ANALYSIS OF WILDLIFE ABUNDANCE ESTIMATION METHODS USING REAL AND SIMULATED DATA

By

SAIF Z. NOMANI

A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2007

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© 2007 Saif Z. Nomani

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To my sister, Samia Nomani

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ACKNOWLEDGMENTS

I thank my advisors M. Oli, R. Carthy, and J. Nichols for their guidance and support. I

thank A. Ozgul, J. Hostetler, K. Aaltonen, A. Singh, I. Ismail, and A. Jaffery for insightful

comments on this study and for assistance with statistical analysis of results. Special thanks go to

L. Thomas, S. Buckland, N. Adams, H. Sultan, M. Christman, and M. Sitharam for assistance

with the simulation program; and to K. Miller, E. Lang, E. Cantwell, J. Martin and M. Voight for

data collection. Thanks go to S. Coates and the Ordway-Swisher Biological Station, University

of Florida for use of the study area and for habitat information. I thank my parents, C. Williams,

and my friends from New Jersey for their support and encouragement. The Department of

Wildlife Ecology and Conservation at the University of Florida and U.S. Army Corps of

Engineers-Construction Engineering Research Laboratory (ACOE-CERL) provided funding for

this study. Funding and logistical support was also provided by the Florida Cooperative Fish &

Wildlife Research Unit at the University of Florida.

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TABLE OF CONTENTS page

ACKNOWLEDGMENTS ...............................................................................................................4

LIST OF TABLES...........................................................................................................................7

LIST OF FIGURES .........................................................................................................................8

ABSTRACT.....................................................................................................................................9

CHAPTER

1 INTRODUCTION ..................................................................................................................11

2 COMPARISON OF METHODS FOR ESTIMATING ABUNDANCE OF GOPHER TORTOISES...........................................................................................................................13

Introduction.............................................................................................................................13 Methods ..................................................................................................................................15

Study Area .......................................................................................................................15 Line Transect Method......................................................................................................16

Pilot study.................................................................................................................16 Data collection..........................................................................................................16 Data analysis ............................................................................................................17

Total Count, Sample Count, and Double Observer Methods..........................................18 Data collection..........................................................................................................18 Data analysis ............................................................................................................19

Burrow Occupancy Rates ................................................................................................20 Data collection..........................................................................................................20 Data analysis ............................................................................................................21

Costs ................................................................................................................................22 Results.....................................................................................................................................22

Line Transect ...................................................................................................................22 Total Count, Sample Count, and Double Observer .........................................................23 Burrow Occupancy Rates ................................................................................................24 Abundance of Gopher Tortoises......................................................................................24 Costs ................................................................................................................................24

Discussion...............................................................................................................................25 Comparison of Abundance Estimation Methods.............................................................25 Burrow Occupancy..........................................................................................................27 Costs of Implementation..................................................................................................28

Conclusion ..............................................................................................................................29

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3 ACCURACY OF ESTIMATES OF ABUNDANCE BASED ON THE LINE TRANSECT METHOD: INFLUENCE OF SPATIAL DISTRIBUTION OF OBJECTS, AND LENGTH, LAYOUT, AND NUMBER OF TRANSECTS .........................................36

Introduction.............................................................................................................................36 Methods ..................................................................................................................................38

Simulation Inputs.............................................................................................................38 Spatial Distribution and Density of Objects ....................................................................38 Layout Pattern of Line Transects ....................................................................................39 Total Length of Line Transects .......................................................................................40 Number of Transects .......................................................................................................40 Data Collection and Analysis ..........................................................................................41

Results.....................................................................................................................................42 Overall Results ................................................................................................................42 Clumped Distribution ......................................................................................................43

Effects of object density ...........................................................................................43 Effects of object density and transect length............................................................44 Effects of object density and transect layout............................................................44 Effects of object density and transect number .........................................................44 Effects of object density, and transect length, layout, and number..........................45

Random Distribution .......................................................................................................45 Effects of object density ...........................................................................................45 Effects of object density and transect length............................................................46 Effects of object density and transect layout............................................................46 Effects of object density and transect number .........................................................46 Effects of object density, and transect length, layout, and number..........................47

Uniform Distribution .......................................................................................................47 Effects of object density ...........................................................................................47 Effects of object density and transect length............................................................48 Effects of object density and transect layout............................................................48 Effects of object density and transect number .........................................................48 Effects of object density, and transect length, layout, and number..........................49

Discussion...............................................................................................................................49 Conclusion ..............................................................................................................................53

4 CONCLUSION.......................................................................................................................73

APPENDIX

OVERALL RESULTS ...........................................................................................................76

LIST OF REFERENCES...............................................................................................................81

BIOGRAPHICAL SKETCH .........................................................................................................87

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LIST OF TABLES

Table page 1-1 Comparison of models fitted to line transect data .............................................................31

1-2 Overall summary of estimates of abundance of gopher tortoise burrows for each abundance estimation method in two strata (G5 and C3/C7), Ordway-Swisher Biological Station, Florida .................................................................................................32

1-3 Estimated number of gopher tortoises in stratum C3/C7, Ordway-Swisher Biological Station, Florida...................................................................................................................33

2-1 Density estimates by object spatial distribution and density .............................................55

A-1 Simulation study results.....................................................................................................76

