situations. For example, climatically unpredictable or unstable environments impose

greater density-independent mortality than do stable environments (Andrewartha and

Birch, 1954; MacArthur, 1972; Zeveloff and Boyce, 1988). As a result, populations

may never reach density-dependence, and never experience intense interspecific

competition. Conversely, more stable envkonments allow populations to approach

density-dependence and interspecific competition should become more intense; in

some cases, intense enough to induce deterministic structure. Hence, gradients in the

degree to which communities are deterministically structured by density-dependent

biotic interactions should coincide with axes characterizing environmental variability.

In isolation, single community studies offer littie insight into this scenario. Moreover,

general conclusions on the structure of communities and the causal factors of

structure are tenuous when only one community is evaluated. Studies involving many

communities must be conducted to assess the generality of hypotheses.

Bat communities represent exceptional systems by which gradients in

structure can be investigated. Bats numerically dominate many communities

(Robinson, 1971; Handley, 1966), are species rich in both tropical and temperate

areas, and occur in all terrestrial biomes except tundra (Nowak, 1991). Furthermore,

several bat communities are well-documented and have been the focus of intensive

ecological investigations (Findley, 1993).

Predictable patterns exist regarding the composition of bat communities

(Findley, 1993). In general, bat communities are composed only of aerial insectivores

at higher latitudes. As one goes toward more tropical environs, species richness

increases within communities (Findley, 1993). Moreover, as structural and resource

diversity increase, so does the number of feeding guilds, from one (aerial insectivore)

to no less than seven guilds (aerial insectivore, frugivore, gleaning animalivore,

molossid insectivore, nectarivore, piscivore, sanguinivore). Consistent morphological

patterns within communities are discernible as well. Most communities are

dominated by a group of morphologically similar species that form a core, whereas

the morphological periphery harbors fewer species of higher morphological disparity

species (Findley and Black, 1983; Fleming, 1986). Few studies have attempted to

negate that observable patterns, such as this, could be a product of chance (Willig and

Moulton, 1989). Moreover, no studies have determined variation in the strength of

patterns, or whether some extrinsic component of the environment influences the

degree to which communities are structured by deterministic processes.

Objectives

Herein, I statistically evaluate 15 bat communities in the New World to

determine whether their structure may be the product of deterministic processes (see

Appendix A). In Chapter n, I develop a model that evaluates community structure

based on patterns in abundance. In Chapter IE, I utilize a null model developed by

Willig and Moulton (1989) to determine whether nonrandom morphological patterns

are pervasive in the fifteen communities. In Chapter IV, I evaluate the ubiquity of

patterns in abundance. Finally, in Chapter V, I evaluate environmental characteristics

associated with each community to determine if the degree to which patterns are

nonrandom is dependent on climatic variables. Specifically, I evaluate whether

gradients exist regarding bat community structure.

Methodological Considerations

Although ecological communities can be defined operationally, they are often

nebulous entities. The boundaries of some communities (e.g., pond-fish community,

herbivores on bracken fern) strongly correspond to physical boundaries (Schluter and

Ricklefs, 1993). However, this may only be true for taxonomically defined

communities representing less mobile organisms. Bats are highly vagile and two or

more plant communities may be traversed within a night's foraging by some species

(Willig and Mares, 1989). As a result, bats may perceive different plant associations

as habitat patches. Discretion must be used to ensure that an appropriate area, large

enough to comprise all interacting species that co-occur, is sampled when evaluating

bat community structure. Conversely, sampling from too great an area may include

species from more than one community, leading to the inclusion of information on

species that have no potential to interact. Special care must be taken when selecting

the areal extent from which to sample communities.

5

In the ensuing investigation, several criteria were utilized to select bat

communities. Data collection must have been from more than one particular locality

(e.g., stock tank, specific trail), but the area that comprises samphng localities must

be limited so that information likely was from a single bat community. This criterion

was fairly subjective. Finally, sampling must have been conducted on a regular basis,

in all seasons during which bats were active, for at least one year. This minimizes the

possibility of missing rare species, and increases the accuracy of relative abundances.

Feeding guilds also can be defined operationally and, like ecological

communities, may be methodologically nebulous. Feeding guilds represent

taxonomic subsets of the community that consume similar resources in similar ways

and, consequentiy, are most likely to compete (Root, 1967). When addressing the

importance of competition in structuring communities, examination of groups of

species with little potential to compete will bias conclusions. Thus, communities

should be decomposed into feeding guilds (Bonaccorso, 1975; Findley, 1993, Willig

1982; Willig and Moulton, 1989). I decomposed each community into seven feeding

guilds (see Appendix B for a description of each): (1) aerial insectivore, (2)

frugivore, (3) gleaning animalivore, (4) molossid insectivore, (5) nectarivore, (6)

piscivore, and (7) sanguinivore (see Appendix B). A species was assigned to a

feeding guild based upon food items that composed the bulk of its diet (e.g., blood,

fish, fruit, animal, nectar). For example, the diet of Artibeus jamaicensis. in most

places, is primarily fruit. Although this species sometimes consumes nectar and

insects, it would be placed in the frugivore guild. Additionally, insectivores were

categorized into one of three guilds based on where and how they foraged.

Other classifications have been suggested to categorize bat communities into

feeding guilds. Bonaccorso (1975) suggested categorizing frugivores into canopy and

sub-canopy frugivores. However, included in the spatiotemporal spectrum of

6

communities that I evaluated are more than one community that lacks a distinction

between canopy and sub-canopy, yet those species believed to be canopy specialists

(stenodermatines) and those believed to sub-canopy specialists (caroliines) coexist.

Canopy and sub-canopy frugivores may be valid designations; however, to make

comparisons of frugivores across all locations where they exist, a more general

designation was necessary. In this investigation, all bats that consumed fruit as the

major component of their diet were included in the frugivore feeding guild.

Moreover, it is commonplace to distinguish gleaning insectivores and gleaning

carnivores. In this study, both of these groups were combined as gleaning

animalivores. There is insufficient evidence to suggest that carnivores exhibit

camivory through all seasons of the year (Willig et al., 1993). Moreover, in many

places, bats that would be designated as carnivores exhibit omnivory (Willig et al.,

1993). Thus, my operational definition of a gleaning animalivore is any species that

consumes principally animals (whether they be vertebrates or invertebrates) that are

gleaned from surfaces. Information on dietary composition of species was obtained

either directly from documents describing the bat community or from other literature

sources.

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Willig, M. R., G. R. Camilo, and S. J. Noble. 1993. Dietary overlap in frugivorous and insectivorous bats from Edaphic Cerrado habitats of Brazil. Journal of Mammalogy 74: 117-128.

Wilson, J. W., m . 1974. Analytical zoogeography of North American mammals. Evolution 28: 124-140.

Zeveloff, S. I., and M. S. Boyce. 1988. Body size patterns in North American mammal faunas. Pages 123-146 in: M. S. Boyce, Editor. Evolution of life histories of mammals: theory and pattern. Yale University Press, New Haven, Connecticut.

11

CHAPTER n

THE RELATIONSHIP BETWEEN ABUNDANCE AND MORPHOLOGICAL

DISSIMILARITY: A MODEL OF COMMUNITY STRUCTURE

Abstract

The role of interspecific competition in structuring communities has been a

highly debated issue for the last two decades. The deterministic nature of

morphological patterns within communities has been at the center of this debate. Null

models, designed as a more rigorous statistical means to evaluate the effects of

competition on the morphology of coexisting species, have failed to provide adequate

resolution. Furthermore, null models addressing community-wide dispersions in

morphology may be based on too restrictive assumptions (e.g., competitive

exclusion), and consequently, lack power to detect deterministic structure in many

communities. Other manifestations of the effects of competition on community

structure should be explored. Morphological uniqueness may allow species to escape

intense competitive pressure and exhibit increased densities. Thus, a positive

relationship should exist between the relative morphological dissimilarity of species

and their abundances. Species may not uniformly impose competitive effects on all

others within a feeding guild, however. Different competitive scenarios that consider

subsets of species in feeding guilds that potentially experience more intense

interactions should be evaluated specifically. Herein, I introduce a suite of models

that evaluate patterns in abundance from a diversity of morphological perspectives

Moreover, I apply these analyses to an ecological community (nocturnal desert

rodents) for which the effects of competition on community structure are well

established. Simulation analyses indicate that these models are powerful enough to

detect nonrandom patterns in abundance at the feeding guild level. Moreover, these

12

models reveal deterministic abundance patterns from all morphological perspectives.

These models are powerful tools to explore factors influencing the role of competition

in community structure.

Introduction

A considerable amount of theory and empirical evidence exists regarding the

role of interspecific competition in the structure of natural communities (Cody and

Diamond, 1975; Diamond and Case, 1986; Kikkawa and Anderson, 1986; Strong et

al., 1984). Nonetheless, competition remains one of the most controversial issues in

ecology. Patterns in the morphology of co-occurring species have been a popular

means to examine competitive interactions and, ultimately, community organization

(Bowers and Brown, 1982; Brown and Bowers, 1985; Case et al., 1983; Dayan and

Simberioff, 1994; Diamond and Case, 1986; Mares, 1976; Moulton, 1985; Moulton

and Pimm, 1983, 1986a, 1986b, 1987; Schoener, 1984; Willig, 1982, 1986; Willig

and Moulton, 1989). An important assumption of this approach, consistent with

competition theory, is that the consumption of food resources is dependent on

morphology. Moreover, substantial evidence indicates that this assumption is

generally true (Bonaccorso, 1975; Brown and Lieberman, 1973; Dayan and

Simberioff, 1994; Findley and Black, 1983; Findley and Wilson, 1982; Freeman,

1979, 1984, 1988; Hespenheide, 1973; Smartt, 1978). If the morphologies of two or

more species are not sufficiently distinct, the resources that they consume likely will

be similar, and interspecific competition will ensue. With enough time and intensity,

competitive interactions should manifest as character displacement or competitive

exclusion (Brown and Wilson, 1956; Case and Sidell, 1983; Gause, 1934; Hardin,

1960). Ultimately, competition should give rise to a hyperdispersion of morphologies

within ecological communities.

13

Prior to the 1980s, demonstration of hyperdispersed morphologies implied

competitively-induced community structure (see Simberloff and Boeklen, 1981).

However, null models have demonstrated boldly that many of the patterns in

morphology originally believed to be the result of interspecific competition can be

generated by chance (Connor and Simberioff, 1979; Grant and Schluter, 1984;

Ricklefs and Travis, 1980; Strong et al., 1979). As a result, equivocal evidence exists

regarding the nature of morphological patterns within communities. Moreover,

competitively induced community structure, based on contemporary interpretations, is

not as common as once believed (Strong et al., 1979). Subsequently, many have

abandoned the notion that competition theory provides substantial insight into

understanding the structure of natural communities (Strong et al., 1984).

As much as null models have engendered critical and rigorous hypothesis

testing, they too have failed to provide incontrovertible evidence concerning the

importance of competition in structuring natural communities. These models make

two implicit assumptions that may limit their power: (1) interactions between nearest

neighbors structure communities, and (2) those interactions must lead to

morphological hyperdispersions to evince deterministic structure. To structure

communities, competition need not affect the dispersion of morphologies through

character displacement or competitive exclusion. Competitive interactions may affect

relationships between abundance and morphological similarity among species;

current null models, based on morphology alone, are incapable of addressing this

possibility.

Nonetheless, species experiencing more competitive pressure should exhibit

lower abundance and this may be another means to evaluate deterministic structure

(Lotka, 1932; Volterra, 1926). If morphological similarity is a viable surrogate for

ecological similarity, then those species that are morphologically dissimilar from

14

other species in the community should experience the least competitive pressure and

exhibit the highest abundance. Thus, a positive relationship should exist between the

morphological distance of a species with respect to potential competitors and

abundance; the strength of this relationship should be greater than that produced by

stochastic processes.

Ecological communities are often complex entities including hundreds, if not

thousands of species (Simberloff and Dayan, 1991). Furthermore, communities

comprise species from different feeding guilds (sensu Root, 1967) and trophic levels.

As a result, competitive interactions should not be expected to exist among all species

within a conmiunity; competitive interactions should be most important within a

trophic level, and especially within a feeding guild. Hence, the best place to begin

examining the manifestations of competitive interactions within communities, should

be within feeding guilds. Herein, I develop a suite of models, based on the

ecomorphological relationships of species, that is designed to detect nonrandom

patterns of abundance within feeding guilds.

The Model

My analyses are predicated on two assumptions. First, measures of

morphological dissimilarity within a guild are suitable surrogates for ecological

dissimilarity. Second, a species with high ecomorphological similarity to one or more

potential competitors should suffer reduced density as a result of interspecific

competition. As a consequence of such competitive effects, a quantitative

relationship should exist between the position of a species in ecomorphological space

and its density within a guild (Fig. 2.1).

I performed simulation analyses to determine if associations between

morphological dissimilarity and abundance within feeding guilds are non-random.

15

Morphological distances among species were calculated based on a Euclidean

distance. I used Pearson product-moment and Spearman rank correlation coefficients

to describe the magnitude of the association between abundance and morphological

distance. Traditional tests determining significance assume that data follow a

specified distribution. For example, hypotheses tests for both Pearson

product-moment and Spearman rank correlation analyses assume that random variates

follow a t-distribution (Sokal and Rohlf, 1995). If variates from the actual data do not

follow this distribution, traditional hypothesis tests may be inaccurate (Noreen, 1989).

Simulation analyses, however, are not subject to these biases. By randomizing the

actual data to yield a distribution to which the observed statistics are compared, such

assumptions are not necessary, and violations of assumptions cannot jeopardize the

accuracy of hypothesis tests (Noreen, 1989).

To evaluate deterministic structure, I compared correlation coefficients from

actual guilds to those of simulated guilds. While preserving the integrity of the

morphological relationships among species, random abundances were assigned to

each species, thereby yielding the structure of a simulated guild. A correlation

coefficient was then calculated between randomized abundances and actual

morphological distances of members within the simulated guild. One thousand

iterations of this process yielded a probability density function for subsequent

hypothesis tests. The correlation coefficient from the actual guild was compared to

the probability density function of simulated correlation coefficients. If the

coefficient for the actual guild occurred within the upper ten percent of the

distribution (p < 0.10), I concluded a non-random association between morphology

and abundance in the actual guild (Fig. 2.2).

Many factors influence the abundance of individual species (Andrewartha and

Birch, 1954, 1988; Begon et al., 1990). As such, strong positive correlations between

16

morphological distance and abundance caused by competition may be obscured by

autecological or other synecological processes (e.g., predation, mutualism).

Consequently, caution should be used to prevent falsely rejecting competition as an

important influence on community structure. To minimize the possibility of such a

Type I statistical error (rejecting a positive correlation between morphological

distance and abundance when it actually exists), I established the alpha level at p <

0.10 as the level of significance.

Competitive Scenarios

Community structure can be produced via a spectrum of possible interspecific

interactions, ranging from pairwise effects, to those based on all possible interactions

among guild members. Ecomorphological dissimilarity can be measured from a

variety of perspectives as well, corresponding to the spectrum of ways in which

competitive effects are manifest in a community. In general, if diffuse competition is

important in structuring communities, then the morphological distance of each species

to all others in a feeding guild primarily determines the density of each species. In

contrast, if interaction between a species and its nearest neighbors is the primary

factor acting on community structure, then the density of a species should be most

affected by its ecomorphological distance to its two nearest neighbors. I evaluated

three competitive scenarios along the spectrum of possibilities (Fig. 2.3). In the first,

the abundance of a given species is the product of its morphological relationships

with all other (n-1) species in the feeding guild. The Euclidean distance (Dt) for each

species represents the ecomorphological (Findley, 1976; Findley and Wilson, 1982;

Mares, 1976) distance of a species with respect to all other (n-1) guild members:

17

n-1 m

Dt=l(E(X,-x,)^)"''. < 2 " i=i j=i

where: n is the number of species; m is the number of morphological characters; Xij

represents morphological character j of species i; Xtj represents morphological

character j of species t.

In the second, interactions between a focal species and its most

morphologically distinct neighbor may be so weak as to have no effect on abundance.

Therefore, simulations were conducted in which the Euclidean distance included all

species in the feeding guild except the most morphologically different neighbor (n-2

of the species in the feeding guild):

n-2 m

Dt=I(I(X,rX,)^r. (2.2) i=l j=i

In the third, the abundance of species is not the product of diffuse

competition; the abundance of each species is the product of interactions with its two

nearest morphological neighbors. Thus, two nearest neighbors of a focal species were

the only members of the feeding guild included in calculations of ecomorphological

distance:

Dt=t(i(X,rX,/)'". (") i=l j=i

18

The Community

I evaluated the validity of this model using a rodent community from the

Sonoran Desert east of Tucson, Arizona. This community was selected based on a

variety of criteria. First, although communities have explicit textbook definitions,

they are often methodologically difficult to circumscribe. I chose this rodent

community because the sampled area was a well-defined system (creosote flat) that

contained all microhabitats necessary for the focal group of species (nocturnal desert

granivores). Second, considerable effort must be spent to ensure accurate relative

abundances. Brown's (1989) bi-monthly census protocol was conducted for two

years and suitably meets this criterion. Third, it was desirable to assess if this model

could detect patterns in abundance in a community whose organization has been

demonstrated to be mediated by interspecific competition (Brown, 1989).

Only one feeding guild from this community was evaluated (Table 2.1). It

included Dipodomys merriami. Perognathus amplus. Mus musculus. Peromyscus

maniculatus. P. eremicus. P. merriami. Chaetodipus penicillatus, and C. baileyi. and

represented nocturnal granivores. Spermophilus tereticaudus. Ammospermophilus

harisii. Neotoma albigula. Sigmodon arizonae. and Onychomys torridus were

excluded because they are either diurnal or the composition of their diet differs

greatly enough for them to be considered members of other distinct feeding guilds.

I utilized a suite of cranial and body characteristics to estimate the position of

each species in ecomorphological space. These included length of body, length of

foot, length of ear, greatest length of skull, greatest width of skull, length of maxillary

toothrow, and interorbital width. Morphological measurements were obtained for at

least four males and four females of each species from Hoffmeister (1986) or from

specimens deposited in The Museum, Texas Tech University.

19

Results

Relative abundance and ecomorphological distance of species in the nocturnal

granivore guild are variable, spanning almost two orders of magnitude for relative

density and approximately five-fold for morphology (Table 2.1). Simulation analyses

indicated a nonrandom, positive relationship between ecomorphological distances of

species and abundance (Fig. 2.4). Species that were more ecomorphologically

distinct from other guild members exhibited higher abundances. Moreover, this

pattern was detected under all three competitive scenarios. The relationship was

strongest for the analysis based on diffuse competition and weakest when each

species most distant neighbor was not considered in calculation of ecomorphological

distance.

Discussion

Previous research and analyses have documented that the Sonoran nocturnal

granivore guild is structured by competition (Brown, 1989). My model was

sufficiently powerful to corroborate these results and detect competitive effects for

each of three morphological scenarios. Consequently, it holds promise as a

quantitative tool for detecting competitive effects that do not manifest as

morphological hyperdispersions at the community level.