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LIST OF FIGURES

Figure page 1-1 Map of Ordway-Swisher Biological Station in north-central Florida, USA, depicting

stratum G5 and stratum C3/C7, and locations of line transects and plots .........................34

1-2 Effects of proportion of plots sampled using sample count method on estimates of abundance in two strata (G5 and C3/C7), Ordway-Swisher Biological Station in north-central Florida ..........................................................................................................35

2-1 Examples of simulated spatial distributions of objects with a density of 2 objects ha-1....56

2-2 Transect layout patterns with objects simulated in a random spatial distribution with a density of 2 objects ha-1, and a transect density of 10 m ha-1..........................................58

2-3 Effect of transect length on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1................61

2-4 Effect of transect length on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1................63

2-5 Effect of transect layout on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1................65

2-6 Effect of transect layout on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1................67

2-7 Effect of transect number on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1 ....69

2-8 Effect of transect number on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1................71

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the

Requirements for the Degree of Master of Science

ANALYSIS OF WILDLIFE ABUNDANCE ESTIMATION METHODS USING REAL AND SIMULATED DATA

By

Saif Z. Nomani

August 2007

Chair: Madan K. Oli Cochair: Raymond R. Carthy Major: Wildlife Ecology and Conservation

For most wildlife species, multiple abundance estimation methods are available and the

choice of a method should depend on cost and efficacy. I field-tested the cost and efficacy of line

transect, total count, sample count, and double observer methods for estimating abundance of

gopher tortoise (Gopherus polyphemus) burrows in two habitats that differed in vegetation

density (sparse and dense) at the Ordway-Swisher Biological Station in north-central Florida.

In the dense vegetation stratum, the density of burrows estimated using the line transect

method (8.58 ± 0.94 burrows ha-1) was lower than that obtained from total count method (11.33

burrows ha-1). In the sparse vegetation stratum, the estimated burrow density using the line

transect method (11.32 ± 1.19 burrows ha-1) was closer to the burrow density using the total

count method (13.00 burrows ha-1). The density of burrows estimated using the double observer

method was identical to that obtained from the total count method in dense vegetation stratum,

but slightly greater than that obtained from the total count method in sparse vegetation stratum.

The density of burrows estimated using the sample count method varied widely depending on the

proportion of sample plots sampled in both strata. The cost of sampling as well as estimates of

burrow density varied with habitat type. The line transect method was the least costly of the

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methods. Using burrow cameras and patch occupancy modeling approach, I also estimated the

probability of burrow occupancy by gopher tortoises (active: 0.50 ± 0.09; inactive: 0.04 ± 0.04),

and used these values to estimate abundance of gopher tortoises. Using estimates of burrow

abundance based on the line transect method, the density of gopher tortoises was 2.75 ± 0.29 ha-

1 in the sparse vegetation stratum.

I then conducted a simulation study to investigate how the spatial distribution and density

of objects, and the total length, layout, and number of transects influence the accuracy of

estimates of abundance obtained from the line transect method. Using MATLAB I generated

objects in different spatial distributions (clumped, random, uniform) with different object

densities in a simulated study area. I varied the length, layout and number of transects used.

The line transect method worked best for a random distribution of objects; root mean

squared error between the estimated density and the true density was 8.5% of the true density.

For all spatial distributions of objects, increasing transect length increased the accuracy of

estimates of abundance. For a clumped distribution, transect layout and transect number did not

seem to significantly influence accuracy of estimates of abundance. For a random distribution,

transect number did not seem to significantly influence accuracy of estimates of abundance. For

a uniform distribution, when transect layout was random, transect number and transect length did

not seem to significantly influence accuracy of estimates of abundance. For a clumped

distribution I recommend using a higher transect length. For a random distribution I recommend

using a systematic transect layout as this provided slightly greater accuracy. For a uniform

distribution I recommend using a random transect layout as this provided substantially greater

accuracy.

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CHAPTER 1 INTRODUCTION

Estimates of abundance are essential for monitoring the population status and recovery

progress of threatened and endangered species (Seber 1982, Williams et al. 2002). For most

wildlife species, multiple abundance estimation methods are available, including line transect,

mark-recapture, and double observer (Krebs 1999, Seber 1982, Williams et al. 2002) and the

choice of a method should depend on cost and efficacy. Using the gopher tortoise (Gopherus

polyphemus) as a test species, I compared the cost and efficacy of different abundance estimation

methods.

The gopher tortoise is a species of conservation concern in the southeastern US. Gopher

tortoises spend much of their time in the shelter of self-constructed underground burrows

(Wilson et al. 1994), and direct observation of tortoises is difficult; consequently researchers

typically estimate abundance of burrows, and frequently use it as an index of tortoise abundance

(Cox et al. 1987, Smith et al. 2005, McCoy et al. 2006).

However, it is not easy to estimate abundance of animals (Seber 1982). Two key issues

involved in abundance estimation are detectability and spatial sampling (Royle and Nichols

2002, Williams et al. 2002). Most sampling methods do not result in the detection of all animals

present in a study area so one must estimate detectability (the probability of observing an animal

or object if it is present). Similarly, a sampling method often cannot be applied to the entire study

area due to time and resource limitations, and typically a fraction of the area is sampled.