Including patterns of abundance in the evaluation of community structure has

definite advantages. The detection of deterministic structure does not necessitate

competitive exclusion or character displacement. Moreover, this approach need not

assume that populations or communities are at equilibrium. Competitive interactions

are believed to be strongest when environments approach saturation and constituent

species are at carrying capacity (Adrewartha and Birch, 1954, 1988; Chesson, 1988;

Lotka, 1932; Volterra, 1926). Thus, predictable environments that persist for long

20

periods of time should be the arena in which hyperdispersions in morphology

manifest. Of course these circumstances may not characterize many systems. A

variety of environmental perturbations or disturbances prevent populations from

reaching equilibrium (Adrewartha and Birch, 1954, 1984; Sale, 1977; Simberioff,

1984). Moreover, research on invertebrate communities has caused many ecologists

to question the existence of environmental equilibria (Resh et al., 1988; Power et al.,

1988). If communities are not at equilibrium, morphologically similar species may

still coexist in the absence of strong biotic interactions, rendering the interpretation of

hyperdispersions in morphology difficult. As long as species are not at such a state of

disequilibrium that no density-dependent effects occur, the effects of competitive

interactions can be assessed if one evaluates abundance.

A considerable amount of information is lost when investigators ignore

abundance and focus only on morphology. Many times, species are only seasonal

residents in communities when resource levels are high (Bonnaccorso, 1975). When

resources become scarce, competition becomes more intense and these species are

unable to persist. When addressing morphological dispersions, seasonal residents can

either be included in analyses and given the same status as full-time residents, or

excluded because of their transient nature. Although these species are seasonal

members of the community, they should still be considered community members, but

with different status. Contemporary null models addressing hyperdispersions in

morphology lack the flexibility to give unequal weight to different species. If

abundance data reflect year-long sampling (summed across sampling periods),

seasonal species likely will exhibit lower abundances than year-round residents, thus

demonstrating their inability to coexist through aU seasons of the year.

Similarly, it is commonplace to exclude rare species from analyses. If species

are abundant because of a lack of competitive pressure (Lotica, 1932; Volterra, 1926),

21

then studies concentrating only on common species may be unable to detect structure

that is the consequence of deterministic processes. As this model demonstrates, rare

species provide considerable information regarding community structure; their

omission from studies may contribute to an inability to detect nonrandom patterns,

and thus, obscure the effects of competition on community structure.

Models addressing abundance evaluate current competitive interactions and

are not complicated by historical and biogeographic effects. Simply demonstrating

that morphologies are hyperdispersed within communities is not enough to invoke

competition. Seemingly deterministic patterns in morphology could result from

random assembly (Simberloff and Boeklen, 1981). If historical phenomena have

affected the distribution of morphologies within faunal pools, then the random

assembly of species into communities may recapitulate a nonrandom distribution of

morphologies within those communities. Models addressing morphology alone must

take into account the distribution of morphologies from source species pools.

However, determination of appropriate faunal pools often represents a considerable

methodological problem (Colwell and Winkler, 1984; Graves and Gotelli, 1983;

Willig and Moulton, 1989).

Several guidelines should be followed to ensure the determination of not only

more accurate abundances, but also community structure. The proper scale should be

selected to ensure that, in actuality, a single and entire unit community is being

sampled. If unit communities are not sampled, considerable potential exists for

measures of abundance to be biased in either of two ways. First, by sampling a

regional fauna, abundance data for a species will be combined across more than one

community, possibly distorting the relationship between abundance and morphology

in any one of the real communities. Second, by sampling only microhabitats, the

actual abundances of species within the community will be misrepresented and

22

critical community members may be excluded, thereby distorting morphological

components of the model.

Scale has substantial implications at many levels of biological organization

(Allen and Starr, 1982; Eldridge, 1985; Levin, 1992; Minshall, 1988), and

communities are no exception. Although communities are easily defined in theory,

they are often nebulous entities from a methodological perspective. For example,

rodent community may not encompass the same aerial extent as a raptor community.

Raptors may perceive individual rodent communities as microhabitats or patches

which differ in resource quality and quantity. Consequentiy, each group should be

sampled at the level appropriate for the constituent taxon, and arbitrary boundaries

should be avoided. The area encompassed by community sampling units should be

fairly uniform, yet possess all of the microhabitats necessary for persistence of

community members. For example, many desert ecosystems can be characterized by

canyons, desert flats, riparian areas, and mountains. Within each of these exist places

under vegetation, places in rock crevices, and places in open areas used by small

mammals. It would be inappropriate to characterize the community only in open

microhabitats. Species that predominate under bushes and crevices possess the ability

to interact with species with open microhabitat affinities, and their exclusion would

bias conclusions. By the same token, it would be inappropriate to combine data

collected from both the riparian area and the desert flat to describe community

structure because species that have little potential for interaction will be included in

this sample. Errors such as these deleteriosly affect the ability of any methodology to

assess the relationship between abundance and morphology.

Measures of abundance should be the product of intensive, long-term

sampling. If species that are morphologically similar to other guild members are

more rare in communities, their membership may go undetected by incomplete

23

sampling. Preston (1948, 1962) demonstrated a general species-area curve whereby

the number of species asymptotically increases as one increases the size of samples.

Rare species contribute to this phenomenon. Moreover, the species area relationship

can be generalized to a species-effort curve or collector's curve (Arata and Vaughn,

1970; Coleman et al., 1982; Thomas, 1972). If sufficient effort (number of traps,

number of nights, etc.) is not expended to sufficiently sample a community, the

potential for poor estimates of the abundance of species or even the failure to detect

rare species is great.

Even if accurate relative or absolute measures of abundance are suspect, this

model allows analyses based on ranks. In analyses of the nocturnal granivore guild,

the Pearson product moment correlation coefficient (PPMCC) was consistently higher

than the Spearman rank correlation coefficient (SRCC), indicating that information is

lost by using a rank correlation coefficient when relationships are linear and

abundances are accurate estimates. Despite this loss of information, SRCC and the

PPMCC yielded similar results when utilized in simulation analyses and significance

tests. Under all three competitive scenarios, the actual correlation coefficient was of

greater magnitude than the vast majority of simulated correlation coefficients.

However, SRCC did lack the power to demonstrate clear significance under the N-2

competitive scenario.

Parametric correlation coefficients are more powerful at detecting linear

associations than are those based on ranks (Sokal and Rohlf, 1995); however,

parametric coefficients require absolute or relative measures of each variable. For

many organisms, the absolute or relative abundance of species within guilds is not

easily or accurately ascertained, rendering the efficacy of such analyses questionable.

Nonetheless, if one is capable of accurately assigning rank abundance to each species

in a guild, evaluation of deterministic guild structure based on rank-analyses is

24

possible, with little reduction in power. Hence, this methodology may have broad

applicability to a diversity of plant or animal communities.

This model has great potential as a means to make comparisons among

communities. If competition is unimportant in the structure of communities, species

abundances will be the product of other phenomena, and thus, species should not

exhibit a strong positive relationship between ecomorphological distance and

abundance. Deterministic structure is operationally defined by the probability of

obtaining the observed pattern by chance (p-value). Thus, deterministic community

structure can range from a probability of 0 (highly unexpected by chance) to 1 (highly

expected by chance). There is considerable consensus that competition is not

important in all communities under all circumstances (Begon et al., 1990; Cody and

Diamond, 1975; Diamond and Case, 1986; Kikkawa and Anderson, 1986; Polls,

1991; Strong et al., 1984, for reviews). If variation in the degree to which

competition structures communities exists, comparisons based on p-values can be

made. If other extrinsic factors influence the degree to which competition is

important, p-values describing the degree of deterministic structure should be a

function of extrinsic factors. If the circumstances under which competition is

important in community structure are to be truly understood, similar analyses should

be applied to a diversity of communities (see Chapter IV).

25

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Strong, D. R., D. Simberioff, L. G. Abele, and A. B. Thistle, Editors. 1984. Ecological communities: conceptual issues and the evidence. Princeton University Press, Princeton, New Jersey.

29

^.

Strong, D. R., L. A. Szyska, and D. S. Simberioff 1979. Tests of community-wide character displacement against null hypotheses. Evolution 33: 897-913.

Thomas, M. E. 1972. Preliminary study of the annual breeding patterns and population fluctuations of bats in three ecologically distinct habitats in southwestern Colombia. Dissertation. Tulane University, New Orleans, Louisiana.

Volterra, V. 1926. Variations in fluctuations of the numbers of individuals in animal species living together. Reprinted in 1931. in: R. N. Chapman, Editor. Animal Ecology. McGraw Hill, New York.

Willig, M. R. 1982. A comparative ecological study of Caatingas and Cerrado chiropteran communities: composition, structure, morphometries, and reproduction. Dissertation. University of Pittsburgh, Pittsburgh, Pennsylvania.

Willig, M. R. 1986. Bat community structure in South America: a tenacious chimera. Revista Chilena de Historia Natural 59: 151-168.

Willig, M. R., and M. P. Moulton. 1989. The role of stochastic and deterministic processes in structuring Neotropical bat communities. Journal of Mammalogy 70: 323-329.

30

Table 2.1.-- Structure of the nocturnal granivore feeding guild from the Sonoran Desert (after Brown, 1989). n-1, n-2, and 2 correspond to three competitive scenarios used in calculations of morphological distance, n-1 indicates all other species in the feeding guild (diffuse competition), n-2 indicates all others except the most distant morphological neighbor, and 2 indicates only two nearest morphological neighbors.

Relative Morphological Distance Species abundance n-1 n-2 2

Dipodomys merriami 71.80 4.26 3.53 0.89

Perognathus amplus 26.96 3.04 2.36 0.51

Mus musculus 0.57 2.47 1.74 0.29

Peromyscus maniculatus 0.29 2.27 1.62 0.23

Peromyscus eremicus 0.10 2.32 1.66 0.20

Peromyscus merriami 0.10 2.44 1.93 0.34

Chaetodipus penicillatus 0.10 2.64 2.17 0.48

Chaetodipus baileyi 0.10 2.64 2.00 0.27

31

\

MORPHOLOGICAL ATTRIBUTE 1

Figure 2.1.~ Theoretical expectations of the relationship between morphological distance and abundance. The sum of the lengths of the bars emanating from a sphere (species) represents the morphological distance of a focal species with respect to all other competitors in the guild. The size of a sphere represents the abundance of the focal species with respect to all other competitors in the guild. If competition is important in structuring guilds, then the larger the sum of the morphological distances, the larger the sphere representing relative abundance.

32

Fig. 2.2.~ Graphical representation of the distribution of r-values generated by chance (Ho) and the location of the rejection region dictated by the alternate hypothesis of deterministic structure. The curve represents the frequency distribution of correlation coefficients between morphological distances of species and random abundances. If the correlation coefficient between observed morphological distances of species and their relative abundances (dot) is > 90% of the randomly obtained correlation coefficients (as in the example), the observed guild is structured by deterministic processes.

33

\

Figure 2.3.-- Three competitive scenarios based on considerations of morphology and abundance. In the first scenario (above), the abundance of the focal species (square) is a function of its relationships with all of its neighbors (dots); Euchdean distances include all species in the feeding guild (N-1). In the second scenario (middle), the morphological relationship between the focal species and its most distant neighbor has no influence on the abundance of the focal species; all but each species' most morphologically distant neighbor are included in the calculation of Euchdean distance (N-2). In the third scenario (bottoni), only the two nearest neighbors influence the abundance of the focal species and only those species are included m the calculation of Euclidean distance (2).

34

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36

CHAPTER m

COMMUNITIES, INTERACTIONS, AND COMPETITIVE EXCLUSION:

A SYNOPTIC EVALUATION OF SIZE ASSORTMENT

Abstract

For at least a quarter of a century, community ecologists have grappled over

which factors are responsible for the structure of communities. Most endeavors

consider a single community and likely provide littie information regarding the process

of community organization in a heterogeneous world. Before generalizations regarding

the importance of phenomena on community organization are cast, the degree of

ubiquity of those phenomena across a gradient of locations must be determined.

Herein, I evaluate the ubiquity of competitively induced morphological overdispersion

in five feeding guilds from each of 15 bat communities from North, Central, and South

America. Overdispersion is detectable at ten of fifteen locations, and in four of five

feeding guilds. Although overdispersed morphological patterns do not exist in all

situations, competitive interactions should not be considered unimportant.

Morphological overdispersion is not the only way competitive interactions manifest at

the community level, and the ubiquity of other consequences should be explored.

Introduction

The search for urefutable, pervasive patterns that identify factors responsible

for the structure of communities has been in the mainstream of ecology for over a

quarter of a century. As a result, many processes such as competition, disturbance,

predation, and mutualism, to name only a few, are disputed as the factor responsible

for the composition of communities (see Cody and Diamond, 1975; Diamond and

Case, 1986; Gee and Giller, 1987; Kikkawa and Anderson, 1986; Polls, 1991;

Ricklefs and Schluter, 1993; Strong et al., 1984; for extensive reviews). Nonetheless, 37

equivocal evidence corroborating most, if not all, of these phenomena seems to be the

only pervasive result. Because no two communities are alike, single community

studies offer littie insight into teasing apart the most important influence from the grab-

bag of possibilities. The world is characterized by substantial temporal and spatial

heterogeneity (Brown, 1992). Moreover, environmental gradients mediate the degree

to which at least some of these phenomena operate (Andrewartha and Birch, 1954,

1988; Chesson, 1988). Lastly, co-occurring feeding guilds and trophic levels provide

additional ecological complexity (Bonaccorso, 1975; Findley, 1993; Simberloff and

Dayan, 1991; Willig, 1982; Willig and Moulton, 1989). Studies of a single community

offer no means of accounting for such heterogeneity. However, community ecologists

have been impulsive in discounting the importance of various phenomena based on data

from a paucity of communities. It would not seem surprising that the environmental

context of a feeding guild, trophic level, or ultimately community, has bearing on the

importance of phenomena that affect structure. Comprehensive, comparative studies at

many geographic locaUties that represent a variety of cUmatic and abiotic conditions

must be conducted before the influence of any factor on community structure can be

ascertained with confidence.

Morphological attributes are informative metrics for inferring the relationships

of species at the community level (Wainright and Reilly, 1994; and citations therein).

They correlate well with ecological characteristics and have been demonstrated to be

good predictors of resource utilization (Bonaccorso, 1975; Brown and Lieberman,

1973; Dayan and Simberloff, 1994; Findley and Black, 1983; Findley and Wilson,

1982; Freeman, 1981, 1984, 1988, 1992; Hespenheide, 1973; Smartt, 1978).

Consequentiy, morphologically similar species should compete more intensely than do

dissimilar ones. Hyperdispersions along resource axes can result from competitive

interactions among coexisting species in the form of character displacement or

38

competitive exclusion, and result in hyperdispersions along morphological axes

(Hutchinson, 1959; MacArthur and Levins, 1967).

Although morphological hyperdispersion is commonplace under a variety of

environmental conditions (see Simberloff and Boeklen, 1981), a comprehensive

account of the ubiquity of hyperdispersion has never been conducted within a particular

taxon. Herein, I evaluate morphological pattems within bat communities throughout

the New World and explore if hyperdispersion is ubiquitous. I address two questions:

(1) does morphological structure, consistent with competition theory, exist within bat

feeding guilds and communities, and (2) are the effects of competitive interactions

pervasive within bat communities throughout the New World?

Methods

I evaluated 15 bat communities from throughout North, South, and Central

America (Appendix A). Several criteria limited the number of communities included in

analyses. First, data must have been the product of regular sampling in all seasons that

bats were active. Second, sampling must have been at least one year in duration.

Tlurd, sampling must have been conducted in a well-delimited local area that

represented an actual community of species that, because of spatial proximity, had the

potential to interact. Faunas of geopohtically bounded areas were not acceptable

because it was difficult to be reasonably sure that only one community was sampled.

Feeding Guilds. Each community was categorized into seven feeding guilds

(sensu Root, 1967): aerial insectivores, frugivores, gleaning animalivores, molossid

insectivores, nectarivores, piscivores, and sanguinivores (see Appendix B for

definitions). The rigid, yet general, nature of this classification enables comparisons

from wide ranging spatial and habitat conditions. Guild associations were based on

designations published in the actual account of the community or on other published

information (Gardner, 1977; Wilson, 1975). 39

Sanguinivores and piscivores were omitted from analyses. At most, real

communities contained one piscivore, rendering detection of a hyperdispersion in

morphology impossible. Moreover, the species pool of sanguinivores could at most

include three (all extant members of the Desmodontinae), and consequentiy no selection

of species, no matter how deterministic, could be shown to be a rare occurrence (Willig

and Moulton, 1989). If a feeding guild at a particular site did not contain at least three

species, it was omitted from analyses.

Morphological Structure. I followed Koopman (1993) for a comprehensive list

of extant New World bats. Seven attributes were utiUzed to ecomorphologically

characterize each species. These include forearm length, greatest length of skull,

condylobasal length, width across the postorbital constriction, breadth of the braincase,

length of the maxillary toothrow, and breadth across the upper molars (see Appendix C

for definitions). Measurements were obtained from Swanepoel and Genoways (1979)

for most phyllostomids, and from museum specimens for others. In most cases, eight

individuals, 4 males and 4 females, contributed to the mean of each character.

Common logarithms of each character were utilized in analyses following

Ricklefs and Travis (1980). Log transformations enhance normality and equalize

variances (Sokal and Rohlf, 1995). Moreover, they minimize the possibility that

differences in larger characters may disguise ecologically meaningful differences in

smaller attributes. Finally, they minimize the distortion of multivariable space when

standardized for data reducing techniques (Ricklefs and Miles, 1994; Ricklefs and

Travis 1980).

Morphological relationships of species were determined for each guild

separately, as suggested by Moulton and Pimm (1986,1987) and Willig and Moulton

(1989), using Principal Components Analyses (PCA) (SAS program PRINCOMP;

Ray, 1982). This technique maintains the morphological relationships among species

by constructing a linear combination of original variables that eUminates redundancy of 40

• \

highly correlated characters. Consequentiy, the number of dimensions necessary to

illustrate relationships is less than the original number of characters (Ricklefs and

Miles, 1994; Ricklefs and Travis, 1980). Via extraction from a covariance matrix, two

principal components characterized relationships among species. Minimum spanning

trees were then calculated to determine the distance of species in two dimensions

(principal components 1 and 2). Minimum spanning trees choose the shortest N-1 line

segments to connect N species (Fig. 3.1). Thus, the length of the minimum spanning

tree reflects the magnitude of interspecific morphological differences. Two descriptive

statistics (mean and variance) were then calculated for minimum spanning tree segment

lengths.

K competition prevents morphologically similar species from coexisting within

communities, overdispersions in morphology should be evinced in one of two ways:

(1) mean segment lengths of actual minimum spanning trees should be greater than

would be expected due to chance, or (2) the variance of minimum spanning tree

segment lengths should be smaller than would be expected due to chance (Moulton and

Pimm, 1986; Willig and Moulton, 1989).

Species Pools. The demonstration of large means and small variances of

minimum spanning tree segment lengths is insufficient to invoke competition. Many

artifacts can give rise to large means and small variances. If some aspect of the history

of a particular taxon created a particular pattern in morphology within a fauna, then the

random assembly of species into a community may recapitulate that pattem. Moreover,

if the community contains morphologically sunilar species, small variance components

may not be unusual. Lastiy, a large mean describing minimum spanning tree segment

lengths may simply be the consequence of an extreme morphological outiier. For these

reasons, species pools representing faunal groups from which communities are

assembled must be utilized in analyses; comparing actual communities must be

compared to those assembled at random from a faunal pool. Simulation provides the 41

basis for an unbiased assessment of guild characteristics. Although the means or

variances of MST segment lengths may be nocuously influenced by morphological

extremes (such as outliers or sets of similar species), these species also are included in

faunal pools. As a result, outiiers should be selected often enough in the assembly of

random communities that hyperdispersions resulting from outiiers will not be unusual.

Thus, the relative magnitude of a certain statistic, as compared to a distribution created

randomly, becomes a more salient point of comparison.

Morphological pattems from each guild were compared to those randomly

drawn from each of seven faunal pools. Species were included in analyses if their

geographic distributions occurred within a particular faunal pool. Distribution maps for

bat species were prepared using Hall (1981) for North and Central America, and

Koopman (1982), Eisenberg (1989), and Redford and Eisenberg (1992) for South

America. The bounds of five of these pools were represented by concentric rings that

equaled 500, 1000, 2000,4000, and 8000 kilometers in diameter (Fig. 3.2). The first

pool represented only those species whose distribution overlapped the actual

community and the last pool represented all those of the New World. For each pool,

randomly drawn guilds were assembled using the algorithm of Moulton (1985),

Moulton and Pimm (1987), and Willig and Moulton (1989). If N species occur in an

actual guild and S is the number of species in a species pool from which random guilds

are drawn, then the number of different guild combinations (C) is given by

S!/{N!(S-N)!}. (3.1)

The number of possible combinations was often large. When C was > 500,1 randomly

selected 500 combinations to calculate random guild statistics. When C was < 500,1

utilized each combination only once to minimize redundancy. As a result, hypothesis

tests for these situations were based on sample sizes that were less than 500. Both sets

of descriptive statistics from randomly assembled guilds form distributions under the

null hypothesis (random guild assembly) to which descriptive statistics from the actual 42

feeding guild can be compared. If the mean segment length from an actual guild was

greater than 90 percent of the simulated values, or the variance of die spanning tree

lengths was smaller than 90 percent of the simulated values, I concluded that

nonrandom morphological combinations existed in the actual guild (Figs. 3.3 and 3.4).

Results

Principal Components Analyses. Results of the five principal components

analyses were similar (Table 3.1). Eigenvalues for the first and second principal

components ranged from 0.022 - 0.073 and 0.003 - 0.005, respectively. Percent

variation accounted for by the fu-st and second principal components ranged from 76.8

- 89.2 and 5.9 - 16.4, respectively. Factor loadings from each of the five covariance

matrices appear in Table 3.2.

Analyses were based on the same suite of morphological characters for all

feeding guilds. In all cases, principal components analyses reduced the seven

morphological characters into two components. Nonetheless, the possibility exists that

the contributions of each character to each principal component may be different

depending on feeding guild. I determined the Pearson product-moment correlation

coefficient between principal components and each of the morphological characters

within each feeding guild (Table 3.3). All characters, regardless of feeding guild, were

positively and significantly correlated with the fu-st principal component; it is hkely a

measure of overall size. With the exception of width across the post-orbital

constriction, no pattem exists among guilds regarding significant correlations between

variables and the second principal component. Shape differs among species in a

guild-specific fashion, and is likely a consequence of modification of structure to

enhance ecological efficiency. Moreover, feeding guild distinctions often correspond

with profound morphological and phylogenetic differences. Thus, it is not surprising

that differences in the relative contribution of variables to the second principal 43

component exist. Nonetheless, the first two principal components extracted from these

seven morphological variables accounted for 87.6 - 95.2 percent of the variation among

species witiiin a particular feeding guild (Table 3.1).

Minimum Spanning Trees. Simulation analyses strongly indicate that

nonrandom morphological pattems, consistent with competition theory, exist within bat

communities. Twelve of the fifteen locations, and three of the five feeding guilds

exhibited mean segment lengths that were significantiy greater than those derived from

random assembly (Table 3.4). Furthermore, segment length variances were

nonrandom at eight locations and in three feeding guilds (Table 3.5). This indicates

that when communities represent nonrandom faunal subsets, morphological pattems

most often manifest as greater distances between species in morphological space.

No conspicuous pattem exists as to which communities or feeding guilds

exhibited nonrandom morphological stmcture. I utilized Fisher's test (Sokal and

Rohlf, 1995) to combine probabilities from all feeding guilds within a community as

well as within feeding guilds across locations to determine whether communities or

feeding guilds in general exhibited nonrandom morphological pattems. Six

communities exhibited unusually high mean segment lengths overall (Table 3.6),

whereas four communities exhibited atypically small variances (Table 3.7). Aerial

insectivores, gleaning animalivores, and nectarivores exhibited unusually higher mean

segment lengths (Table 3.8), whereas frugivores exhibited significantiy smaller

variances of segment lengths (Table 3.9).

Discussion

Although seemingly hyperdispersed morphological pattems are not uncommon

within communities, recent statistical evaluations using neutral models have determined

that statistically nonrandom hyperdispersions are in the minority (Simberioff and

Boeklen, 1981). Recent evaluations of bat communities have corroborated tiiese 44

findings (Willig and Moulton, 1989). Nonetheless, my results identified numerous

instances in which species within feeding guilds exhibit statistically nonrandom

hyperdispersions that are consistent with competition theory. Moreover, in a few

cases, entire bat communities exhibited deterministic structure. Obviously, variation

exists regarding tiie degree to which feeding guilds and communities exhibit

hyperdispersed morphological pattems. Evaluating the stmcture of communities along

gradients may shed hght onto which environmental conditions foster the production of

non-random structure (Chesson, 1988; Chapter V).

Morphological overdispersion is not uncommon in the bat communities I

evaluated. Nonetheless, simply observing morphological overdispersion in a sample

(s^ < x) is not a sufficient demonstration of deterministic structure. Nonrandom

structure is indicated only when the sample variance is statistically smaller than the

mean (Sokal and Rohlf, 1995). To these ends, ascertaining the deterministic nature of

hyperdispersions by comparison with guilds created randomly from faunal pools is

necessary to warrant against wrongfully positing the operation of competitive

interactions on community organization. Nonetheless, the utilization of faunal pools to

evaluate statistical hyperdispersions is not an infallible means of evaluating

morphological pattems (Diamond and Case, 1986; Strong et al., 1984), and

interpretations of results from faunal pools must be conservative.

Faunal pools represent different biogeographic scenarios from which

communities are sampled and care must be taken in choosing their appropriate size

(Willig and Moulton, 1989). Knowledge of species distributions is incomplete

(Patterson, 1994). Moreover, temporal heterogeneity and rescue effects probably

impart a dynamic nature to distributional boundaries. Faunal pool 0 in these

simulations almost certainly includes potential invaders of contemporary feeding guilds.

Furthermore, faunal pools 1 and 2 probably correspond to potential pools occurring in

the ecological time of a contemporary community. From an ecological perspective, 45

^

however, species pools 3 and above probably are unrealistic and provide little insight

into contemporary sources of colonists. These pools undoubtedly contain species that,

because of biogeographic and ecological barriers, lack the potential to invade the

community. Nonetheless, the identity of the faunal pool that is the most appropriate

remains uncertain, and an exhaustive scheme most likely minimizes the possibility of

deriving false conclusions. Results from all pools regarding either communities or

feeding guilds were similar. In most cases, increasing the size of faunal pools

increases the number of candidate species for assembly into random communities, yet

no consistent trend in P-values with increased faunal pool size was detectable and little

change in P-values existed between the largest and smallest faunal pool.

Competitive interactions are density-dependent phenomena (Begon et al.,

1990). Moreover, environmental variability and stochasticity can prevent populations

from approaching carrying capacity, and thus mediate the degree of density-dependence

(Andrewartha and Birch, 1954, 1988; Chesson, 1988). To these ends, it is reasonable

that differences exist in the degree to which nonrandom morphological pattems occur

and these differences may be a product of climatic differences among sites. Although

deterministic structure occurred in all biomes sampled, no conspicuous pattems exist

regarding which were likely to give rise to deterministic stmcture.

Three feeding guilds (aerial insectivores, fmgivores, and nectarivores) exhibited

fairly ubiquitous deterministic structure at all locations, whereas the molossid

insectivore guild ubiquitously exhibited stochastic stmcture. Fmgivores exhibited

morphological pattems that were more even than were those in faunal pools, whereas

aerial insectivores, gleaning animahvores, and nectarivores were characterized by

statistically large segment lengths. Fmgivores never exhibited mean segment lengtiis

that were unusually large, and nectarivores never exhibited variances that were

unusually small. The morphological diversity of these groups may be constrained by

other phenomenon, and the assembly of species into these guilds is determined 46

consistentiy by only one attribute: either the mean distance or the variability of the

distances between species.

Despite the detection of deterministic stmcture in many situations, nonrandom

morphological pattems were not ubiquitous. The spatio-temporal circumstances in

which competitive interactions manifest as morphological pattems may be fairly

restrictive. For size assortment to be pervasive in a community, competitive

interactions must be strong, include most if not all species, and be persistent (Moulton

and Pimm, 1986). Considerable fluctuations in resource levels or climatic conditions

occur in many environments. If narrow spatio-temporal, climatic, or resource

conditions are necessary for the manifestation and persistence of size assortment, then

much of the observed lack of significance may indicate appreciable environmental

variability.

Morphological pattems within feeding guilds may be the result of either

adaptation by constituent species or evidence that community assembly has reached

equilibrium (Case and Sidell, 1983; Strong et al., 1979). The explanation for the

occurrence of both of these phenomena is usually based on an evolutionary time frame.

Bats are highly mobile organisms (Hill and Smith, 1984; Rayner and Norberg, 1987;

Thomas, 1987); they may be present in a community at one time but absent at others

(Bonaccorso, 1975). Morphological pattems may exist only when resource levels are

low, during which times competitive interactions are most intense, and only core

species persist within the community. At other times, when resources are bountiful,

competitive interactions may not be intense, and invading species may occur within

communities; when this occurs, deterministic pattems in morphology will not be

detectable. Evaluating community stmcture in a number of communities through many

years, as well as at various times of the year (such as during the dry season and wet

season), would be a good means to test this hypothesis.

47

Hyperdispersion in morphology was detectable in many situations, and was

pervasive in some feeding guilds and within some communities. Nonetheless, these

pattems lack ubiquity. Morphological pattems are not the only way in which

competitive interactions can be detected at the community level. Pattems regarding

other consequences of competitive interactions may appear in the absence of size

assortment, and may serve to be more consistent or informative metrics (see Chapter

IV).

48

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Figure 3.1.-- Graphical representation of a minimum spanning tree (MST). MSTs connect N points with N-1 line segments. Dots represent the centroid of species attributes in morphological space, whereas line segments represent the magnitude of the differences between nearest neighbors. PCI and PC2 are axes summarizing the morphological relationships of species in multidimensional space.

72

Figure 3.2.-- Graphical representation of faunal pools. The sohd dot represents the location of a hypothetical community. Faunal pool 0 corresponds to all species whose distributions overlap the hypothetical community. Faunal pools 1, 2, 3,4, and 5 correspond to the set of all species whose distributions fall in concentric rings 1, 2, 3, 4, and 5, respectively. Concentric rings 1, 2, 3,4, and 5 have diameters of 500, 1000, 2000,4000, and 8000 kilometers, respectively. Faunal pool 6 corresponds to all species of bats from the mainland of the New World.

73

Figure 3.3.~ Graphical representation of the null hypothesis regarding mean minimum spanning tree (MST) segment lengths. The probability density function represents a randomly generated distribution of means from 500 MSTs. If the observed mean (dot) in a feeding guild is larger than 90% of means from the randomly-generated distribution, then species in the feeding guild are ecomorphologically hyperdispersed and the feeding guild is stmctured by deterministic processes.

74

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Figure 3.4.-- Graphical representation of the null hypothesis regarding the variance of the minimum spanning tree (MST) segment lengths. The probability density function represents a randomly generated distribution of segment variances from 500 MSTs. If the observed segment variance (dot) in a feeding guild is smaller than 90% of variances from the randomly-generated distribution, then species in the feeding guild are ecomorphologically hyperdispersed and the feeding guild is stmctured by deterministic processes.

75

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CHAPTER IV

COMMUNITIES, INTERACTIONS, AND THE LACK OF

COMPETITIVE EXCLUSION: A SYNOPTIC

EVALUATION OF DENSITY COMPENSATION

Abstract

Ecomorphological approaches are a popular means of inferring resource

utiUzation, ecological interaction, and ultimately, the stmcture of natural

conmiunities. Traditionally, ecologists have explored hyperdispersed morphological

pattems as a means of identifying competitively induced deterministic stmcture.

Recent research, however, has been equivocal in identifying nonrandom

morphological pattems within communities. Alternative approaches for identifying

deterministic stmcture must be explored to assess if competitive interactions

consistently affect organization. Density compensation is the phenomenon whereby

the abundances of species depends upon morphological relationships with other taxa

in a feeding guild. Close competitors, evinced by morphological similarity, should

exhibit lower abundances because of increased competitive affects. As a

consequence, a statistical relationship should exist whereby the morphological

distance of species is positively correlated with its abundance. Density compensation

exists within bat feeding guilds and communities. Nonrandom pattems in abundance

and morphology were detected in seven conununities, in three feeding guilds, and for

three competitive scenarios. Nonetheless, density compensation is neither a pervasive

nor consistent attribute of community or guild organization. These data add to new

information suggesting that no one measure of stmcture pervades all communities.

Future studies should be directed at environmental gradients in order to understand

76

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the circumstances that promote or deter the production of nonrandom pattems in

community organization.

Introduction

Ecomorphological approaches in community ecology have become a popular

avenue to explore pattems that explain the coexistence of sympatric species (Findley,

1993, 1976; Findley and Black, 1983; Hespenheide, 1973; Mares, 1976; Ricklefs and

Miles, 1994; Smartt, 1978; Wainwright and Reilly, 1994). Reasons for their

popularity are numerous. The mensural nature of morphological attributes yields

quantitative data that can be scmtinized and manipulated from a statistical standpoint.

Thus, more quantitative tests of hypotheses ultimately provide more rigor in

evaluating variation within and among species (Blackith and Reyment, 1971; Rohlf,

1990).

Morphological variation is a populational attribute molded by natural selection

to produce phenotypic optimization (Darwin, 1859; Endler, 1986). As a result, the

morphological phenotype has become a standard metric to evaluate fitness and

ultimately the evolution of organisms (Clarke, 1995; Jones, 1987; Leary et al., 1984;

Palmer and Strobeck, 1986). Furthermore, morphology may be among the most

important phenotypic attributes relevant to the ecology of organisms (Wainright and

Reilly, 1994); implications are profound. A species ability to invade a community,

and hence occur in a given area, is dependent on its morphology (Brown, 1981;

Drake, 1990; Fox, 1989; Hutchinson, 1959; Law and Morton, 1993). Consequently,

morphological attributes of species play important roles regarding conmiunity

composition and stability, and ultimately affect community equilibria (Drake, 1990;

Fox, 1989; Huston, 1994; Hutchinson, 1959). As such, ecomorphological approaches

77

are integral in understanding higher order ecological phenomena (Findley, 1976;

Findley and Wilson, 1982; Mares, 1976; Wainright and Reilly, 1994).

At the center of theory addressing community organization lies the notion

that, via optimization, natural selection drives the morphological attributes of species

populations to diverge within communities (Case and Sidell, 1983; Cody and

Diamond, 1975; Hutchinson, 1959; MacArthur and Levins, 1967). Morphological

characteristics are important in the consumption of resources (Bonaccorso, 1975;

Brown and Lieberman, 1973; Dayan and Simberioff, 1994; Findley and Black, 1983;

Findley and Wilson, 1982; Freeman, 1981, 1984, 1988, 1992; Hespenheide, 1973;

Smartt, 1978), and for species to coexist, there should be a limit to morphological

similarity (Abrams, 1983; MacArthur and Levins, 1967). If two species are similar,

the resources they consume will be similar, and they should compete with such

intensity that interactions culminate in local extinction or morphological shifts of one

or both species. From a community perspective, morphological optimization occurs

when sympatric species exhibit hyperdispersed morphologies that minimize

interspecific competition (Cody and Diamond, 1975; Case and Sidell, 1983;

Hutchinson, 1959; MacArthur and Levins, 1967; Moulton and Pimm, 1986).

The documentation of hyperdispersions along putatively important

morphological axes is commonplace for many taxa in many contexts (see Simberloff

and Boeklen, 1981, for a review). Nonetheless, an equal mass of evidence fails to

support hyperdispersions (Connor and Simberloff, 1978, 1979; Simberloff and

Boeklen, 1981; Willig and Moulton, 1989). Such equivocal results could be the result

of either of two aspects of competitive interactions: (1) species within feeding guilds

do not compete at all locations, or (2) competitive interactions lack the intensity to

govern the central tendency of morphological attributes of species in all cases.

78

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Hyperdispersions probably manifest as population densities approach carrying

capacity. For example, to cause size assortment, competitive interactions must be

intensive enough to produce local extinction, extensive enough to affect all species

utihzing a limiting resource, and these effects must predominate at a specific locality;

no other influences, such as disturbance or predation, may supersede the importance

of competitive interactions (Moulton and Pimm, 1986). Nonetheless, many

populations never approach carrying capacity and density-dependent phenomena are

circumvented by factors such as environmental stochasticity, seasonality, parasatoids,

or predators (Andrewartha and Birch, 1954, 1988; Petraitis et al., 1989; Strong,

1984). Competitive exclusion may not occur in these communities.

Demonstration of hyperdispersions along morphological axes need not be the

only indication of stmcture induced by competition. Density compensation also may

exist within feeding guilds (Hawkins and MacMahon, 1989; Root, 1973). Density

compensation is the phenomenon whereby the total abundance of individuals of all

species within a feeding guild tends toward a maximum density set by the

environment. The distribution of abundances of constituent species, however, is

dependent upon their relationships with other guild members. Those species that

experience the greatest competitive pressure exhibit the lowest density.

Morphological attributes have been demonstrated to be good surrogates for

ecological relationships of many animal taxa, including bats (Bonaccorso, 1975;

Brown and Lieberman, 1973; Dayan and Simberloff, 1994; Findley and Black, 1983;

Findley and Wilson, 1982; Freeman, 1981, 1984, 1988, 1992; Hespenheide, 1973;

Smartt, 1978). Moreover, the position of species on resource axes are mirrored by

positions on morphological axes. Species that exhibit a high degree of morphological

similarity to other species within a feeding guild should experience the greatest

competitive effects, and exhibit lower abundances. Therefore, a positive relationship

79

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should exist between the morphological distance of species and their abundance, and

density compensation should be a predictable attribute of feeding guilds (Fig. 2.1).

Herein, I evaluate bat communities from North, South, and Central America, to

determine whether density compensation exists and is pervasive.

Methods

Communities. Fifteen bat communities from throughout the New World were

evaluated for evidence of density compensation (see Appendix A). A number of

criteria limited the number of communities selected for analyses. First, sampling

must have been conducted in a well-delimited local area that represented an actual

community of species that, because of their spatial proximity, exhibit the potential to

interact. Faunas of geopoliticsdly bounded areas were not acceptable because it was

difficult to be reasonably sure that only one community was sampled. Second,

sampling must have been continual for at least one year. This minimizes the failure

to detect rare species. Lastly, data must have been the product of regular sampling in

all seasons that bats were active. If density compensation occurs, it may manifest

through the absence of species during portions of the year when resources are rare.