Abundance can then be estimated considering detectability and spatial sampling simultaneously.

These issues apply to the estimation of gopher tortoise abundance as well. An additional

problem involved in the estimation of gopher tortoise abundance is that not every burrow is

occupied by tortoises. Thus, an important issue relevant to gopher tortoise abundance estimation

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is the burrow occupancy rate (probability that a burrow is occupied by a gopher tortoise)

(Diemer 1992). Estimates of abundance of gopher tortoises are then obtained by applying burrow

occupancy rates to estimates of burrow abundance.

Methods of estimating abundance of gopher tortoise burrows vary with respect to efficacy

and cost, and given the pivotal role of gopher tortoises in ecosystems where they are found, it is

essential to use rigorous methods for estimating and monitoring gopher tortoise abundance. I

conducted a field study to investigate the cost and efficacy of line transect, total count, sample

count, and double observer methods for estimating gopher tortoise burrow abundance, and to

estimate the probability of burrow occupancy by gopher tortoises using burrow cameras and the

patch occupancy modeling approach in the Ordway-Swisher Biological Station, Florida.

I determined that the line transect method is an effective method for estimating abundance

of gopher tortoise burrows, however, accuracy of estimates of abundance obtained from the line

transect method may vary depending on the spatial distribution and density of objects, and the

length, layout, and number of line transects. The spatial distribution and density of objects

cannot be changed, however it is possible to design a study by varying the length, layout, and

number of transects in order to maximize accuracy of estimates of abundance for a given spatial

distribution and density of objects.

I used a simulation-based approach in MATLAB (Mathworks 2006) to determine the

influence of length, layout and number of transects on accuracy of estimates of abundance for

different object spatial distributions and density levels.

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CHAPTER 2 COMPARISON OF METHODS FOR ESTIMATING ABUNDANCE OF GOPHER

TORTOISES

Introduction

One of the most relevant questions in wildlife management is: how many are there?

Indeed, estimates of abundance are a prerequisite for listing or delisting of a species, and for

monitoring recovery progress (Seber 1982, Cassey and Mcardle 1999, Williams et al. 2002).

Furthermore, estimates of abundance are needed for understanding density-dependent

relationships, for parameterizing and evaluating population models, and for formulating or

evaluating management programs (Williams et al. 2002).

The gopher tortoise (Gopherus polyphemus) is a species of conservation concern in the

southeastern US. It is federally listed as a threatened species in the western portion of its range

(western Alabama, Mississippi, and Louisiana) (Lohoefener and Lohmeier 1984, Federal

Register 1987). In Florida, gopher tortoise populations have been declining for some time

(Auffenberg and Franz 1982, Schwartz and Karl 2005), and the species has recently been

approved for reclassification to Threatened pending approval of a species management plan

(FFWCC 2006). Several state and federal agencies in the gopher tortoise range are charged with

monitoring their status and population trends which require reliable estimates of abundance.

Estimating abundance of gopher tortoises is a two step process: estimation of burrow

abundance and estimation of burrow occupancy rates. Gopher tortoises spend much of their time

in the shelter of self-constructed underground burrows (Wilson et al. 1994), and direct

observation of tortoises is difficult. These burrows are relatively easy to see due to their half-

moon shape and large mound of sand (commonly referred to as the apron) at the burrow

entrance. Because gopher tortoises are rarely seen outside their burrows, researchers typically

estimate abundance of burrows, and frequently use it as an index of tortoise abundance (Cox et

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al. 1987, Smith et al. 2005, McCoy et al. 2006). The most commonly used methods for

estimating the abundance of gopher tortoise burrows include line transect, total count, and

sample count methods (Doonan 1986, Mann 1993, Epperson 1997, Doonan and Epperson 2001).

A second issue involved in the estimation of gopher tortoise abundance is that not every

burrow is occupied by tortoises; there are typically more burrows than gopher tortoises and the

number of burrows does not always correspond to the number of tortoises (McRae et al. 1981,

Diemer 1992, Smith et al. 1997, Eubanks et al. 2003, McCoy et al. 2006). Thus, an important

issue relevant to gopher tortoise abundance estimation is the burrow occupancy rate (probability

that a burrow is occupied by a gopher tortoise) (Diemer 1992). The estimates of abundance of

gopher tortoises are then obtained by applying burrow occupancy rates to estimates of burrow

abundance. Auffenberg and Franz (1982) reported that 61.4% of all burrows (active and inactive)

were occupied in their study. Some studies have used this or other similar values (e.g., Ashton

and Ashton (in press)) as a “correction factor” to convert the burrow abundance into an estimate

of tortoise abundance (Kushlan and Mazotti 1984, Doonan 1986, Doonan and Epperson 2001,

FFWCC 2006, Gregory et al. 2006). Burrow occupancy rates vary over time and space, and

unreliable estimates of occupancy rates can lead to erroneous estimates of gopher tortoise

abundance (Burke and Cox 1988, Breininger et al. 1991, McCoy and Mushinsky 1992, Moler

and Berish 2001).

The methods of estimating abundance of gopher tortoise burrows vary with respect to

efficacy and cost, and rigorous field tests of these methods are needed to evaluate the efficacy

relative to costs. Moreover, recent advances in the patch occupancy modeling framework

(Mackenzie et al. 2002, Mackenzie et al. 2006) offer the possibility of statistically rigorous

estimates of burrow occupancy rates which were not possible previously.

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My objectives were to 1) investigate the cost and efficacy of line transect, total count,

sample count, and double observer methods for estimating gopher tortoise burrow abundance,

and 2) estimate the probability of burrow occupancy by gopher tortoises using burrow cameras

and the patch occupancy modeling approach in the Ordway-Swisher Biological Station, Florida.

I then combined estimates of burrow abundance with estimates of the probability of burrow

occupancy to estimate abundance of gopher tortoises.

Methods

Study Area

This study was conducted in the Ordway-Swisher Biological Station

(http://www.ordway.ufl.edu) located in Putnam County, Florida (29°41' N and 82° W) (Figure

1-1) in the fall of 2005. The Biological Station encompasses approximately 4000 ha, and offers

over 1600 ha of potential gopher tortoise habitat with old fields, pine plantations, and sand hill

habitats of several burn frequency categories.

I selected a portion of the Ordway-Swisher Biological Station and stratified it into two

strata (G5, and C3/C7) based on habitat maps, burn history and visual observation. Stratum G5,

comprising of management unit G5, covered an area of approximately 110.3 ha, and was last

burned in 2003 (two years before this study was conducted). Stratum C3/C7, comprising of

management units C3 and C7, covered an area of approximately 116.5 ha, and was last burned in

Feb 2005 (same year as this study). Due to the recent burn, stratum C3/C7 was more open with

less dense vegetation than stratum G5 (R. R. Carthy, unpublished data). The study was

conducted in two strata to investigate whether the probability of burrow detection, burrow

abundance, and cost of the methods differed between the sandhill habitats with relatively high

versus low vegetation density (Buckland et al. 2001).

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Line Transect Method

TPilot study

I conducted a pilot study in the Ordway-Swisher Biological Station to estimate the

transect length needed for robust estimates of burrow abundance using methods described in

Buckland et al. (2001). I estimated that, to achieve a coefficient of variation of ≤15% I needed to

sample approximately 8 km of total transects in each stratum.

Data collection

I placed 8 km of transects in each stratum systematically at predetermined distances. I

allowed sufficient spacing (30 to 60 m) between transects to ensure that burrows would not be

double-counted, while providing an adequate sample size for statistically robust results

(Buckland et al. 2001). I oriented transects so that they did not run parallel to roads or other

linear topographical features (Buckland et al. 2001, Williams et al. 2002) because they can affect

the distribution of gopher tortoises. I placed flags and recorded GPS coordinates at the origin and

end of all transects.

A team of observers, consisting of an observer and an assistant, walked along each transect

line. The observer (Observer 1) identified all burrows detected and the assistant then measured

the perpendicular distance from the transect line to the burrow (Buckland et al. 2001, Williams et

al. 2002). Perpendicular distance was measured from the transect line to either the burrow's

mouth or the beginning of the burrow apron, whichever was closest to the transect line. The

assistant also recorded the GPS coordinates for the burrow, measured the burrow width 50 cm

inside the burrow, and classified each burrow according to width as juvenile (<14 cm wide), sub-

adult (14 to 23 cm wide), and adult (>23 cm) (Alford 1980, Smith 1992). The observer classified

each burrow into one of two burrow status categories: active and inactive. Active burrows had

burrow aprons and entrances with little or no debris, and had evidence of tortoise occupation.

Inactive burrows, on the other hand, had debris and leaf litter on the apron, at the mouth, and in

the burrow tunnel. In some cases burrow mouths were degraded so that they did not have the

classic, half-moon tortoise shape.

The assistant did not participate in detecting burrows but simply collected and recorded

data for burrows detected by the lead observer. All detected burrows were temporarily marked

with a numbered tag so as to avoid double counting of burrows. Tags were hidden from view of

the second observer, but were placed in a consistent location at burrows so they were easily

located by the second observer's assistant upon close examination of the burrows detected by the

second observer.

Once the first team completed sampling transects I used a second team to collect data in

stratum G5 using the same protocol. These data were used to test for inter-observer variability in

detection probability and estimates of burrow abundance.

One critical assumption of line transect sampling is that all objects located on the line

transect are seen and recorded (Buckland et al. 2001, Williams et al. 2002). Gopher tortoise

burrows are conspicuous, and are associated with mounds that are hard to miss from a close

distance (Lohoefener 1990, Doonan and Epperson 2001). I am, therefore, confident that all

tortoise burrows that were directly on the line were detected.

Data analysis

I used Program DISTANCE (Thomas et al. 2003) to analyze the line transect data to

estimate the abundance of gopher tortoise burrows. The program provides a flexible framework

for parameterization and comparison of alternative models (Buckland et al. 2001). I ran several

different parametric models, each consisting of a key function and a series adjustment term

(Buckland et al. 2001), using Program DISTANCE. I used Akaike's Information Criterion

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( AIC ) values for model comparison and selected the model with the lowest AIC (Burnham and

Anderson 2002). I excluded 5% of the observations (furthest from the line) from the analysis to

remove possible outliers Buckland et al. (2001).