By totaling abundance from all seasons, density compensation can be evaluated from

a yearly perspective.

Feeding Guilds. Each community was categorized into seven feeding guilds

(sensu Root, 1967): aerial insectivores, fmgivores, gleaning animalivores, molossid

insectivores, nectarivores, piscivores, and sanguinivores (see Appendix B for

definitions). Assignment of species to guilds was based on designations from the

original authors description of the community or from Wilson (1975) and Gardner

(1977). I only examined five guilds (aerial insectivores, fmgivores, gleaning

animalivores, molossid insectivores, nectarivores). The piscivore and sanguinivore

80

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guilds were not included in analyses because at least three species are necessary for

correlation analysis. Piscivores never met this criterion, sanguinivores did, but at

only one location.

Morphological Stmctore. Seven ecomorphological attributes characterized

each species. These were forearm length, greatest length of skull, condylobasal

length, width across the postorbital constriction, breadth of the braincase, length of

the maxillary toothrow, and breadth across the upper molars (see Appendix C for

definitions). Morphological measurements were obtained from museum specimens.

In most cases, the mean of each morphological character was based on eight

individuals, usually 4 males and 4 females. Special care was taken to select

specimens for measurement from geographic locations as close as possible to that of

each community. In most cases, specimens for each community were from the same

phytogeographic area within 700 km of the actual community. In all cases,

specimens were from the same subspecies as those found in the actual community.

Common logarithms of each character were used in analyses following

Ricklefs and Travis (1980). Log transformations enhance normality and

homoscedasticity (Ricklefs and Travis, 1980; Sokal and Rohlf, 1995). Moreover, log

transformations minimize the disparity in size among morphological characters of a

species, thereby reducing the propensity for differences in large characters to disguise

differences in small characters.

Community stmcture can be produced via a spectmm of interspecific

interactions, ranging from pairwise effects, to those based on all possible interactions.

Ecomorphological dissimilarity can be measured from a variety of perspectives as

well, corresponding to the ways competition could stmcture communities. If diffuse

competition pervades a feeding guild, than the abundance of a species will be the

product of its morphological relationship with all other species. This should be tme

81

when all guild members are fairly general in their dietary requirements and possess

resource spectra that in at least some way overlap among neighbors. In contrast,

interactions between a species and its most ecologically similar neighbors may be the

primary factor acting on community stmcture, and the morphological relationships

between a species and its nearest neighbors should most affect abundance. This

should be tme when species possess fairly narrow dietary requirements and resource

overlap involves few species in a feeding guild.

I evaluated three competitive scenarios along the spectmm of possibilities

(Fig. 2.2). In the first scenario, the abundance of a given species is the product of its

morphological relationships with all other (n-1) species in the feeding guild. The

Euclidean distance for each species represents the ecomorphological (Findley, 1976;

Findley and Wilson, 1982; Mares, 1976) distance of a species with respect to all other

(n-1) guild members:

n-1 m

Dt=I ( I (X , rX/ r . f ') i=l j=I

where: Dt represents the morphological distance of species t; n is the number of

species; m is the number of morphological characters; Xy represents morphological

character j of species i; and Xtj represents morphological character j of species t.

In the second scenario, interactions between a focal species and its most

morphologically distinct neighbor may be so weak as to have no effect on abundance.

Therefore, simulations were conducted in which the Euclidean distance included all

species in the feeding guild except the most morphologically different neighbor (n-2

of the species in the feeding guild):

82

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n-2 m

Dt=i(i:(x,-x/r. <«) i=i j=i

In the third scenario, the abundance of species is not the product of diffuse

competition; abundance is a consequence of interactions with nearest morphological

neighbors. Thus, two nearest neighbors of a focal species were the only members of

the feeding guild included in calculations of ecomorphological distance:

2 m

Dt=I(I(X.i-X,/)'". («) i=l j=l

Null Hypotheses. Analyses are predicated on two assumptions. First,

measures of morphological dissimilarity within a guild are suitable surrogates for

ecological dissimilarity. Second, a species with high ecomorphological similarity to

one or more potential competitors should suffer reduced density as a result of

interspecific competition. As a consequence of such competitive effects, a

quantitative relationship should exist between the proximity of species in

ecomorphological space and density (Fig. 2.1).

I used Spearman rank correlation coefficients (SRCC) to describe the

magnitude of the relationship between morphological distance and abundance within

feeding guilds for many reasons. The association between morphological

dissimilarity and abundance may be nonlinear. I was most interested in the general

form of this relationship (does abundance increase as dissimilarity increases), and

thus utilized a rank coefficient to identify any monotonic association. Furthermore, it

is difficult to assess the abundance of bats with great accuracy based on contemporary

sampling techniques (Jones, 1965; Kunz and Kurta, 1988). SRCC provides for a

more appropriate analysis because the abundance of species need only be ranked

83

\

within feeding guilds from most abundant to least abundant; absolute measures of

abundance are unnecessary.

Although SRCC analysis is a nonparametric method, its traditional hypothesis

test assumes that variates follow a specified distribution (t-distribution). As a result,

the possibility exists that traditional hypothesis tests yield slightly inaccurate results

when assumptions regarding the distribution of data are not met (Noreen, 1989).

Assessment of significance based on simulation analyses, however, are not subject to

these inaccuracies. Simulation creates a unique distribution of Spearman correlation

coefficients for each null hypothesis. Moreover, the actual data are used to create this

distribution. No assumptions about the actual data are necessary, and hypothesis tests

are based on a distribution that is perfectly suited for the data (Noreen, 1989). Thus,

no violations of assumptions can jeopardize the accuracy of hypothesis tests.

To determine significance, I compared the correlation coefficients from each

actual guild to a distribution of correlations produced by the following stochastic

process. While preserving the integrity of the morphological relationships among

species, random abundances were assigned to each species. A correlation coefficient

was then calculated between randomized ranked abundances and actual

morphological distances of members within the simulated guild. One thousand

iterations of this process yielded a probability density function for subsequent

hypothesis tests. The correlation coefficient from the actual guild was compared to

the probability density function of simulated correlation coefficients. If the

coefficient for the actual guild occurred within the upper ten percent of the

distribution (p < 0.10), I concluded a nonrandom positive association between

morphology and abundance in the actual guild (Fig. 2.3). Many phenomena operating

totally independently of guild-wide competitive interactions, however, can influence

the abundance of species. Positive associations between abundance and

84

morphological distance, consistent with competition theory, may be obscured

partially by species experiencing autecological influences (i.e., differential response

to resources or disturbance) or by a plethora of other influences (i.e., predation,

mutualism) occurring at the community level. To safeguard against these possibilities

and wrongfully failing to reject the null hypothesis, I set alpha at 0.10.

Results

Density compensation was detected in seven communities (Table 4.1:

Guanacaste [LaVal and Fitch, 1977], Guanacaste [Fleming et al., 19721, Sherman,

Barro Colorado Island, Pern, Cerrado, and Caatinga) and in three feeding guilds

(Table 4.1: aerial insectivores, fmgivores, gleaning animahvores). Statistically

significant positive correlations between abundance and morphological distance

ranged from r = 0.42 to r = 1.00. Nonetheless, no community was strongly

characterized by deterministic stmcture in all its constituent feeding guilds, and no

feeding guild was deterministically stmctured at all locations. Obvious pattems as to

which communities or feeding guilds consistently exhibit deterministic stmcture are

unclear overall.

Despite a lack of statistical concordance, the possibility exists that when

results are combined, either across all locations for a particular feeding guild or across

all feeding guilds in a particular community, overall deterministic stmcture may be

revealed (Sokal and Rohlf, 1995). I used Fisher's exact test (Sokal and Rohlf, 1995)

to evaluate this possibility. Two communities (Guanacaste [LaVal and Fitch, 19771

and Sherman) exhibited deterministic stmcture overall (Table 4.2), whereas, none of

the feeding guilds exhibited deterministic stmcture overall (Table 4.3).

Density compensation was detected for each of three competitive scenarios

(Table 4.1). However, when nonrandom abundances occur within feeding guilds only

85

\

rarely do they pervade all three competitive scenarios. Moreover, density

compensation was detectable most often when only nearer neighbors were utilized for

the determination of competitive pressure. Only rarely were nonrandom pattems in

abundance the product of diffuse relationships with all other taxa in a feeding guild.

Discussion

Recenfly, the role of competitive interactions in stmcturing communities has

been questioned critically (Strong et al., 1984, and references therein), and the

importance of competition theory and its implications to community organization has

been discounted. At the heart of recent criticism have been questions conceming the

validity and ubiquity of morphological pattems. Many morphological pattems have

been shown to lack statistical vaUdity (Simberloff and Boeklen, 1981). Moreover, a

preponderance of reported morphological pattems come from vertebrate communities

and may not be a fair representation of the stmcture of all communities (Strong,

1984). Morphological hyperdispersions within bat communities have been evaluated

only recently (Chapter 3; Willig and Moulton, 1989). Although morphological

pattems are well-documented in bat communities (Findley, 1976; Fleming, 1986,

McKenzie and Rolfe, 1986; WiUig, 1986), hyperdispersions are not a consistent

attribute of stmcture (Chapter IE, this thesis; Willig and Moulton, 1989).

Morphological pattems, however, are not the only possible manifestation of

competitive interactions at the community level. Before the effects of competitive

interactions on community stmcture are discounted, the existence and ubiquity of

other manifestations (i.e., density compensation) should be explored.

Rejection of the null hypothesis of random pattems of abundance is highly

dependent on the morphological scenario under consideration. Every species in a

feeding guild need not intensely compete with all others to impose stmcture.

86

Contemporary morphological models implicitly assume that the competitive

interactions that stmcture communities occur only between nearest neighbors.

Although these interactions probably are most intense, my results indicate that

interactions that lead to stmcture can be more diffuse. A limited focus on only

nearest neighbors will likely lead to a limited understanding of community

organization. Moreover, exploring the breadth at which interactions operate may

provide added insight into the process of community organization.

The breadth of interaction may shed light on community characteristics as

well. If species compete along a single resource axis, such as fmit size, resource

spectmm will be unidimensional. In this case, species' nearest neighbors most likely

impose a preponderance of the competitive pressure realized by a particular species.

However, in feeding guilds or communities where resource utilization is

multispectral, pressures from more species may be the mle. For example,

omnivorous rodent species may compete and divide resources with regard to seed size

on one axis and chitin hardness of insects on another. If the positions of species are

not mirrored on both resource axes, combinations of close competitors from both axes

could be different, and a species' two nearest ecological neighbors could, in tum, be

different, depending on the axis. Thus, scenarios involving more than just nearest

neighbors would be necessary to understand competitive interactions.

Density compensation is not a pervasive attribute of communities or feeding

guilds. Nonetheless, it is an additional approach for characterizing the influence of

interspecific competition on community organization. Community ecologists have

been hasty to discount the validity of competition theory based on rejections of single

predictions. An approach like "strong inference" (Piatt, 1964) would be more

appropriate to evaluate the validity of competition theory. For example, one might

first evaluate morphological hyperdispersions within communities. Upon failure to

87

\

appropriate to evaluate the validity of competition theory. For example, one might

first evaluate morphological hyperdispersions within communities. Upon failure to

reject the null hypothesis of random morphological dispersion, one would then

evaluate a null hypothesis of no association between morphological distance and

abundance. Upon rejection of this null hypothesis, one might then evaluate another

putative manifestation of competitive interaction. Failure to reject single null

hypotheses should not be an end, but rather a beginning.

Interspecific competition is a density-dependent phenomenon (Begon et al.,

1990). Manifestations of competitive interactions may assume a hierarchical

organization, with levels corresponding to the degree to which populations approach

carrying capacity. For example, in environments where populations are at or near

carrying capacity, competitive interactions may be intense (strong enough to meet the

assumptions of size assortment), and capable of causing the extinction of species that

share much morphological similarity with one or more species; size assortment

pervades. In intermediate situations, population densities may be lower (relative to

resources), and competitive interactions may not be sufficiently strong to cause

extinction. However, lower species abundances may be the consequence of

interactions with similar community members. Lastly, competitive interactions may

be too weak to cause extinctions or manipulate abundances. Nonetheless, species

may maximize resource consumption by some behavioral attribute that allows them

competitor-free space or time (e.g., habitat or temporal segregation). Thus, density

compensation may be a manifestation of competitive interactions of intermediate

intensity.

These data partly corroborate those of James and Boeklen (1984), who found

little evidence that species abundance was associated with morphology in birds. It is

important to point-out that both studies address competitive interactions among

88

highly mobile organisms. More mobile organisms may simply leave a community

when local resources are low and thereby escape strong competitive effects.

Furthermore, more mobile species may easily recolonize when communities regain

sufficient resource levels. This may explain why some bat species are only seasonal

residents in some communities (Bonaccorso, 1975). Moreover, this may explain a

lack of ubiquity of density compensation. The lower mobility of organisms such as

plants, rodents, and lake fishes, may explain why such profound manifestations of

competitive interactions sometimes obtain (Brown, 1989; Brown et al., 1979; Fowler,

1986; Holbrook and Schmitt, 1992; Kodric-Brown and Brown, 1993; Price, 1986;

Robinson et al., 1993; Silvertown and Dale, 1991).

Considerable variation exists regarding the degree of density compensation

within feeding guilds and communities. Competitive interactions are not the only

constraints on the abundance of species. Other biotic factors, such as mutualism,

predation, and parasitism, along with abiotic influences such as environmental

productivity and climatic variability, influence abundance as well (Andrewartha and

Birch, 1954, 1988; Begon et al., 1990). These influences may modulate abundances

to such an extent that the effects of competitive interactions are obfuscated. Gradients

in the degree of alternative influences on community composition should correspond

with gradients in the degree to which competitive interactions stmcture communities.

Moreover, the exact circumstances that lead to competitively induced community

stmcture should be explored (Chapter V).

89

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94

Table 4.1.-- Results of simulation analyses evaluating nonrandom pattems in abundance within fifteen bat communities (Appendix A), n-1, n-2, and 2 represent three competitive scenarios; rs and ps represent the Spearman rank correlation coefficient and the probability that the observed correlation coefficient comes from a simulated distribution where rs = 0, respectively. Bold values indicate deterministic guild stmcture at p < 0.10 level.

Community Feeding guild

n-1 rs Ps

n-2 rs Ps rs Ps

Iowa

Aerial insectivore 0.228 0.298

Cahfomia


Chiapas

Fmgivore

Gleaning animalivore

Molossid insectivore

0.154 0.304

-0.162 0.732

1.000 0.152

Guanacaste (LaVal and Fitch, 1977)


Fmgivore

Gleaning animahvore


Nectarivore

0.174 0.340

0.409 0.125

-0.200 0.607

0.400 0.371

Guanacaste (Fleming et al., 1972)

Aerial insectivore -0.419 0.834

0.228 0.336

0.190 0.336

0.156 0.347

0.071 0.422

0.113 0.365 -0.118 0.633

-0.105 0.632

0.866 0.836

-0.295 0.817

1.00 0.171

0.720 0.009 0.679 0.008

-0.087 0.547

0.443 0.122

-0.400 0.803

-0.087 0.520

0.298 0.206

-0.400 0.784

-0.600 0.846 -0.600 0.833

-0.419 0.836 -0.419 0.832

Fmgivore

Gleaning animahvore

;nas

Aerial insectivore

Fmgivore

0.407

-0.239

-0.009

-0.238 95

0.179

0.715

0.500

0.718

0.323

-0.037

-0.230

-0.238

0.207

0.571

0.711

0.750

0.503

-0.110

-0.426

-0.286

0.098

0.610

0.877

0.767

Table 4.1. Continued


Nectarivore

Heredia

Aerial insectivore

Fmgivore

Gleaning animahvore

Nectarivore

Sherman

Aerial insectivore

Fmgivore


Rodman

Aerial insectivore

Fmgivore

Gleaning animahvore

Barro Colorado Island

Fmgivore

Gleaning animahvore

Zabehtas

Fmgivore

Gleaning animahvore

Nectarivore

Pance

Fmgivore

n-] rs

-0.200

-0.110

-0.047

-0.351

-0.638

0.464

0.258

-0.049

-0.632

0.314

-0.406

0.455

-0.498

0.211

0.091

0.100

-0.301

96

[

Ps

0.631

0.656

0.556

0.924

0.898

0.185

0.188

0.526

0.848

0.145

0.811

0.081

0.941

0.189

0.485

0.485

0.836

n-2 rs

-0.200

-0.245

-0.052

-0.316

-0.174

0.754

0.326

0.049

-0.632

0.388

-0.063

0.448

-0.402

0.179

-0.030

0.100

-0.329

1

Ps

0.653

0.791

0.590

0.916

0.668

0.032

0.117

0.438

0.835

0.118

0.556

0.079

0.905

0.255

0.567

0.465

0.856

2 rs

-0.429

-0.084

-0.333

-0.312

-0.667

0.493

-0.204

-0.025

-0.632

0.300

0.381

0.007

-0.411

-0.126

0.030

-0.300

-0.483

Ps

0.816

0.609

0.879

0.892

0.932

0.136

0.524

0.515

0.826

0.171

0.154

0.488

0.900

0.694

0.567

0.738

0.933

Table 4.1. Continued


n-1 rs Ps

Pern


Gleaning animalivore -0.215 0.780

Molossid insectivore -1.000 1.000

Nectarivore

Edaphic Cerrado

Aerial insectivore

-0.600 0.829

-0.198 0.702

Fmgivore 0.321 0.259

Gleaning animalivore 0.316 0.387


Caatinga


Fmgivore 0.179 0.374

Gleaning animalivore 0.683 0.047


n-2 rs Ps rs Ps

Nectarivore -0.500 0.845

-0.460 0.931 -0.519 0.947

-0.109 0.636 0.415 0.055

-0.866 0.814 -1.000 1.000

-0.600 0.811 -0.600 0.818

-0.198 0.676 -0.126 0.586

0.250 0.308 0.036 0.461

0.949 0.040 0.949 0.040

0.000 0.486 -0.500 0.836

-0.718 0.943 -0.667 0.948

0.214 0.355 0.214 0.307

0.683 0.029 0.311 0.231

-0.667 0.942 -0.757 0.982

-0.866 0.828 -0.500 0.845

97

Table 4.2.-- Results of Fisher's test assessing overall deterministic stmcture of bat communities when probabilities from all feeding guilds are combined, n-1, n-2, and 2 represent three competitive scenarios. Boldfaced print indicates overall deterministic community stmcture at p < 0.10.

Communitv

Iowa

Califomia

Chiapas

Guanacaste (LaVal and Fitch, 1977)

Guanacaste (Fleming, 1972)

Puntarenas

Heredia

Sherman

Rodman

Barro Colorado Island

Zabelitas

Pance

Pem

Edaphic Cerrado

Caatinga

n-1

0.298

0.348

0.327

0.040

0.600

0.813

0.959

0.228

0.564

0.272

0.369

0.836

0.998

0.680

0.557

n-2

0.336

0.336

0.612

0.109

0.575

0.904

0.934

0.043

0.394

0.259

0.471

0.856

0.982

0.201

0.421

2

0.347

0.422

0.554

0.128

0.413

0.975

0.984

0.342

0.237

0.798

0.454

0.933

0.593

0.309

0.845

98

Table 4.3.-- Results from Fisher's test assessing overall deterministic stmcture of each of five feeding guilds when probabilities are combined for all locations, n-1, n-2, and 2 represent three competitive scenarios. No feeding guild exhibited deterministic stmcture (p > 0.10).