Of the parametric models discussed above, I selected the most parsimonious model that

allowed covariates and tested for the effect of the width of the burrow entrance (in cm) on the

detection probability for Observer 1 in both strata. I then compared the AIC values for models

with and without burrow width as a covariate to determine the effect of the burrow width on

estimates of detection probability and density. Using the same procedure, I used observer as a

covariate to test for the inter-observer variability in detection probability in stratum G5. Data for

the two observers were pooled together to test for inter-observer variability, and the resulting

AIC value was compared to the sum of the AIC values obtained from the separate analyses of

data collected by the two observers without observer as a covariate (Buckland et al. 2001).

Total Count, Sample Count, and Double Observer Methods

Data collection

I conducted a total count of burrows after line transect data had been collected. I selected

six 1-ha plots in each stratum. I overlaid these plots over portions of each stratum where line

transect data were collected. The four corners of the plots were flagged and their coordinates

were determined using a GPS unit. I further subdivided the plots into ten 20x50 m subplots. Each

plot was comprehensively searched for burrows by two observers so detectability could be

estimated (Nichols et al. 2000, Williams et al. 2002). Initially, I used three observers; however,

the third observer consistently failed to detect any additional burrows so I continued with two

observers. The observers recorded all pertinent information for detected burrows. Sample count

was the total count in a sample of plots.

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I implemented the dependent double observer method following Nichols et al. (2000) and

Williams et al. (2002). Each of the 20x50 m subplots was comprehensively searched for burrows

by two dependent observers (primary observer and secondary observer, where the secondary

observer is aware of the burrows detected by the primary observer). The primary observer

surveyed the plots, and flagged and called out burrows detected to the secondary observer. The

secondary observer recorded the information and proceeded to survey the plots to detect

additional burrows (Nichols et al. 2000). At the completion of sampling of each subplot, the data

were comprised of burrows detected by the primary observer, and burrows missed by the

primary observer but detected by the secondary observer. Observers alternated roles on

consecutive subplots, as recommended by Nichols et al. (2000).

I conducted the total count, sample count and double observer methods on the same six

1-ha plots and the field methods for the three methods were identical. I used the data collected

for the total count method for the sample count calculations by selecting a subset of plots where

total counts were conducted. This has been described in detail in the next section.

Data analysis

The estimated abundance of burrows using total count was the total number of burrows

detected by both observers. Estimates of cost and abundance obtained from the sample count

method can vary depending on the proportion of total area sampled, spatial distribution of

burrows and the choice of the sample plots. Thus, I evaluated the effects of selecting different

proportions of plots on the estimate of burrow abundance by utilizing data collected for the total

count method. I selected all possible combinations of 3, 4, and 5 out of the 6 plots; each of these

plots was thoroughly surveyed by two observers as described previously. The number of burrows

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in the sampled plots was then extrapolated to obtain an estimate of the number of burrows to the

entire 6-ha area sampled. Sampling a 100% of the plots (6 out of 6) is the total count.

I used Program DOBSERV (Hines 2000) to analyze the double observer data. The overall

detectability was estimated as (Nichols et al. 2000):

( )12 21 22 11ˆ 1p x x x x= − (1-1) Where p̂ = estimate of overall detectability of both observers, 11x = number of burrows detected by observer 1 in a primary role, 21x = number of burrows detected by observer 2 in a primary role, 12x = number of additional burrows detected by observer 1 in a secondary role, and

22x = number of additional burrows detected by observer 2 in a secondary role. This estimate of overall detectability ( p̂ ) was used to obtain the estimate for the

population size for the sampling area ( N̂ ) by dividing the total number of burrows detected by

all observers ( ..x ) by p̂ (Nichols et al. 2000). The standard error ( ˆ( )SE N ) and the 95%

confidence interval for N̂ were estimated using Program DOBSERV.

I divided N̂ obtained from each method by the area of the study site sampled to estimate

the burrow density ( D̂ ) (burrows haP

-1P). I multiplied D̂ by the area of the stratum to obtain an

estimate of burrow abundance in each stratum.

Burrow Occupancy Rates

Data collection

To estimate the probability that a burrow is occupied by a gopher tortoise (burrow

occupancy rate) I conducted burrow occupancy surveys in management unit C3 of stratum

C3/C7 (Figure 1-1). I examined a sub-sample of burrows from C3 that were marked during the

total counts with a burrow camera on three consecutive days (beginning either in the morning or

early afternoon) to determine occupancy status. This sub-sample contained both active and

inactive burrows. I used the Econo GeoVision, Jr. camera system designed by Marks Products,

Inc. (Williamsville, Virginia) for use in borehole and water well systems. I sanitized the

21

equipment with diluted Nolvasan® after examining each burrow, to minimize the risk of disease

transmission. I classified the burrows as “empty” if the operator was certain that she/he had

reached the end of the burrow and no gopher tortoise was present. Burrows were considered

“occupied” only if the operator could identify a gopher tortoise with absolute certainty. Burrow

occupancy was considered "undetermined" if the operator could not maneuver the camera to the

end of the burrow due to burrow architecture (e.g., dramatic turns or tunnel size) or debris (e.g.,

leaf litter and/or sand). Burrows with undetermined occupancy status were not used in analysis

of occupancy rates.