Feeding guild nA n-2

Aerial insectivore

Fmgivore



Nectarivore

0.477

0.252

0.827

0.725

0.948

0.331

0.271

0.389

0.870

0.984

0.510

0.858

0.194

0.816

0.999

99

CHAPTER V

GRADIENTS IN THE STRUCTURE OF NEW WORLD

BAT COMMUNITIES

Abstract

One of the most debated issues in ecology is the importance of competitive

interactions in stmcturing communities. Ecologists only recently have begun to

consider that the density-dependent nature of competitive interactions sometimes make

predictions based on classical equilibrium theory invalid. More specifically,

coexistence within a community of competitors that would be unexpected under

equihbrial theory may be possible by virtue of unutihzed resources resulting from the

disequilibrial densities of populations. As a consequence, many ecologists have

abandoned equilibrial competition theory because it is unable to predict stmcture in

many situations. Determining the environmental conditions that mitigate the

consequences of competitive interactions on community stmcture would be an

important advance in theoretical ecology. Herein, I evaluate the degree to which

measures of the deterministic stmcture of bat communities and feeding guilds are

associated with mean measures of precipitation, productivity, and temperature; their

associated variability; and latitude.

Stmcture was evaluated from three perspectives. Numerical stmcture was

determined by the degree to which correlations between the abundance of a species and

its morphological distance with other competitors was nonrandom. The way that

competition produces hyperdispersed morphological pattems was evaluated in two

ways. Interactions may influence the mean or the variance of the distance between

species centroids. Thus, hyperdispersion was defined by the degree to which the mean

and variance of interspecific distances differed from random expectations.

100

Variation in the degree of competitively induced stmcture of feeding guilds

coincides with variation in environmental parameters; however, variation in overall

community stmcture does not. The overall response of bat communities may be

confounded by the unique response of each feeding guild to environmental variation.

Unique responses by feeding guilds suggest that species at higher trophic levels

respond to more complex characteristics, such as productivity and latitude, whereas

species at lower trophic levels respond to simpler factors such as temperature.

Measures of numerical stmcture were more sensitive to environmental characteristics

than were measures based on morphology alone. Nonetheless, these results

demonstrate that the environmental context of a community should be considered before

casting predictions regarding deterministic organization.

Introduction

A paradigm pervading modem ecology is that biotic, abiotic, and historical

processes act on hfe history attributes to determine the distribution and abundance of

species (Andrewartha and Birch, 1954, 1988; Begon et al., 1990). Consequently,

understanding the spatial and temporal scales, ecological levels, and circumstances

under which each of these processes prevail is a major thmst of contemporary ecology.

Competitive interactions often transpke within trophic levels, but are probably

most intense within feeding or other resource guilds (Cody and Diamond, 1975;

Diamond and Case, 1986; Gee and Giller, 1987; Hawkins and MacMahon, 1989;

Kikkawa and Anderson, 1986; Pimm, 1982, 1991; Polls, 1991; Ricklefs and Schluter,

1993; Simberloff and Dayan, 1991). Ultimately, interspecific competition mediates

community stmcture when populations are at or near equilibria (Begon et al., 1990;

Krebs, 1985; Ricklefs, 1979). An equilibrium is defined as the state at which the rate

of death of organisms equals the rate of birth (MacArthur and Wilson, 1967). More

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operationally, however, equilibria refer to demographic states at which population

densities fluctuate only slightly about carrying capacity (Begon et al., 1990; Huston,

1994; Krebs, 1985). At equilibrium, limiting resources effectively are exhausted, and

the potential for competitive interactions is greatest. If two species are not sufficiently

different ecologically, their resource spectra will overlap to such an extent that both

species will consume and compete for the same resource (Abrams, 1983; Hutchinson,

1959; MacArthur and Levins, 1967). As a result of increased competition species

exhibiting ecological overlap should suffer reduced fitness, possibley stimulating

divergence with regard to utihzation of resources (Hardin, 1960; MacArthur and

Levins, 1967). Under equilibrial conditions, competitive interactions drive natural

selection in either of two directions: competitive exclusion or character displacement.

To these ends, repeatable, quantitative predictions regarding the coexistence of species

and ultimately the stmcture of communities are possible if populations within

communities are at equilibrium (Huston, 1994; Pielou, 1975; Ricklefs, 1979;

Vandermeer, 1969).

Equilibrial conditions may be unreasonable expectations for many systems.

Empirical confirmation of aspects of disturbance theory, as well as a focus away from

vertebrates, has demonstrated profoundly that many systems are not at equilibrium

(Power et al., 1988; Resh et al., 1988; Strong, 1984). Moreover, the predictions of

traditional competition theory are invahd and provide httle understanding conceming

coexistence under non-equilibrial conditions (Chesson, 1986; Strong et al., 1984). If

co-existing populations are not at equilibrium, the effects of density-dependent

interactions (e.g., competition) are variable and lead to potentially unpredictable

community stmcture. For example, species with inferior competitive ability can coexist

and competitive hierarchies may be dismpted when species are added under

nonequilibrial conditions (Armstrong and McGehee, 1976; Koch, 1974; Levins, 1979;

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Park, 1954; Rotenberry, 1978). Nonetheless, competitive interactions may still

influence community organization despite nonequilibrial conditions. New theory

addressing the dynamics of density- or frequency-dependent phenomena under

nonequilibrial conditions may provide greater insight and suggest productive avenues

of future research in community ecology.

Predictions of community organization under non-equilibrial conditions have

been developed only recently, and are slow in development (Chesson, 1986; Levin,

1970; Levin and Paine, 1974; Weins, 1977). These models are quantitatively more

complex than equihbrial models, and result in outcomes that are difficult to interpret

because of nonlinearity (Chesson, 1986). Nonetheless, non-equilibrial population

dynamics probably occur in most species and their ramifications on community

organization should be examined from a variety of perspectives (Strong, 1984).

Furthermore, environmental change as a consequence of anthropogenic activity

continues to accelerate, resulting in increased destmction of habitat and ultimately an

increase in the number of populations experiencing disequihbrial population densities

(Wilson, 1988). The importance of understanding ecological phenomena under

nonequilibrial conditions becomes even more critical in this context.

Abiotic factors have considerable effects on demographic attributes of

populations (Andrewartha and Birch, 1954, 1988). These effects can influence

coexistence by modifying life history traits of species such as body mass, adult survival

rate, and age at parturition (Zammuto and Millar, 1985). Moreover, these effects on

populations can emerge at the community level by many avenues. Abiotic conditions

modify the potential intensity of biotic interactions at the community level (Dunson and

Travis, 1991). By affecting the composition of species pools from which communities

are assembled, environmental conditions also may dictate which species potentially

interact (Roughgarden and Diamond, 1986). Moreover, environmental fluctuations or

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disturbances that indiscriminately lower population densities can result in diminished

competition, or in extreme cases, drive species to extinction (Sousa, 1984).

Nonequilibrial community organization might be better understood if the degree to

which abiotic factors, especially envkonmental variability, influence deterministic

stmcture is discemed.

Herein I evaluate whether variation in environmental parameters mediates the

degree to which competitive interactions manifest as deterministic stmcture at the level

of ecological guilds and communities. I predict that if environmental variabihty

decreases the degree of deterministic stmcture in bat communities, then gradients in

stmcture should coincide with environmental variability.

Methods

Selection of Communities. I evaluated gradients in the stmcture of bat

communities based on nine sites distributed throughout the New Word (Table 5.1).

Bat communities were selected for many reasons. Bats are distributed widely and in

sufficient numbers throughout the New World such that communities from many

different biomes could be represented in analyses. Moreover, bats are numerically

dominant in many systems and represent keystone species (Handley, 1966; Robinson,

1971). Lastly, bats occupy at least three trophic levels (primary, secondary, and

tertiary consumers) and seven feeding guilds (aerial insectivores, fmgivores, gleaning

animalivores, molossid insectivores, nectarivores, piscivores, and sanguinivores).

Thus, comparisons of the stmcture of bat communities are possible from a number of

ecological perspectives (Findley, 1993).

Characterization of Community Stmcture. Bats were categorized into feeding

guilds based on designations pubhshed in the actual account of the community, or on

other published information (Gardner, 1977; Wilson, 1975). Piscivore and

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sanguinivore feeding guilds were not used in analyses because they comprise too few

species. The molossid insectivore guild was not included in analyses because it was

represented by sufficient numbers of species at only three locations, and thus does not

lend itself to regression analyses. Consequently, analyses were restricted to aerial

insectivores, fmgivores, gleaning animalivores, and nectarivores. Feeding guilds from

particular locahties were not included in analyses if they did not contain at least three

species. In general, I used two suites of Monte Carlo simulations to characterize the

degree to which communities exhibited stmcture with regard to morphology or density.

Morphological Stmcture. Deterministic, morphological stmcture occurs if a

feeding guild exhibits statistically hyperdispersed morphologies. Hyperdispersion may

manifest in either of two ways: species within feeding guilds may have larger mean

nearest neighbor distances than expected by chance, or the variance of the distances

between nearest neighbors may be smaller than expected by chance (Willig and

Moulton, 1989). I evaluated both scenarios. Significant hyperdispersions were

determined by comparing statistics from actual feeding guilds to those randomly

generated from faunal pools. Four faunal pools were used for comparison: all species

whose distributions overlapped the geographic location of the actual community, as

well as all species whose distribution fell within a circle centered at the location of the

community and had diameters of 500, 1000, or 2000 km (Fig. 3.2). Species were

randomly drawn from faunal pools in numbers equal to those of the actual community.

Seven morphological characters were used to characterize relationships among species

(Appendix C). Principal components analyses were used to reduce to two the number

of dimensions describing morphological relationships. The mean and variance of

interspecific morphological distances were then calculated between nearest neighbors.

This was iterated 500 times to yield a random distribution of each statistic. The

position of the actual mean and variance with regard to their respective random

105

distributions determined the degree to which stmcture was nonrandom. More in-depth

descriptions of these models of community organization are provided in Willig and

Moulton (1989) and in Chapter m.

Numerical Stmcture. Numerical stmcture was defined by the degree of

association between the morphological distance of species from other taxa and

abundance. A species with a high degree of morphological similarity to other members

of its feeding guild (low ecomorphological distance) should experience greater

interspecific competition, and consequently exhibit reduced density. Hence,

deterministic numerical stmcture exists if a nonrandom positive correlation was

detectable between morphological distance and abundance. Monte Carlo simulations

were used to evaluate the statistical significance of such correlations.

Morphological distance was evaluated from a number of perspectives

representing a range of ways in which competitive interactions influence abundance

(Fig. 2.1). In all cases, Euclidean distances characterized the morphological distances

among competitors. In the first approach, the calculated morphological distance for

each species was from the perspective of all other (n-1) guild members:

n-1 m

Dt=I(I (X, -X/ ) '" . (5.1) i=l j=l

where: Dt represents the morphological distance of species t; n is the number of

species; m is the number of morphological characters; Xy represents morphological

character j of species i; Xtj represents morphological character j of species t.

In the second approach, the calculation of morphological distance for a species included

all species in the feeding guild except its most morphologically distant neighbor (n-2 of

the species in the feeding guild):

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n-2 m

D,= I(I(X,j-X,P'r. <5-2) i = l j=l

In the third scenario, the two nearest neighbors of each species were the only members

of the feeding guild included in calculations of ecomorphological distance:

2 m

Dt^IdCXg-X,/)"'. (5.3) i = l j = l

Distributions of random correlation coefficients were created to facilitate

detection of significance. To create null stmcture, abundance was randomized while

the morphological relationships of the species in the actual feeding guild were

maintained. A Spearman rank correlation coefficient was then calculated between

random abundance and morphological distance. This process was iterated 1000 times,

thereby yielding a distribution of random correlation coefficients. The position of the

correlation for an actual feeding guild with respect to this random distribution

determined the degree to which stmcture was nonrandom. More in-depth descriptions

of these models appear in Chapters n and IV.

In all, 11 measures (four regarding mean distance of species in morphospace,

four regarding the variance of distance between species in morphospace, three

regarding abundance pattems) characterized the stmcture of each feeding guild. A

composite value of each measure of stmcture was calculated from the P-values of each

feeding guild analyzed in a community. This composite P-value characterized the

overall stmcture in each community and was calculated as directed for Fishers test of

combined probability (Fisher, 1954; Sokal and Rohlf, 1995). Thus, 11 measures of

stmcture described each community as well.

For communities and each of five feeding guilds, separate principal components

analyses were conducted on all original measures of stmcture to produce more general

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indices of organization. The 11 measures of stmcture from all locations were entered

into separate principal components analyses for each guild. The same is tme for

communities. Principal components analysis is a technique whereby a linear

combination of the original variables is selected that ehminates redundancy and reduces

the number of dimensions necessary to illustrate relationships (Tobachnick and Fidell,

1989). Thus, each derived principal component represents a unique axis characterizing

stmcture.

Environmental Characterization. I used seven descriptive statistics to

characterize the regime of each of three environmental variables (precipitation, r;

productivity, p; and temperature, t) for each community (Table 5.2). Measures

included the mean (M) of the mean monthly value of each environmental parameter

(MMD MMt» MMp; Table 5.2), as weU as six measures of variabihty. Variability was

evaluated fi"om a number of perspectives including both absolute and relative scales.

Relative variability (CV) was characterized using the coefficient of variation, whereas

absolute variabihty (V) was described by the variance.

Three measures describe absolute variabihty for each parameter. Variances

within years were averaged across all years to yield a measure of average absolute

within-year variability (Mvr, Mvt, Mvp; Table 5.2). Variance among years in the mean

of a parameter was calculated also (VMT, VMI* VMp; Table 5.2). Finally, the variability

among years regarding the within-year variance of a parameter was calculated (Vvr,

Vvt, Vvp; Table 5.2).

Similarly, three measures of relative variabihty characterized each community.

The relative variabihty within years was described by the within-year coefficient of

variation averaged across years (Mcvr» Mcvt. Mcvp; Table 5.2). Year-to-year relative

variabihty was determined using the coefficient of variation of the mean across years

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(CVMH CVMI, CVMp; Table 5.2). Lastly, the variability across years of the

within-year, relative variability was calculated (Vcvr, Vcvt, Vcvp; Table 5.2).

Environmental data (mean monthly temperature and precipitation) for each

community were obtained from weather stations in the same phytogeographic region

and from no more than 150 km from the actual site (U. S. Department of Commerce,

1966, 1979, 1989). These criteria likely provide data that are sufficiently similar to that

of the focal sight so that comparisons among widely distributed (spatially as well as

phytogeographically) sites are possible.

Net, above-ground, primary production (NAPP) in grams per square meter can

be calculated from actual evapotranspiration (AE) following the recommendations of

Rosenzweig (1968) as:

NAPP= 1.66(logAE) - 1.66. (5.4)

Unfortunately, AE was not available for any of the sites from which bat communities

were studied. Consequently, I quantified the relationship between NAPP and both

temperature and precipitation based on AE, temperature, and precipitation data from 48

other sites (Thomthwaite and Associates, 1964) distributed throughout the biomes from

which bat communities were obtained. Data for AE were used to predict NAPP for the

48 sites. Stepwise multiple regression analysis (SPSS, 1990) identified the best

relationship between temperature and precipitation to estimate NAPP. The algorithm

derived from this analysis was then used to estimate productivity for each bat

community based on temperature and precipitation data.

Principal Components Analvsis. I used principal components analysis to

delineate important environmental gradients based on 21 chmatic characters (Table 5.2).

Conducting multiple bivariate correlations between raw environmental variables and

measures of stmcture would greatly enhance experiment-wise error rate. Moreover,

many of the envu-onmental parameters I measured were highly correlated with one or

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more variables. Instead of using all 21 environmental variables in subsequent analyses,

principal components analyses enabled measures that are highly correlated to be

integrated into fewer composite environmental gradients (i.e., the principal

components). Original environmental variables that were correlated highly with a

principal component elucidate the identity of that composite gradient.

Multiple Regression and Correlation Analyses. The degree to which

deterministic stmcture was a linear function of composite environmental gradients was

evaluated by stepwise multiple regression analysis (SPSS, 1990). Nonetheless, the

response of stmcture to environmental parameters may not be linear. Hence, I used

Kendall's rank correlation analysis to determine if sUncture changed in a consistent

direction along each environmental gradient. To protect from inflated experiment-wise

error rate associated with conducting numerous bivariate correlations, I decreased

comparison-wise error rate of each correlation based on Bonferroni's sequential

adjustment (Rice, 1989). Nonetheless, many phenomena acting independently of

density-dependent competitive interactions possibly influence the stmcture of

communities (e.g., predation, mutualism, parasitism). As a consequence, associations

between stmcture and environmental parameters may be obscured. To safeguard

against this, I set alpha at 0.10 in multiple regression and correlation analyses.

Results

Environmental Axes. The sites of the ten bat communities differed greatly with

regard to both climatic variables and latitude (Tables 5.3-5.5). Among-site variation

in temperature was consistently lower than that for precipitation or productivity,

whether assessed by central tendency or absolute and relative variability. For example,

means for precipitation, as well as productivity, differed among sites by two orders of

magnitude, whereas means for temperature were much less variable (e.g.,

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< 1/2 order of magnitude). Among-site variation in absolute measures of variability

(Vvr» Vvt, Vvp) were greater than that for corresponding relative measures of

variability (CVMF, CVMI, CVMp).

Multiple regression analysis identified the best algorithm to estimate

productivity (P) based on mean monthly temperature and precipitation as:

P = -61.9 -I- 9.39 [temperature] + 7.52 [precipitation] (5.5)

it accounted for a highly significant proportion of the variation in productivity (R =

0.795, p < 0.001).

Principal Components Analysis. Principal components analysis of the 21

environmental characters accounted for 93.4% of the variation among the ten

communities (Table 5.6). Four environmental gradients were extracted (Table 5.7).

Eigenvalues for the first four significant principal components (PCs) ranged from 1.35

to 10.94.

PCI was correlated highly with MvpVMr. Vvr, Vj p, and Vvp (Table 5.8).

PCI constitutes an axis of absolute variabihty in precipitation and productivity.

Locations on the negative portion of this axis represent areas of low absolute

variabihty, whereas locations on the positive end represent areas of high variability of

these parameters. This axis essentially depicts a gradient from dry to wet habitats. Wet

tropical areas experience high precipitation and productivity, but a pronounced dry

period as well. This results in high average rainfall as well as high variability. On the

other hand, deserts experience little rainfall, and as a consequence experience httle

absolute variabihty.

PC2 was highly correlated with Mvt, Mcvt, Vvt. and Vcvt (Table 5.8). It

represents an axis of the variabihty of temperature. Locations on the negative portion

of this axis experience low variability, whereas locations on the positive end experience

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high variability. PC2 recapitulates the latitudinal gradient in temperature, whereby

mean monthly temperature increases toward the equator and variability decreases.

PC3 was highly correlated with measures of the relative variability of rainfall

and productivity (CVMF, Vcvr, and CVMp: Table 5.8). Locations on the negative

portion of this axis represent areas of low relative variability, whereas locations on the

positive end represent areas of high variability.

PC4 was correlated highly with Mcvp (Table 5.8), representing an axis of the

within-year variability in productivity. Locations on the negative end of this axis are

characterized by low relative variability in productivity, whereas areas on the positive

end of this gradient are characterized by high degrees of variabihty.

Axes of Stmcture. Results from principal components analyses for communities

and each of the four feeding guilds were similar (Table 5.9). In most cases, PCA

extracted three gradients of stmcture. Eigenvalues for the first principal component

ranged from 4.9 to 8.6, and the amount of variation ranged from 44.1 to 78.1 %. PC2

accounted for variation ranging from 15.0 to 38.2%; eigenvalues ranged from 1.65 to

4.2. A third principal component was extracted for three of the feeding guilds and for

communities. Nectarivores were examined at too few locations for extraction of a third

principal component. Variation accounted for by PC3 ranged from 10.6 to 15.5%, and

eigenvalues ranged from 1.32 to 1.71.

Axes representing overall community, aerial insectivore, and fmgivore stmcture

were similar. Measures of morphological stmcture regarding the variance of the

interspecific distance in a feeding guild were most highly correlated with PCI (Table

5.8). Measures of morphological stmcture regarding the mean distance between

species within feeding guilds were most highly correlated with PC2. Lastly, measures

of numerical stmcture were most highly correlated with PC3. The farther in the

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positive dkection on each principal component, the weaker is the degree of

deterministic stmcture.

For gleaning animalivores, the three types of stmcture were segregated on

distinct axes, however their identity was different from those of communities, aerial

insectivores, and fmgivores (Table 5.10). The first principal component represented an

axis in morphological stmcture defined by the mean differences between species. The

second principal component represented an axis in stmcture regarding the variance of

interspecific differences. Finally, principal component three represents an axis in

numerical stmcture. The farther in the positive direction on each principal component,

the weaker is the degree of deterministic stmcture.

Principal components analyses extracted only two axes of stmcture for

nectarivores (Table 5.10). The first principal component characterized morphological

stmcture regarding the variance in interspecific morphological distances, whereas the

second principal component characterized numerical stmcture. On the first axis,

deterministic stmcture decreases as one moves to the right, whereas deterministic

stmcture increases as one moves to the right on the second axis.

Multiple Regression Analyses. The stmcture of three feeding guilds statistically

were affected by combinations of environmental attributes (Table 5.11, Fig. 5.1). The

numerical stmcture of the fmgivore guild was positively related to temperature

(R = 0.761, p = 0.047). As the mean temperature decreased and its variabihty

increased, the degree to which this guild exhibited deterministic stmcture decreased.

Fmgivores exhibited more deterministic stmcture in areas with warmer and less

variable temperatures (e.g., Guanacaste, Rodman, Sherman).

The stmcture of the gleaning animalivore guild was affected by two

environmental gradients (Table 5.11, Figs. 5.2 and 5.3). Morphological stmcture

regarding the mean distance of species within a feeding guild was a significant function

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of the relative variability in productivity (R = 0.782, p = 0.038). As the relative

variability of productivity increases, the degree to which morphological stmcture is

deterministic decreases (e.g., Guanacaste, Sherman, Caatinga). Numerical stmcture,

however, was dependent on the absolute variabihty of productivity and precipitation (R

= 0.776, p = 0.044). As variability increased, the degree to which the gleaning

animalivore guild was stmctured deterministically decreased. In general, gleaning

animahvores exhibit more deterministic stmcture in areas of less variable productivity

and precipitafion (e.g., Guanacaste, Heredia, Sherman).

Numerical stmcture of the nectarivore guild was related to the mean and

variability in temperature (R = -0.908, p = 0.092; Table 5.11, Fig. 5.4). The N-2

scenario essentially defined the stmcture axis, and was oriented such that stmcture

increases as one moves to the right. Moreover, the relationship between stmcture and

the temperature axis was negative. Thus, stmcture of the nectarivore guild was more

deterministic in areas with less variability in temperature (e.g., Heredia).

Gradients in the stmcture of communities in general, and the aerial insectivore

guild in particular, did not coincide with environmental axes in a linear fashion. None

of the environmental attributes significantly predicted the stmcture of these

organizational units.

Correlation Analyses. Correlation analyses identified two measures of stmcture

in two feeding guilds that were associated with environmental gradients (Table 5.12,

Fig. 5.5). Morphological stmcture regarding the mean interspecific difference of the

aerial insectivore guild was negatively associated with the relative variability of

productivity and precipitation (r = -0.674, p = 0.004). Deterministic stmcture occurred

in areas of greater variability. Fmgivores exhibited a positive association between

numerical stmcture and the gradient of mean and variabihty of temperature (rKendaii =

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0.683, p = 0.017). As the mean temperature increases and its variabihty decreases,

numerical stmcture becomes more deterministic.

Discussion

In 1959, Hutchinson published his pioneering work on food webs, community

stmcture, and diversity. Although various facets have come under scmtiny (Simberloff

and Boeklen, 1981), his work certainly provided order and direction for much of

contemporary ecology. Coupled with consequences of quantitative models of

competitive interactions (e.g., Lotka-Volterra), Hutchinson's mle (species should differ

by a ratio of 1.3 linear units) set the stage for quantitative considerations of competitive

exclusion, limiting similarity, and much of the subsequent theoretical advancement

regarding biotic interactions (Huston, 1994).

Nonetheless, ecology might have advanced more quickly over the last 30 years

if there had been less acceptance of the dogma that density-dependent phenomena, such

as competition, are pervasive and substantial determinants of pattems of diversity and

community stmcture, and more attention had been directed to a lesser known

publication by Hutchinson (1961). Hutchinson (1961) attributed the high diversity of

plankton to the circumvention of equilibrial processes. He contended that

envkonmental variability enhanced the number of available niches, resulting in higher

diversity, and demonstrated that coexistence could be a nonequilibrial phenomenon.

The world is a heterogeneous and variable place (Brown, 1992). Even in supposedly

stable environments, such as tropical rainforests, environmental variability may be

pronounced. Areas that exhibit high degrees of environmental stability and invariability

(prerequisites for density-dependent outcomes) probably are in the minority.

Nonetheless, the assumption that populations are operating at equilibrium is implicit to

much of contemporary theory in ecology (Huston, 1994). If most populations or

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communities do not experience equilibrial dynamics, then nonequilibrial approaches

must be employed to model community organization.

Bat communities do not exhibit deterministic stmcture in a ubiquitous fashion

(Chapters in and IV). However, the degree to which feeding guilds and communities

exhibit nonrandom stmcture, as predicted by competition theory, is dependent on

environmental parameters. In a majority of situations, variability with regard to

precipitation, productivity, or temperature, was an important influence on the degree of

deterministic stmcture.

Because of morphological and behavioral variabihty, bats are functionally

diverse, and occupy many feeding guilds and trophic levels (Findley, 1993; Fleming,

1988; Willig, 1982, 1986). As a consequence, it is not surprising that results differed

among feeding guilds. The variance of interspecific morphological differences

accounted for a majority of the variation in stmcture among locations regarding the

aerial insectivore, fmgivore, and nectarivore guilds (44.1% to 78.1%). However,

gleaning animalivores responded differently; the mean interspecific difference

accounted for a majority of variation among sites (57.9%). All feeding guilds did

respond similarly, however, in that numerical stmcture accounted for the least amount

of variation among locations.

Four feeding guilds exhibited significant associations with environmental

parameters, however, feeding guilds did not respond in the same manner. Aerial

insectivores and gleaning anunahvores were responsive to variability of productivity

and precipitation, whereas fmgivores and nectarivores responded to variability in

temperature. Because of the diminution of matter and energy moving from lower to

higher levels, more primary productivity is necessary for the sustenance of higher

trophic levels (Connell and Orias, 1964; Rosenzweig, 1977, 1995). Thus, it is not

surprising that animalivores and insectivores responded to variability in productivity.

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Nonetheless, primary consumers too are affected by levels and variability of primary

productivity, and there is no explanation as to why fmgivores and nectarivores do not

respond in the same fashion.

Temperature has been shown to control photosynthesis, plant growth rates, and

the timing of phenological states (Jones, 1992; Podolsky, 1984). Variabihty of

temperature affects fmit phenology as well (Jones, 1992). Most tropical bats are

precise thermoregulators with fakly invariant body temperatures, yet do not utilize

bouts of torpor or rely on fat reserves to enhance increased metabolic rates during

colder conditions (Fleming, 1988). Thus, bats probably must forage nightly to

overcome an energeticaUy precarious metabolic situation. In more variable

environments, energy balance is probably a more critical consideration than in less

variable environments. To these ends, both direct and indirect effects of variability in

temperature probably has important imphcations regarding fitness, and ultimately

survival for fmgivores and nectarivores. Nonetheless, the same may be said for

insectivores and animalivores; their resources are probably dependent on fmit

phenology, and temperature probably has similar ramifications to their fitness and

survival. These two differences probably are important distinctions underlying the

stmcture of feeding guilds at these two trophic levels.

Stmcture at the community level did not exhibit a significant response to

envu-onmental parameters. Many biotic (e.g., competition, mutualism, parasitism,

predation) as well as abiotic factors (e.g., variation in nutrients, climatic fluctuations,

disturbance) operate simultaneously at the community level. Communities represent an

amalgam of feeding guilds and trophic levels, all of which respond differentially to

biotic and abiotic gradients. Thus, differences in the way feeding guilds respond to

each environmental gradient (i.e., insectivores and animalivores versus fmgivores and

nectarivores) probably confounds any consistent association between communities and

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environmental parameters. This reason, among others, highlights the importance of

focusing on guilds when evaluating ecological phenomena.

Although stmcture regarding the variance of morphological distances accounted

for a majority of the variation among sites in all but one feeding guild, it did not

respond to any environmental gradients. This does not necessarily mean that this form

of stmcture is uninformative. Species morphologies are constrained by phenomena

occurring over their entire geographic ranges (Ricklefs and Travis, 1980). Moreover,

functional, phylogenetic, and physiological phenomena also constrain the ways

morphology may vary. Either stmcture regarding interspecific variance of morphology

is controlled by some other factor, such as biogeographic or evolutionary constraints on

the variability of morphology, or it is not sensitive to extrinsic attributes of the

community.

Numerical stmcture was most sensitive to environmental parameters. The

abundances of species are probably much more malleable in ecological time than are

morphological attributes. Differential extinction and invasion of morphotypes, or

morphological evolution, must occur to influence the morphological stmcture of a

community (Case and SideU, 1983). Moreover, competitive interactions leading to the

elimination of species probably need be of greater intensity and longer duration than

those that eliminate individuals and alter numerical stmcture. Numerical stmcture, on

average, probably manifests more rapidly than does morphological stmcture. This may

be inferred by its sensitivity to environmental variation. If this were tme, community

organization may be better understood if considered from two time frames. Processes

occurring in evolutionary time, such as size assortment and size adjustment, may set the

stage for the coarse-grained stmcture of a community. In concert, numerical

adjustments occurring over ecological time may be a means of fine-tuning stmcture.

When selection from abiotic environmental variation supersedes that due to biotic

118

interactions, deterministic stmcture may not obtain. The degree to which

morphological or numerical relationships deviate from expectations of competition

theory should be a function of selective forces associated with environmental

variability.

119

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124

Table 5.1.-- Bat communities used to evaluate gradients of stmcture. A, F, G, and N refer to the aerial insectivore, fmgivore, gleaning animalivore, and nectarivore feeding guilds, respectively.

Community

Cahfomia

Iowa

Guanacaste

Guanacaste

Heredia

Puntarenas

Sherman

Rodman

Pem

Caatinga

Country

USA

USA

Costa Rica

Costa Rica

Costa Rica

Costa Rica

Panama

Panama

Pem

Brazil

Reference

Supemant, 1977

Kunz, 1973

Fleming et al., 1972

Laval and Fitch, 1977





Ascorra, in litt

Willig, 1982

Feeding guilds examined

A

A

A,F,G

A, F, G, N,

A, F, G, N

A,F,N

A,F,G

A, F,G

A, G, N

A, F, G, N

125

Table 5.2.— Environmental parameters and their associated acronym in parentheses.

Latitude

Centr2d Tendency

Mean of Mean Monthly Precipitation (MMF)

Mean of Mean Monthly Temperature (MMI)

Mean of Mean Monthly Productivity (MMp)

Within Year Variabihty

Average Across Years of the Within Year Absolute Variability of Precipitation (Mvr)

Average Across Years of the Within Year Absolute Variability of Temperature (Mvt)

Average Across Years of the Within Year Absolute Variabihty of Productivity (Mvp)

Average Across Years of the Within Year Relative Variability of Precipitation (Mcvr)

Average Across Years of the Within Year Relative Variabihty of Temperature (Mcvt)

Average Across Years of the Within Year Relative Variability of Productivity (Mcvp)

Among Year Variabilitv

Absolute Variability Across Years of the Yearly Average Precipitation (VMT)

Absolute Variability Across Years of the Yearly Average TemperaUire (VMI)

Absolute Variability Across Years of the Yearly Average Productivity (VMp)

Relative Variability Across Years of the Yearly Average Precipitation (CVMT)

Relative Variabihty Across Years of the Yearly Average Temperature (CVMO

Relative Variabihty Across Years of the Yearly Average Productivity (CVMp)

126

Table 5.2 Continued

Within Year Variabihty Across Years

Variabihty Across Years of the Within Year Absolute Variability of Precipitation (Vvr)

Variability Across Years of the Within Year Absolute Variability of Temperature (Vvt)

Variability Across Years of the Within Year Absolute Variability of Productivity (Vvp)

Variability Across Years of the Within Year Relative Variabihty of Precipitation (Vcvr)

Variability Across Years of the Within Year Relative Variabihty of Temperature (Vcvt)

Variability Across Years of the Within Year Relative Variabihty of Productivity (Vcvp)

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Principal

component

EPCl

EPC2

EPC3

EPC4

Eigenvalue

10.94

4.37

2.93

1.35

Percent

variation

52.1

20.8

14.0

6.5

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variation

52.1

72.9

86.9

93.4

131

Table 5.7.-- Factor loadings for all climatic variables on the first four environmental principal component axes. EPCl - EPC4 refer to the four gradients extracted fromthe suite of climatic variables. Productivity values were calculated minus the intercept (61.9). Variable acronyms are defined in Table 5.2.

Variable

MMT

Mvr

McVr

VMr

CVMT

Vvr

Vcvr

MMt

Mvt

Mcvt

VMt

CVMt

Vvt

Vcvt

MMP

Mvp

Mcvp

VMP

CVMP

Vvp

Vcvp

EPCl

0.067

0.161

0.021

0.153

-0.002

0.201

0.008

-0.017

0.022

0.024

0.004

0.026

0.031

0.040

0.065

0.167

0.126

0.145

0.084

0.199

0.073

EPC2

0.022

0.001

-0.114

0.025

-0.077

0.027

-0.017

-0.014

0.173

0.177

-0.045

0.142

0.201

0.220

0.011

0.007

0.041

0.025

-0.025

0.028

0.082

EPC3

-0.081

-0.008

0.211

0.042

0.246

0.082

0.204

-0.152

-0.020

-0.028

-0.037

-0.038

-0.068

-0.133

0.046

-0.006

-0.044

0.040

0.246

0.083

0.148

EPC4

-0.117

0.191

0.292

-0.014

-0.452

0.116

-0.032

0.036

-0.039

-0.027

0.309

0.153

-0.015

0.064

-0.111

0.189

0.579

-0.033

0.009

0.108

-0.026

132

Table 5.8.-- Pearson's product-moment correlations of each climatic variable with the four environmental principal component axes (EPCl - EPC4). Boldface represents those variables that dominate each principal component. Variable acronyms are defined in table 5.2.

Variable

MMT

Mvr

McVr

VMr

CVMT

Vvr

VcVr

MMt

Mvt

Mcvt

VMt

CVMt

Vvt

Vcvt

MMP

Mvp

McVp

VMP

CVMP

Vvp r

Vcvp

EPCl

0.752

0.823

-0.427

0.933

-0.204

0.975

-0.239

0.226

-0.203

-0.204

-0.421

-0.371

-0.159

-0.116

0.742

0.850

-0.086

0.919

0.167

0.970

0.049

EPC2

-0.305

-0.330

-0.082

-0.159

0.087

-0.102

0.341

-0.841

0.932

0.943

-0.020

0.802

0.978

0.984

-0.350

-0.307

0.154

-0.159

0.213

-0.095

0.647

EPC3

-0.470

-0.315

0.714

-0.037

0.957

0.080

0.890

-0.369

0.268

0.240

0.100

0.133

0.097

-0.078

-0.466

-0.305

-0.264

-0.037

0.927

0.090

0.739

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-0.327

0.100

0.481

-0.251

-0.092

-0.077

-0.054

0.011

-0.011

0.009

0.566

0.325

0.029

0.079

-0.317

0.090

0.908

-0.276

0.098

-0.087

-0.099

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143

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144

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145

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147

CHAPTER VI

SYNTHESIS

Traditionally, community ecologists have pursued single processes to explain

the organization of natural communities (for a review, see Polls, 1991). Competitive

interactions often have been implicated for inducing the observed morphological

pattems that characterize stmcture. Nonetheless, throughout the 1970s and 1980s

morphological pattems came under intense scmtiny. Many supposedly deterministic

pattems were shown to be more likely the product of chance (Simberloff and Boeklen,

1981). Moreover, as ecologists switched their focus from vertebrates to invertebrates,

especially those living in streams, the fact that competitive interactions do not stmcture

a majority of animal communities became obvious (Power et al, 1988; Strong, 1984).

The expectation that a single factor (i.e., competition) stmctures all communities is

unrealistic. Furthermore, competitive interactions have the potential to operate through

a number of avenues. Consequently, decisions may have been hasty regarding the

frequency at which competitive interactions stmcture communities.

Density compensation is a demonstrable means whereby competitive

interactions give rise to deterministic stmcture. This is tme not only for rodent

systems, where the effects of competitive interactions on community organization are

well understood, but also for bats. In the absence of morphological hyperdispersion

produced by either size adjustment or size assortment, species that are morphologically

similar to other competitors in a feeding guild sometimes exhibit lower relative

abundance because of greater competitive pressure.

Nonetheless, morphological hyperdispersions and density compensation are not

consistent attributes of die organization of bat feeding guilds and communities. Simple

bat communities composed of only the aerial insectivore guild consistentiy exhibit

deterministic stmcture, as predicted under a scenario of size assortment, whereas 148

results from more complex communities are equivocal. The aerial insectivore guild

consistentiy exhibited size assortment in temperate areas, whereas in tropical areas,

stmcture was equivocal. Deterministic morphological stmcture for fmgivores involved

only the variance of interspecific differences, whereas deterministic stmcture for

nectarivoresonly involved the mean interspecific difference. Lastiy, molossid

insectivores consistentiy exhibited stochastic stmcture.

Environmental conditions play an important role in providing the context for the

induction of deterministic stmcture. In fact, the degree to which fmgivores, gleaning

animalivores, and nectarivores exhibited deterministic stmcture was differentially

predictable based on environmental parameters. The specific spatiotemporal context of

environmental factors experienced at a location determines the extent to which

competitive interactions manifest.