Data analysis

Occupancy data were collected using a burrow camera and a statistically robust occupancy

modeling approach (Mackenzie et al. 2002) implemented in Program MARK (White and

Burnham 1999) to estimate detection probability and burrow occupancy rate. Occupancy survey

was conducted as described previously. A burrow was considered occupied by a tortoise (coded

1) if the observer was certain that a tortoise was present; it was considered unoccupied (coded 0)

if the observer was certain the burrow was not occupied. Using these occupancy data collected

over 3 sampling occasions, I fitted the patch occupancy model (Mackenzie et al. 2002). I used

AIC to select the most parsimonious model. Using the most parsimonious model identified, I

tested for the effect of the width of the burrow entrance (in cm) on the detection probability and

the occupancy rate by modeling the logit of each rate as a linear function of burrow width. If the

95% confidence interval for the slope parameter (β ) did not include 0, the relationship was

considered statistically significant (Williams et al. 2002).

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Costs

I recorded the time taken for data collection for each method in person-hours. The amount

of time needed for analysis of data varied widely among individuals depending on mathematical

background, computer skills, and learning curves, and thus are not reported. The costs of

equipment required for analysis may also vary tremendously and thus are not reported.

Results

Line Transect

A total of 28 line transects was placed in stratum G5 with a total length of 8025 m.

Observer 1 detected 163 burrows and Observer 2 detected 150 burrows. For Observer 1, the

model with the lowest AIC was Uniform Cosine (Table 1-1). Based on this model, the estimated

burrow density (± SE ) was 8.58 ± 0.94 burrows ha P

-1P ( cv =11.0%). For Observer 2, the model

with the lowest AIC was also Uniform Cosine (Table 1-1). Based on this model, the estimated

burrow density was 8.49 ± 0.98 burrows ha P

-1P ( cv =11.5%) (Table 1-2).

A total of 16 line transects was placed in stratum C3/C7 with a total length of 8003 m. The

first observer (Observer 1) detected 262 burrows. For Observer 1, the models with the lowest

AIC were Hazard Rate Cosine and Hazard Rate Simple Polynomial (Table 1-1). The results for

these two models were identical, so I selected the Hazard Rate Cosine model. Based on this

model, the estimated burrow density was 11.32 ± 1.19 burrows ha P

-1P ( cv =10.5%) (Table 1-2). I

did not analyze the line transect data for Observer 2 for stratum C3/C7 because Observer 2 did

not collect data independently of Observer 1.

In stratum G5, I evaluated the effect of burrow width on detection probability for Observer

1 using the Half Normal Cosine model. The difference between the probability of detecting

smaller burrows and the probability of detecting larger burrows was not substantial ( AIC for

model with burrow width as a covariate: 475.86; AIC for model without burrow width as a

23

covariate: 477.87). Consequently, estimates of burrow density were very similar (with burrow

width as a covariate: 8.99 ± 1.06 burrows ha P

-1P; without burrow width as a covariate:

8.58 ± 0.94 burrows haP

-1P). In stratum C3/C7, I evaluated the effect of burrow width on detection

probability for Observer 1 using the Hazard Rate Cosine model. Although the burrow width

seemed to influence detection probability ( AIC for model with burrow width as covariate:

867.97; AIC for model without burrow width as covariate: 957.48), the difference in the

estimate of burrow density was not substantial (with burrow width as covariate: 11.26 ± 0.84

burrows haP

-1P; without burrow width as covariate: 11.32 ± 1.19 burrows haP

-1P).

Additionally, in stratum G5, I evaluated inter-observer variability in detection probability

using pooled data collected by the two independent observers and the Half Normal Cosine

model. There seemed to be no difference in detection probability between the two observers

( AIC for model with pooled observations: 1871.19; sum of AIC values for models analyzed

separately for Observer 1 and Observer 2: 1871.21), and the difference in the estimate of burrow

density was not substantial (model with pooled observations: 8.55 ± 0.71 burrows ha P

-1P; model

analyzed separately for Observer 1: 8.68 ± 0.97 burrows haP

-1P; model analyzed separately for

Observer 2: 8.41 ± 1.01 burrows haP

-1P).

Total Count, Sample Count, and Double Observer

In stratum G5, the total number of burrows in the 6-ha (six 1-ha plots) sampled was 68

(Table 1-2). In stratum C3/C7, the total number of burrows in the 6-ha (six 1-ha plots) sampled

was 78 (Table 1-2). The extrapolated abundance of burrows based on the sample count method

varied widely in both strata based on the proportion of sample plots used (Figures. 1-2A and

1-2B, Table 1-2). In stratum G5, when 50%, 66%, and 83% of the plots were sampled, the

extrapolated number of burrows in the sampling area ranged from 48 to 88, 54 to 81, and 60 to

74 burrows, respectively. In stratum C3/C7, when 50%, 66%, and 83% of the plots were

24

sampled, the extrapolated number of burrows in the sampling area ranged from 64 to 92, 69 to

87, and 73 to 83 burrows, respectively.

In stratum G5, the overall detectability ( p̂ ) estimated using the double observer method

was 1.0, and ..x and N̂ were 68. Because p̂ was 1.000, ˆ( )SE N or 95% confidence interval

could not be estimated (Table 1-2).

In stratum C3/C7, p̂ estimated using the double observer method was 0.997 ± 0.003, ..x

was 78, and N̂ was 78.23 ± 0.53 (Table 1-2).