This has many implications. First, the role played by competitive interactions,

and probably all other influences on stmcture, is not consistent across sites, and

therefore not pervasive. Nonetheless, this should not discount the relevance of

understanding the ways in which competitive interaction influences community

organization. Moreover, no one determinant of stmcture should be expected to

dominate in all situations. Second, it should not be assumed that phenomena that give

rise to stmcture act independently of other biotic and abiotic influences. Interactions

between causal factors may obscure any consistent indication of deterministic stmcture.

Accordingly, these interactions must be considered before tiie role of a given

phenomenon is dismissed. Lastly, as suggested by Weins (1984), tiie organization of

all communities should not be thought of as dichotomous (deterministic versus

stochastic), but probably is better viewed from the perspective of a continuum from

deterministic to stochastic.

Altiiough tiie predictions of competition theory may have limited apphcability to

all communities, they do provide a template from which communities may be viewed. 149

Environmental parameters such as productivity, precipitation, temperature, and latitude

are only a few of the additional factors that influence the significance of competitive

interactions. Moreover, many other factors such as morphological constraints and

biogeographic radiations of congeners probably serve to modulate the role of

competition in community assembly and ultimately species coexistence. The basis of

coexistence should be viewed from the perspective of equilibrial competition theory.

However, a complete understanding probably necessitates appreciation of abiotic

factors that influence equilibrium. In an invariable worid, there is no disturbance,

population densities may mildly oscillate around carrying capacity, and limiting

similarity defines which species coexist. Nonetheless, the worid is not invariant.

Disturbances do exist and variability does induce density-independent mortality

(Andrewartha and Birch, 1954,1988). These factors, and more, determine a

communities position on a continuum describing stmcture.

150

Literature Cited

Andrewartha, H. G., and L. C. Birch. 1954. The distribution and abundance of animals. The University of Chicago Press, Chicago, Illinois.

Andrewartha, H. G., and L. C. Birch. 1988. The ecological web: more on the distribution and abundance of animals. The University of Chicago Press, Chicago, Illinois.

Pohs, G. A., Editor. 1991. The ecology of desert communities. The University of Arizona Press, Tucson, Arizona.

Power, M. E., R. J. Stout, C. E. Gushing, P. P. Herper, F. R. Hauer, W. J. Mathews, P. B. Moyle, B. Statzner, and I. R. Wais de Badgen. 1988. The role of disturbance in stream ecology. Joumal of the North American Benthological Society 7: 456-479.

Simberloff, D., and W. Boeklen. 1981. Santa Rosedia reconsidered: size ratios and competition. Evolution 35: 1206-1228.

Strong, D. R., Jr. 1984. Exorcising the ghost of competition past: phytophagous insects. Pages 28-41 in: D. R. Strong, D. Simberloff, L. G. Abele, and A. B. Thistie, Editors. Ecological communities: conceptual issues and the evidence. Princeton University Press, Princeton, New Jersey.

Weins, J. A. 1984. On understanding a non-equilibrium world: myth and reality in community pattems and processes. Pages 439-437 in: D. R. Strong, D. Simberloff, L. G. Abele, and A. B. Thistle, Editors. Ecological communities: conceptual issues and the evidence. Princeton University Press, Princeton, New Jersey.

151

APPENDIX A

LOCATION AND ANNOTATED DESCRIPTION OF

FIFTEEN BAT COMMUNITIES

1. IOWA: Boone County, Honey Creek and its adjacent areas.

42°0'N, 94°0'W. This community occurred in primary and secondary

deciduous forest along two tributaries of the Des Moines River: Honey Creek

and Pease Creek (Kunz, 1973).

2. CALIFORNIA: Inyo County, Surprise Canyon, 5 km East of Ballarat.

36°0'N, 117°15'W. Located at Chris Wicht Camp, in the Panamint Mountains,

just west of Death Valley. Habitat is described as typical of that of the Mojave

Desert. Larrea tridentata and Atriplex sp. are conspicuous vegetative

components (Supemant, 1977).

3. MEXICO: Estado de Chiapas, La Selva La Candona, Reserva de la Biosfera

Montes Azules. 16''6TSf, 90°57'W. Habitat described as lowland humid

rainforest. Conspicuous floral components consist of Talauma sp., Licania sp.

Brosimum sp., Swietenia sp., Dialium sp., and Ficus spp (Medellin, 1993).

4. COSTA RICA: Provincia de Heredia, 1 km upstream from Puerto Viejo.

10°30'N, 84°0'W. Tropical wet forest, in the Caribbean lowlands (LaVal and

Fitch, 1977).

5. COSTARICA: Provincia de Puntarenas, near the town of Monteverde on the

Pacific slope of the Cordillera deTilleran. lO'SO'N, 84°45'W. Premontane

moist and wet tropical forests (LaVal and Fitch, 1977).

6 COSTARICA: Provincia de Guanacaste, 4 km Northwest of Canas. 10°28'N,

8 5 " 9 ^ . Habitat described as tropical dry forest. This community was

sampled during two time periods (Fleming et al., 1972; LaVal and Fitch, 1977).

152

7. PANAMA: Canal Zone, Fort Sherman Military Reservation, 3 km West of

Cristobal. 9^201^, 79°57'W. Habitats sampled were riparian, swamp, and

secondary growth tropical forests (Fleming et al., 1972).

8. PANAMA: Canal Zone; Lake Gatun, Barro Colorado Island. 9°10TSf, 79''51'W.

Habitat described as tropical moist forest (Bonaccorso, 1975).

9. PANAMA: Canal Zone, Rodman Naval Ammunition Depot, 8 km West of

Balboa. 8''57'N, 79°37'W. Habitats sampled were riparian, swamp, and

secondary growth tropical forests (Fleming et al., 1972)

10. COLOMBIA: Departmento Del Valle, El Topacio Farm, 2 km South of Pance.

4''30'N, 76°45'W. Habitat characterized as secondary subtropical forest

(Thomas, 1972).

11. COLOMBIA: Department del Valle, near the village of Zabelitas. 4°30'S,

76''30'W. Habitat was tropical rainforest (Thomas, 1972).

12. PERU: Departmento de Loreto; Provincia de La Requena, Centro de

Investigacciones Janero Herrera, 140 km South Southwest of Iquitos.

4*'55'S, 73°45'W. Vegetation characterized as low-terrace broadleaf tropical

rain forest (Ascorra, in litt).

13. BRASIL: Municipio de Crato, Ceara, in the Floresta Nacional Araripe-Apodi'.

7''14'S, 39° 23IV. Vegetation characterized as sclerophyllous and semi-

diciduous (Edaphic Cerrado; Willig, 1982).

14. BRASIL: Municipio de Exu, Pemambuco. 7''35'S, 39°40'W.

Described as a xerophytic flora with members of the Cataceae and

Euphorbiaceae conspicuous components (Caatinga; Willig, 1982).

153

Liturature Cited


Fleming, T. H., E. T. Hooper, and D. E. Wilson. 1972. Three Central American bat communities: stmcture, reproductive cycles, and movement pattems. Ecology 53:555-569.

Kunz, T. H. 1973. Resource utilization: temporal and spatial components of bat activity in central Iowa. Joumal of Mammalogy 54: 14-32.

Laval, R. K., and H. S. Fitch. 1977. Stmcture, movements, and reproduction in three Costa Rican bat communities. Occasional Papers of the Museum of Natural History 69: 1-28.

Medellin, R. A. 1993. Estmctura y diversidad de una comunidad de murcielagos en el tropico humedo Mexicano. Pages 333-354 in: R. A. Medellin and G. Ceballos, Editors. Avances en el estududio de los mamiferos de Mexico. Asociacion Mexicana de Mastazoologia, Mexico City.

Suprenant, H. R. 1977. Noctumal activity pattems in a bat fauna of southem Califomia with comments on the physiological ecology of Pipistrellus hespems. Thesis. Califomia State University, Fullerton.

Thomas, M. E. 1972. Preliminary study of the annual breeding pattems and population fluctuations of bats in three ecologically distinct habitats in southwestern Colombia. Dissertation. Tulane University, New Orleans, Louisiana.

Willig, M. R. 1982. A comparative ecological study of Caatingas and Cerrado chiropteran communities: composition, stmcture, morphometries, and reproduction. Dissertation. University of Pittsburgh, Pennsylvania.

154

Figure A. 1.-Graphical representation of the approximate location of each community evaluated.

155

APPENDDC B

DESCRIPTION OF FEEDING GUILDS

Aerial Insectivore -Those bat species that principally consume insects which are

obtained from the air while in flight. Members of the families

Mormoopidae, Emballonuridae, Furipteridae, Thyropteridae, and

Vespertilionidae are commonly associated with this mode of feeding.

Fmgivore -Those bat species that primarily consume fmit. Members of the

phyllostomid subfamilies CaroUiinae, Stenodermatinae, and Brachyphyllinae

are commonly considered fmgivores.

Gleaning animalivore —Those bat species that principally consume invertebrates as

well as vertebrates that are gleaned from surfaces, such as the ground, leaves,

and the bark of trees. Members of the nominal subfamily of the

Phyllostomidae are commonly considered gleaning animalivores.

Molossid insectivore —Those bat species that principally consume insects that are

obtained from high altitudes (30-300 m). Most members of the family

Molossidae obtain resources in this fashion.

Nectarivore -Those bat species that principally consume nectar and pollen from

flowers. Members of the subfamilies Lonchophyllinae, Phyllonycterinae, and

Glossophaginae (Phyllostomidae) commonly are nectarivores.

Piscivore -Those bat species that principally consume fish. Noctilio leporinus

(Noctilionidae) and Myotis vivesi (Vespertilionidae) are representatives of this

feeding guild.

156

Sanguinivore -Those bat species that primarily consume blood. Desmodus

rotundus. Diamus voungi. and Diphylla ecaudata are representatives of this

feeding guild.

157

APPENDDC C

DESCRIPTIONS OF MORPHOLOGICAL CHARACTERS

Forearm length - Distance between the most distal edge of the elbow and

wrist.

Greatest length of skull - Distance between the anterior most point on the

rostmm and the most posterior point on the skull.

Condylobasal length — Distance between the anterior most edge of the

premaxillae and the posterior most edge of the occipital condyles.

Postorbital constriction - Least width of the skull between the orbits.

Breadth of the braincase - Greatest width of the braincase between the parietals.

Breadth across the upper molars Greatest distance between the widest set of upper

molars.

Length of the maxillary toothrow — Length from the anterior edge of the first tooth

present in the maxillae to the posterior edge of the last molar.

158

APPENDDC D

STRUCTURE OF FIFTEEN BAT COMMUNITIES

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APPENDIX E

SIMULATION PROGRAM TO

EVALUATE DENSITY COMPENSATION

203

#include <iostream.h> #include <string.h> #include <correlation.h> #include <quicksort.h> #include <console.h> #include <time.h> #include <math.h> #include <stdlib.h>

#defme NUM.SIMS 1000

void Morph_Dif(int a,int b,int d, double sumLength[l, double morph[l);

void main(void) {

char File l[50],File2[50]; FILE *fp; int numSims; //number of times to run simulation int numSp; //number of species in community int numCh; //number of morphological characters int x,y,count; //looping variables double PearsonAb; //Pearson correlation for abundance double SpearmanAb; //Spearman correlation for abundance

//get input data c o u t « "Enter name of input file: "; cin.getline(Filel,52); c o u t « "How many times to run simulation:"; cin » numSims;

//start the timer unsigned int begin = clock();

/ * * * * * • * * * * * * * * * * * • * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Read species abundances,morphological data, and weights * * * • * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /

if ((fp=fopen(Filel,"r"))=NULL) { printf("Cannot open file\n"); exit(l);

fscanf(fp,"%d\n",&numSp); fscanf(fp,"%d\n",&numCh); cout « "Number of species = " « numSp « endl; c o u t « "Number of morphological characters = " « numCh « endl;

//create new arrays to hold abundances, morphological data double* actualAb = new double[numSp]; int index = numSp*numCh; double* morph = new double [index!;

204

double sumAb = 0.0;

//read abundance and morphological data double dist; for (x=0; x<numSp; x-H-)

fscanf(fp,"%Lf',&actualAb[x]); //read abundance sumAb -1-= actualAb[xl; //record abundance sum for (y=0; y<numCh; y-f-f-) {

index = numCh*x + y; fscanf(fp,"%Lf,&dist); morph[indexl = loglO(dist);

}

fclose(fp);

Transform abundances into percentages

for (x=0; x<numSp; x++) actual Ab[x]=100.0*actualAb[x]/sumAb;

//create dynamic arrays for storing simulation info double* abundance = new double[numSp]; double* sumLength = new double[numSpl; double* pearsonAb = new double[numSimsl; double* spearmanAb = new double[numSims];

Begin cycle for three methods of calculating distances

for (int m=0; m<3; m-H-)

double PearAbProb=0.0; double SpearAbProb=0.0;

//Calculate sums of morphological distances Morph_Dif(m,numSp,numCh,sumLength,morph);

//Calculate Pearson and Spearman correlation coefficients //for actual abundances PearsonAb = Pearson(actualAb,sumLength,numSp); SpearmanAb = Spearmans_Rank(actualAb,sumLength,numSp);

Assign random abundances and convert to percentages * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /

205

double maxAb = 100.0-numSp*0.1;

//set the random seed with the current time int s = (unsigned int) clockO; srand(s);

for (count=0; count<:numSims; count-H-)

sumAb=0.0; for (x=0; x<numSp; x++)

abundance[xl=100.0*rand()/32767.0; sumAb-i-=abundance[x];

}

double convertToPercent=maxAb/sumAb;

for (x=0; x<numSp; x++) {

abundance[x]=abundance[x]*convertToPercent-i-0.1; }

Calculate Pearson and Spearman correlation coefficients for simulated abundances, and calculate p's ^h ^p ^F ^F ^h ^ ^F ^h ^h ^^ ^ ^p ^ ^h ^ ^ ^F ^h ^h ^ ^h ^h ^ ^F ^h ^ ^h ^h ^ ^h ^n ^ ^P ^h ^ ^h T * ^F • P *!* ^ ^ ^ "I* ^h ^h •!* "F ^ * l* *n • I * ^F "P ^ •P * l* /

pearsonAb [count] = Pearson(abundance,sumLength,numSp); if (pearsonAb[count]>=PearsonAb) PearAbProb-»-=l/(double)

numSims;

spearmanAb[countl = Spearmans_Rank(abundance,sumLength,numSp);

if (spearmanAb[countl>=SpearmanAb) SpearAbProb-i-=l/(double) numSims;

}

Sort simulated correlation coefficients

quicksort(pearsonAb,0,numSims-1); quicksort(spearmanAb,0,numSims-1);

Determine name of output file * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /

strcpy(File2,Filel);

206

Determine name of output file

strcpy(File2,Filel); switch (m) {

case 0: strcat(File2,".n-l"); break;

case 1: strcat(File2,".n-2"); break;

case 2: strcat(File2,".n-(n-2)"); break;

}

Write simulation data to output file with tab delimiters

if ((fp=fopen(File2,"w"))==NULL) { printf("Caimot open file\n"); exit(l);

} fputs("Actual Data\n",fp); fputs("Species ",fip); j^utsfSum Dist. ",fp); fputs("% Density\n",fp); for (x=0; x<numSp; x-H-) {

fprintf(fp,"%d ",x); ft)rintf(fp,"%lf ",sumLength[x]); fprintf(fp,"%lAn",actualAb[x]);

} fiputs("\n",fp); fputs("%Density\n",fp); fputsf Pearson ",fp); fputs("Spearman\n",fp); fputs("r ",fp); fprintf(fp,"%Lf ",PearsonAb); fprintf(fp,"%Lf\n",SpearmanAb); fputs("p '\fpy, fprintf(fp,"%Lf ",PearAbProb); fprintf(fp,"%Lf\n",SpearAbProb); fputs("\n",fp); fputs("SIMULATION\n",fp); fputsr%Density\n",fp); fputsfPearson ",fp); fputs("Spearman\n",fp); for (count=0; count<numSims; count-H-) {

^rintf(^,"%Lf ",pearsonAb [count]); 207

unsigned int elapsed = (clockQ - begin)/CLOCKS_PER_SEC; cout « "Time to run simulation: " « elapsed « endl;

}

void Morph_Dif(int m, int numSp, int numCh, double sumL[], double morph[]) {

double distance; //store total distance between two species double theLargest; //store the largest distance for a species double smaller; //store the 2nd smallest distance double smallest; //store the smallest distance double sumDifSqr; //use for calculating distance int x,y,z; //looping variables int fix_index; //index of fixed species int rel_index; //index of iterative species

for (x=0; x<numSp; x-H-) {

theLargest=0.0; smallest=100000.0; smaller=1000000.0; sumL[x] = 0.0; for (y=0; y<numSp; y-H-) {

sumDifSqr=0.0; for (z=0; z<numCh; z-H-)

fixjndex = x*numCh -i- z; rel_index = y*numCh + z; sumDifSqr+=pow((morph[fix_index] -

morph[rel_index]),2.0); } distance=sqrt(sumDifSqr); sumL[x] += distance; if (theLargest < distance) theLargest = distance; if(y!=x)

if (distance < smallest)

smaller=smallest; smallest=distance;

else if (distance < smaller)

smaller=distance; }

}

if (m==l) sumL[x] -= theLargest; if (m==2) sumL[x] = smaller + smallest;

} }

208

APPENDK F

SIMULATION PROGRAM TO EVALUATE SIZE ASSORTMENT

209

#include <iostream.h> #include <fstream.h> #include <stdlib.h> #include <stdio.h> #include <string.h> #include <math.h> #include <time.h> #include "general.h" #include "write_file.h" #include "spanningtree.h" #include "constants.h"

struct name { char filename[40]; name* next;

} ;

double fact (int); void combination (int,int,int,cell[],char[]); voidrandom_combination(int,int,cell[],char[]); voiddistance_matrix(int,int,cell[],cell[]);

void main() {

c o u t « "Welcome to the MST Simulation Center" « endl;

ifstream Input; //input stream charfilename[40]; //input file name double c; //calculated number of combinations int pools; //number of species pools to use int s; //size of real community int n; //number of species int v; //number of variables measured char outfile[40]; //output file name

//get input file name from user c o u t « "Enter input file name:"; cin » ws; cin.getline(filename,42);

//start time int start = (unsigned int) clock();

//try to open specified file, exit if error occurs Input.open(filename,ios: :in); if(!Input)

cerr « "This file cannot be opened or does not exist"; exit(l);

}

//read in specs 210

endl;

Input» s; Input» n; Input» v; Input» pools; c o u t « "The file indicates that" « s « " species comprise the community," «

c o u t « "there are " « n « " species in the pool," « endl; c o u t « "there are " « v « " variables," « endl; c o u t « "and there are " « pools « " pools." « endl;

//read in output file names //Input» ws; name* outlist = new name; name* tempname = outlist;

for (int i = 0; i < pools; i-H-) {

tempname->next = new name; Input»tempname->next->filename; tempname = tempname->next;

} int* pool = new int[pools-i-l]; //array to hold pool size for each

range cell* variables = new cell[n-i-l]; i = l ;

of pool number

//array of lists containing variables //counter to keep track

matnx

//read in morphological data for (int count=l; count < (n-»-l); -H+count) {

int current_pool; Input» current_pool; variables[count].next = new cell; cell* temp = variables [count].next; for (int X = 0; X < v; -H-x) {

Input»temp->var; temp->next = new cell; temp = temp->next;

} if (current_pool > i)

pool[i] = count-1; -H-i;

} } pool[i] = n; Input.closeO;

//calculate the morphology difference matrix cell* dist = new cell[n-»-l];

distance_matrix(n,v,variables,dist);

211

//list to contain distance

//iterate through the pools and generate combinations //this block will lead to the minimum spanning tree calculations tempname = outlist; for (1=1; i<(pools-l-l); -H-i) {

//determine output file name tempname = tempname->next; strcpy(outfile,tempname->filename); c o u t « "Current outfile is: " « outfile « endl; int m = pool[i];

//calculate combinations c = fact(m)/(fact(s) * fact(m-s)); c o u t « "Number of combinations: " « c « endl; c o u t « "Cutoff point for combinations is currently " «

MAX_COMBINATIONS*2 « endl;

//if number of combinations is too large, use random set, otherwise use //all combinations if (c > MAX_C0MBINATI0NS*2) {

c o u t « "Simulated distributions will be generated randomly " « MAX_COMBINATIONS « " times." « endl;

random_combination(s,m,dist,outfile); } else {

c o u t « "Simulated distributions will use all combinations" « endl;

}

combination (s,m, (int) c,dist,outfile); }

}

int elapsed = ((unsigned int) clock() - start)/CLOCKS_PER_SEC; c o u t « "Elapsed time was " « elapsed « " seconds" « endl;

//procedure distance_matrix //This procedure uses sum of squared distances of all variables for each // pair of species in the pool to construct a matrix //Parameters: // n - size of the species pool // V - number of variables // variables[] - array of lists containing measurements for each species

// dist[][] - array of morphological distances

void distance_matrix(int n,int v,cell variables[], cell dist[])

for(inti = 2;i<n-i-l;-H-i) {

dist[il.next = new cell; cell* d_temp = dist[i].next; for (int j = l;j<i;-i"HJ) {

double sum = 0.0; 212

cell* i_temp = variables[i].next; cell* j_temp = variables [j].next; for (int k=0; k<v; -H-k)

sum += pow((i_temp->var - j_temp->var),2); Ltemp = i_temp->next; j_temp = j_temp->next;

d_temp->var = sqrt(sum); if (j == (i - 1)) d_temp->next = NULL; else {

}

d_temp->next = new cell; d_temp = d_temp->next;

}

//function fact // function calculates the factorial of a number

double fact (int n) {

if (n< 2) return (1); else return (n * fact(n-l));

}

//procedure combination //This procedure finds all possible combinations of s numbers drawn from // a pool of n. It does not count the first combination (1 to s) because // that is assumed to be the "real" community. For each combination the // spanning tree function is called to build variance and mean arrays //Parameters: // s - size of community // n - size of pool // dist[] - morphological distance matrix //Calls // procedure spanning_tree // procedure write_to_file;

void combination (int s, int n, int c, cell dist[], char outfile[])

int* sp = new int[s+l]; //array containing the combination sequence double real_mean; //mean of spanning tree lengths for real community double real_variance; //variance of span, tree lengths for real community double mean; //variable to hold mean length for simulated

comm. double var; //variable to hold mean var for simulated

community

for (int X = 1; X < (s-i-1); -H-x) sp[x]=x; if (sp[s] == n)

213

c o u t « "only one combination" « endl-spanning_tree(sp,s,real_mean,real_variance,dist)-c o u t « ||Mean for real community:" « real.mean « endl; c o u t « Variance for real community:" « real_variance « endl;

//calculate spanning tree for real community spanning_tree(sp,s,real_mean,real_variance,dist);

int count = 0; double* means = new double[c]; double* variance = new double[c]; while (sp[l] !=(n-s-i-l))

int check = 0; inty = 1; while (y < (s-i-1) && check == 0) {

if((sp[y] + s-y)==n)

check = 1; ++sp[y-l]; inti = sp[y-l]; for (int z = y; z < (s-i-1); -H-Z)

++i; sp[z] = i;

} } -H-y;

} if (check == 0) -H-sp[s]; else check=0; spanning_tree(sp,s,mean, var,dist); means[count] = mean; variance[count] = var; -H-count;

} c o u t « "Through iteration, found " « count« " combinations different from

real"« endl; write_to_file(count,s,n,means,variance,real_mean,real_variance,"Actual",outfile); delete[] means; delete[] variance; delete[] sp;

}

//This procedure operates similar to combination() except it doesn't iterate through //all possible combinations, but calculates them randomly void random_combination (int s, int n,cell dist[],char outfile[]) {

double real_mean; //mean of sp. tree for real com.

double real_variance; //var of sp. tree for real com. 214

double mean; //mean of sp. tree for simulation ^

double var; //var of sp. U-ee for simulation

double means[MAX_COMBINATIONS]; //array of sp. tree means double vanance[MAX_COMBINATIONS]; //array of sp. tree variances int* randjist = new int[n-»-1 ]; //array to check for dupUcations int* sp = new int[sH-l]; //array containing

combinations int seed = (unsigned int) clock(); //seed for randomization

//use the seed to initialize randomization srand(seed);

//calculate spanning tree for real community for (int X = 1; X < (s-Hl); -H-X) sp[x]=x; spanning_tree(sp,s,real_mean,real_variance,dist);

//generate random combinations for (X = 0; X < MAX_COMBINATIONS; -H-x) {

for (int y = 1; y < (n-i-1); -H-y) rand_list[y] = 0; int count = 0; while (count < s) {

int value = n*rand()/RAND_MAX -i- 1; if (value <= n && rand_list[value] == 0) {

-H-count; sp [count] = value; rand_list[value]= 1;

} } spanmng_tree(sp,s,mean,var,dist); means[x] = mean; variancefx] = var;

write_to_file(MAX_COMBINATIONS,s,n,means,variance,real_mean,real_varian ce, "Random",outfile); }

//constants const MAX_COMBINATIONS = 500;

struct cell { double var; cell* next;

};

//prototypes void spanning_tree(int sp[],int s,double &mean, double &var,

cell dist[]);

215

' ' i i j i

/ /

// File: Spanning Tree / /

// Programmer: Alec Shaner //Date: 1/15/94 / /

// This file finds the minimum spanning lengths based on a distance // matrix. It returns (by reference) the mean and variance of the lengths

#include "general.h" #include "spanningtree.h" #include <MFSET.h> #include <stats.h>

struct edge {

int vl; int v2; double cost;

};

double find_cost(int,int,cell[]);

void sparming_tree(int sp[],int s,double &mean, double &var, cell dist[]) {

//initialize MFSET int* Parent = new int[s-f-l]; for (int X = 1; X < (s-J-1); -H-x) Parent[x] = -1;

//generate available edge list edge* avail = new edge[s*(s-l)/2]; //create mst edges double* mst = new double[s-l];

int count = 0; for(x= 1; x<s;-H-x) {

for (int y = x-f-1; y < (s+1); -H-y) {

avail[count].vl =x; avail[count].v2 = y; avail [count] .cost = find_cost(sp[x],sp[y],dist); -H-count;

} } //sort avail list for (x=0; x<count-l; -H-x) {

for (int y=x-i-l; y<count; -H-y) {

if (avail[x].cost > avail[y].cost) 216

{ inttl =avail[x].vl; int t2 = avail[x].v2; double tc = avail[x].cost;

avail[x].vl = avail[y].vl; avail[x].v2 = avail[y].v2; avail [x] .cost = avail [y].cost;

avail[y].vl =tl; avail[y].v2 = t2; avail[y].cost = tc;

}

count = 0; int i = 0;

//find edges in minimum spanning tree while (i<(s-l)) {

int V = avail[count].vl; int w = avail[count].v2; int pv = find(v,Parent); int pw = find(w,Parent); if (pv != pw ) {

mst[i] = avail [count] .cost; merge(pv,pw,Parent); -H-i;

} -H-count;

}

//calculate mean and variance for spanning tree mean = Calculate A verage(SumXdouble(s-l,mst),s-l); var = CalculatePVar(SumXdouble(s-l,mst),SuniX2double(s-l,mst),s-l);

//clean up delete[] Parent; delete[] avail; delete[] mst;

}

double find_cost(int i,int j,cell dist[]) {

int index; //indicates index of list int pos; //indicates position in list

i f ( i > j ) {index = i; pos =j;} else {index =j; pos = i;}

217

V.VS*

cell* d_temp = dist[index].next; int count = 1; while (count < pos)

-H-count; d_temp = d_temp->next;

return d_temp->var; }

//function prototypes void write_to_file(int c,int s,int n,double means [],double variance[],

double real_mean,double real_variance, char type[],char[]);

/ / * * * * * * : i c 4 : * * * * * * 4 ( 4 : * * 4 : * * * * * 4 : * * * * 4 : * * : | c * * * 4 : * * * 4 : * : i c * * * * 4 : 4 : * * 4 : * * 4 : * : | c * : i : : ) : : t : 4 : 4 : * * * : t : * * 3 ) :

* * * *

/ / // File: Write.File / / // Programmer: Alec Shaner //Date: 1/15/95 / / // Purpose: This procedure creates an output file containing the simulation // results with tab delimiters / /

* * * *

#include "write_file.h" #include <iostream.h> #include <fstream.h> #include <stdlib.h> #include <console.h> #include <quicksort.h>

void write_to_file(int c,int s,int n,double means[],double variance[], double real_mean,double real_variance, char type[],char outfile[])

{ FILE *fp; //ofstream Output; double p_means; double p_variance; char delimeter = Vt';

//sort the two arrays quicksort(means,0,c-1); quicksort(variance,0,c-1);

//calculate p-values by iteration 218

N.'—

inti = c-l; while (real_mean < means[i] && i >= 0) --i; p_means = (double)(c-i)/(double)c; i = 0; while (real_variance > variance[i] && i < c) ++'i; p_variance = (double)i/(double)c;

//write information to output file if ((fp=fopen(outfile,"w"))==NULL) {

printffCannot open file\n"); exit(l);

} fputs("Community ",fp); fprintf(fp,"%d\n",s); fputs("Pool ",fp); ^rintf(fp,"%d\n",n); fputs("Combinations ",fp); fprintf(fp,"%d\n",c); fputs("Type ",fp); fprintf(fp,"%s\n",type); fputs("\n",fp); fputs("Real Community\n",fp); fputs("Mean ",fp); fprintf(fp," %lf\n" ,real_mean); fputs(" Variance ",fp); fprintf (fp," %lf\n" ,real_variance); fputs("\n",fp); fputs("P-Values\n",fp); fputs("Mean ",fp); fprintf(fp,"%lf\n",p_means); fputs("Variance ",fp); fprintf(fp,"%lf\n",p_variance); fputs("\n",fp); fputs("Simulations\n",fp); fputs("Means ",fp); fputs("Variances\n",fp); for (int X = 0; X < c; ++x)

fprintf(fp,"%lf ",means[x]); fprintf(fp,"%lf\n",variance[x]);

} fclose(fp);

}

//function prototypes void swap (float [],int,int); int partition (float [],int,int); void quicksort (float[],int,int);

void merge (int i, int j , int Parent[]); int find (int i, int Parent[]);

#include <quicksort.h> #include <MFSET.h>

219

\r.Tm

/ / // File: MFSET / /

// Programmer: Alec Shaner //Date: 1/15/95 / / // This file contains simple merge-find set functions using an // array based set system. It utilizes weighted merges and // path compression so the Parent array must be initialized to // -1. Children index to their parent, roots index to the // negative of the number of children / / / / s i : * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

void merge (int i, int j , int Parent[]) {

int X = Parent[i] -I- Parent[j]; if(Parent[i]>Parent[j]) {

Parent[i]=j; Parent[j] = x;

} else {

Parent[j] = i; Parent[i] = x;

} }

int find (int i, int Parent[]) {

intj = i; while (ParentOl > 0) j = Parent[)]; int k = i; while (k !=j)

int t = Parent[k]; Parent[k]=j; k = t;

} return j ;

}

/ / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

/ /

// File: quicksort / /

// Programmer: Alec Shaner*

// *: This is basically the quicksort routine from an example in Object // Oriented Programming Using C-H-, by Ira Pohl, with the code modified

220

// to work with an array based // implementation. / / / / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

//Function wrong_order // This function takes as inputs an array, the indices from and to, and // an order value: 0 specifes check for 2-lex-precedes order and 1 // specifes 1-lex-precedes order. The function returns TRUE if the two // coordinates are out of lexiographic order

void swap (float v[],int from,int to) I

float temp = v[from]; v[from] = v[to]; v[to] = temp;

}

int partition (float v[],int from,int to)

int front = from-I-1; int back = to; float compare = v[from];

while (front < back)

//search forward for out of order element while ((front<back) && (compare > v[front])) {

-H-front;

//search backward for out of order element while ((front<back) && (compare <= v[back])) {

—back;

swap(v,front,back); }

//insert mid position comparison element if (compare >= v[front])

swap(v,from,front); return front;

} else

swap(v,from,front-1); return (front-1);

} }

221

void quicksort (float v[],int from, int to)

int mid;

if (from < to) { if (from == to - 1) //2 elements

if ( v[from] > v[to])

swap(v,from,to);

} else {

mid = partition(v,from,to); quicksort(v,from,mid-1); quicksort(v,mid-f-1 ,to);

} }

This is a general header for calculating simple statistics. It calculates the following statistics:

Mean Standard Deviation Variance Standard Error

NOTE: It also contains functions to sum and sum the squares of arrays. Two copies are provided, one for integer arrays and the other for double arrays.

All functions return float values.

float SumXint(int arraySize, int *Y); float SumX2int(int arraySize, int *Y); float SumXfloat(int arraySize, float *Y); float SumX2float(int arraySize, float *Y); float CalculateAverage(float SumX, int n); float CalculateSE(float SumX, float SumX2, int n); float CalculateSD(float SumX, float SumX2, int n); float CalculateVar(float SumX, float SumX2, int n); float CalculatePVar(float SumX, float SumX2, int n);

/ / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* *

/ /

// File: Stats / /

// Programmer: Alec Shaner //Date: 1993 / /

// This file contains a set of statistical fiinctions used for descriptives 222

V . T l l

/ / / / * * * * * * * * * * * * * * * ; ^ ; ^ 5 ^ 5 ^ ^ j ^ j ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ _ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ _ ^ _ ^ ^ _ ^ ^ _ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

* *

#include <math.h> #include "stats.h"

y * * * * * * * * * * * * * * 5 | e * * * * * * : ) c : ( : : | . : ( . 4 . 5 | ( s ) . ^ j ( , j ^ 5 , . ^ ^ j ^ j ^ ^ ^ j ^ ^ j ^ j ^ j ^ ^ j j , j ^ j j , j ^ j | , j j , j j j j | j j ^

Sum the values of an array of integers, return sum as a float * * * * * * * * * * * * * * * * * ^ 5 l . : ^ C 5 | j j J . : j 5 j , , j ^ 5 ^ j , j ^ j , j ^ j ^ j , j j ^ j ^ j j . j ^ ^ j | , ^ j ^ j j j j | j j ^ . j | , j ^ j | , j j . j j , j ^ j ^ j | j

float SumXint(int arraySize, int *Y)

int count; float SumX=0;

for (count=0; count<(arraySize); count-H-) { SumX-i-=*(Y-K:ount);

} return SumX;

}

/^ t ^ t ^ t ^ ^ ^ ^ ^# ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ -I)- ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ »X. -J,- ^^ .Jf. ^ ^ ^ ^ ^^ ||- ^^ -J^ ^^ ^ ^ ^^ ^^ J)- ^^ ( ^ ^ ^ ^ ^ >|- ^ ^ ^ - -J- ^^ ^ ^ ^ ^ ^^ ^ ^ ^U ^^ ^ ^ ^ ^ ^ ^ 4 ^ ^ ^ ^ ^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^* ^* ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ P ^^ P P ^^ P P ^p P p K ^p P P K p p ^p p p p ^p p ^» ^p p ^p p ^p ^^ P p ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ *T* ^^ ^^ ^^ ^^ ^^

Sum the squared values of an array of integers, retum sum as a float 3|C !|C 9|C 5|C «|C 3fC 3|C 9|C SfC SfC 3JC 3|C SfC 3|C 9|C 9|C 9|C 3|C 3)C 9)C 3|C 3|C 3|C 3|C 3|C 3|! 3|» SfC SfC 3|C 3|C 3|C 3|C 3|C !^ 3|C SfC 3f» S ^ 3|C 3|C j|C 9|C 9)C 3fC 3]C s|C 3|£ 3|C 3|C 3|C 3|C 3fC 3|C 3|C 3|C S|C SfC 3(C « ^ 9|C 3|C 9fC ^ 3 p 3 ^ ^ ^ /

float SumX2int(int arraySize, int *Y) {

int count; float SumX2=0;

for (count=0; count<(arraySize); count-H-) { SumX2-i-=pow(*(Y-i-count),2.0);

} retum SumX2;

}

/ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Sum the values of an array of floats, retum sum as a float * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /

float SumXfloat(int arraySize, float *Y) {

int count; float SumX=0.0; for (count=0; count<(arraySize); count-H-) {

SumX-f=*(Y-K:ount); } retum SumX;

}

/ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Sum the squared values of an array of floats, retum sum as a float * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /

float SumX2float(int arraySize, float *Y)

223

• — ^ ^ ^ ^ — ^ - ^ ^ —

)

int count; float SumX2=0.0;

for (count=0; count<(arraySize); count-H-) { SumX2-i-=pow(*(Y-i-count),2.0);

} retum SumX2;

y * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * : ( . : | . : | c : | c : ) t ; ( . : ^ : ( : 5 | s : ( . : j ( : ^ ; , . j ^ ^ : ^ ; ^ ; ^

CalculateAverage takes as its arguments a sum and the number of observations comprising the sum * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * : ( : : ( . : ( £ * * * * * * * * * * * * /

float CalculateAverage(float SumX, int n) {

float average,N=n;

average = SumX/N; retum average;

}

CalculateSD calculates the standard deviation, taking as its arguments a sum, a sum of squares, and the number of observations

float CalculateSD(float SumX, float SumX2, int n) {

float SD,N=n;

if (n>l) SD=sqrt((SumX2-pow(SumX,2.0)/N)/(N-1.0)); retum SD;

}

/ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Calculate Var calculates the sample variance, taking as its arguments a sum, a sum of squares, and the number of observations * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /

float CalculateVar(float SumX, float SumX2, int n) {

float Var,N=n; if (n>l) Var=pow(sqrt((SumX2-pow(SumX,2.0)/N)/(N-1.0)),2.0); retum Var;

} / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Calculate Var calculates the parametric variance, taking as its arguments a sum, a sum of squares, and the number of observations * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /

float CalculatePVar(float SumX, float SumX2, int n)

float Var,N=n;

224

if (n>l) Var=pow(sqrt((SumX2-pow(SumX,2.0)/N)/(N)),2.0); retum Var;

} / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

CalculateSE calculates the standard error, taking as its arguments a sum, a sum of squares, the number of observations, and the average * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /

float CalculateSE(float SumX, float SumX2, int n) {

float SE,N=n;

if(n>l){ SE=sqrt((SumX2-pow(SumX,2.0)/N)/(N-1.0))/sqrt(N); retum SE;

} else retum 0.0;

}

225

\:.:^ .^r^tAaMHCiiga

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