Burrow Occupancy Rates

The most parsimonious model indicated that the detection probability (probability of

observing a gopher tortoise if it was in the burrow) was 0.92 ± 0.04 and did not differ between

burrows classified as active or inactive. However, the occupancy rates were significantly

different between the two groups (active: 0.50 ± 0.09; inactive: 0.04 ± 0.04). There was no

evidence that width of the burrow entrance influenced the occupancy rate or the detection

probability.

Abundance of Gopher Tortoises

Using the occupancy rates for active and inactive burrows, and based on the proportion of

active and inactive burrows I estimated the abundance of gopher tortoises in stratum C3/C7. The

estimated abundance varied from 223.68 – 329.70 tortoises in stratum C3/C7 (total area: 116.5

ha), depending on the method used, and in the case of sample count, depending on the proportion

of plots sampled (Table 1-3).

Costs

The cost of sampling varied from 0.52 – 2.38 person-hours ha P

-1 Pin stratum G5, and from

0.46 – 2.08 person-hours haP

-1 Pin stratum C3/C7, depending on the methods used, and in the case

of sample count, depending on the proportion of plots sampled (Table 1-2). I did not analyze cost

of line transect data collected by Observer 2. Observer 2 did not lie out transects or measure and

record information for burrows that had already been detected by Observer 1. Costs of

implementing the double observer method were identical to the cost for the total count method.

The cost of sampling burrows with a burrow camera to determine occupancy status was

0.16 person-hours per burrow camera observation. A total of 168 burrow camera observations

were performed (three observations for each of the 56 burrows scoped) requiring a total time of

26.88 person-hours.

Discussion

Comparison of Abundance Estimation Methods

To monitor the population status, and for appropriate recovery efforts for gopher tortoises,

reliable estimates of abundance are needed. Methods that are currently used to estimate the

abundance of gopher tortoises vary with respect to statistical rigor, efficacy, and cost. Given the

pivotal role of gopher tortoises in ecosystems where they are found (Eisenberg 1983, Wahlquist

1991), it is essential to use rigorous yet cost effective methods for estimating and monitoring

tortoise abundance.

I field-tested the efficacy and cost of line transect, total count, sample count, and double

observer methods for estimating abundance of gopher tortoise burrows. In the dense vegetation

stratum (G5), the estimated burrow density using the line transect method for both observers

(8.58 and 8.49 burrows ha-1, respectively) was nearly 3 burrows ha-1 less than burrow density of

11.33 burrows ha-1 obtained from total count method. Estimates based on total count method did

not fall within the 95% confidence intervals of those obtained from line transect method (Table

1-2). In the sparse vegetation stratum (C3/C7), the estimated burrow density estimated using the

line transect method (11.32 burrows ha-1) was closer to the burrow density obtained from the

25

26

total count method (13.00 burrows ha P

-1P). The total count fell within the 95% confidence interval

for estimates obtained from the line transect method (Table 1-2).

Mann (1993) compared estimates of tortoise burrow abundance obtained from line

transect and total count methods, and found that line transect method overestimated burrow

abundance by as much as 49% in 13 sites and 32% on seven sites. Results from similar studies

suggest a tendency for line transects to overestimate abundance when compared to total counts

(Doonan 1986, Epperson 1997, Doonan and Epperson 2001). I used ≥2 observers to thoroughly

search the sampling area, and ensured that detection probability was 1.0. I also had a large

sample size for a reasonable coefficient of variation. My results do not agree with findings that

the line transect method tends to overestimate burrow numbers. In fact, estimates of burrow

abundance obtained from the line transect method were lower than those obtained from total

count in stratum G5; they did not differ significantly in stratum C3/C7 (Table 1-2). These results

suggest that the estimated burrow abundance obtained from the line transect method are not

consistently greater or smaller than those obtained from the total count method. Therefore, the

line transect method likely captured a greater amount of spatial variability in distribution and

abundance burrows in the study area.

Consistent with previous studies (McCoy and Mushinsky 1995, Epperson 1997, Marques

et al. 2001, McCoy and Mushinsky 2005), my estimates of burrow density varied with habitat

type and burn frequency. Density estimates obtained from all methods were higher in stratum

C3/C7 which had comparatively sparse vegetation and a higher burn frequency. The higher

density of burrows and tortoises in stratum C3/C7 likely indicates that this stratum offered a

better habitat for the tortoises.

27

Burrow Occupancy

My estimates of burrow occupancy rates (active: 0.50 ± 0.09; inactive: 0.04 ± 0.04) were

substantially lower than Auffenberg and Franz’s ‘correction factor’ of 61.4 % for active and

inactive burrows (Auffenberg and Franz 1982). Some studies have used this or a similar

correction factor (e.g., Ashton and Ashton (in press)) for converting estimates of burrow

abundance to tortoise abundance (Kushlan and Mazotti 1984, Doonan 1986, Doonan and

Epperson 2001, FFWCC 2006, Gregory et al. 2006). However, this approach ignores the spatial,

temporal or habitat-specific variation in occupancy rate and can cause estimates of gopher

tortoise abundance to be unreliable (Burke and Cox 1988, Breininger et al. 1991, McCoy and

Mushinsky 1992, Moler and Berish 2001). Moreover, my study is the first to apply the patch

occupancy modeling approach (Mackenzie et al. 2002) to estimate and model burrow occupancy

rates. When appropriate data are available, this approach also provides framework for testing

relevant biological hypotheses.

Because of time and resource limitations, I conducted burrow occupancy surveys only in

management unit C3 of stratum C3/C7, and I did not have empirical estimates of burrow

occupancy rates for stratum G5. Assuming that the burrow occupancy rate was the same in both

strata (C3/C7 and G5), estimates of tortoise abundance in stratum G5 (total area 110.3 ha) varied

from 148.68 - 230.45 tortoises depending on the method used, and in the case of sample count,

depending on the proportion of plots sampled. Based on the line transect method, the estimated

density of gopher tortoises was 2.06 ± 0.23 ha P

-1 Pin stratum G5.

Occupancy rates may vary among habitats due to the ecological needs of gopher tortoises,

and habitat-specific estimates of occupancy rates should be used whenever possible. Estimates of

occupancy rates may also be influenced by the season, time of the day when data are collected,

and time interval between successive samples; these factors should be considered whenever

possible. Additionally, there is the possibility of the same tortoise occupying more than one

burrow during the burrow occupancy surveys, resulting in an overestimation of the occupancy

rate. These potential problems can be minimized by appropriate sampling design. Nonetheless, I

found that patch occupancy models (Mackenzie et al. 2002, Royle and Nichols 2002, Mackenzie

et al. 2006) offer statistically robust approach to estimating burrow occupancy rates and should

be considered in future studies.

Costs of Implementation

The total count and sample count methods were relatively straightforward to implement,

and required no sophisticated software for data analyses. However, these methods are costly,

particularly when a substantial proportion of the sites need to be sampled. Moreover, these

methods do not offer rigorous estimates of precision or meaningful approaches to obtaining

statistical inferences. The double observer method partially addressed some of these concerns by

providing estimates of precision (when detectability is less than 1.0), but is costly to implement.

Using the sample count method, the range of extrapolated estimates for burrow density became

narrower as the sampling proportion increased (Figures 1-2A and 1-2B). However, there was a

cost tradeoff in that more time was needed to collect the data (Table 1-2).

The line transect method was the least costly of the methods, and I was able to sample a

larger effective area with the same effort. The method is considered statistically rigorous and

robust, provides statistical measures of precision, and provides a framework for statistical

inferences (Buckland et al. 2001, Krzysik 2002, Williams et al. 2002). However, the low cost of

sampling in the field may be somewhat offset by increased costs of study design and data

analysis, as a good understanding of underlying theory, sampling protocol and working

knowledge of Program DISTANCE is needed for effective implementation of this method.

28

Costs of data collection differed between the two strata in the study site. The sparse

vegetation stratum (C3/C7) had a lower relative cost of sampling for all the abundance

estimation methods than dense vegetation stratum. In my study, sample counts and total counts

were substantially more costly than line transects in both strata. Detection time may be

substantially less in sparse vegetation (Lohoefener and Lohmeier 1984, Burke and Cox 1988,

Diemer 1992), and prescribed burns prior to sampling may further reduce cost of sampling

(Smith 1992, Mann 1993, Moler and Berish 2001).

Conclusion

Among other factors, the selection of an abundance estimation method should consider the

habitat type of the study area, and available time and resources (Ellis and Bernard 2005). With a

stratified sampling design, and an adequate sample size, the line transect method is perhaps the

most efficient method for estimating gopher tortoise burrow abundance because: 1) it is less

costly than total and sample count methods, 2) it is more likely to capture a wider range of

spatial variation in the distribution and abundance of burrows, 3) it offers statistically robust

estimates of measures of precision, and 4) provides a flexible framework for evaluating effects of

covariates on estimates of abundance.

If one wishes to implement the total (or sample) count method, I recommend using

multiple observers in order to obtain estimates of detectability. I note, however, that the total (or

sample count) method does not provide an estimate of variance, nor does it provide a framework

for statistical test of hypothesis. The double observer approach is reasonable if one wishes to

implement a count-based method, but is unsure that detectability is equal to 1.0.

I recommend that burrow cameras (or similar technologies) should be employed, along

with a patch occupancy modeling approach for data analysis, to estimate burrow occupancy rates

and to test hypothesis regarding the occupancy rate or detection probability. If a study is

29

conducted in >1 habitat types, I recommend obtaining habitat-specific estimates of occupancy

rates. Finally, I suggest that gopher tortoise monitoring programs should simultaneously consider

burrow abundance and burrow occupancy rates. This is because changes in gopher tortoise

abundance may be reflected in changes in one or both of these parameters (i.e., burrow

abundance and burrow occupancy rate), and changes in one may not be interpreted as an

indicator of changes in tortoise abundance.

30

31

Table 1-1. Comparison of models fitted to line transect data Observer 1 Observer 2 Stratum Model AIC∆ Parameters AIC∆ ParametersG5 Uniform CosineP

aP 0 1 0.00 1

Half Normal Cosine 0.13 1 0.93 1 Half Normal Hermite 0.13 1 0.93 1 Uniform Simple Polynomial 1.46 2 0.98 2 Hazard Rate Cosine 2.22 2 2.31 2 Hazard Rate Simple Polynomial 2.22 2 2.31 2 C3/C7 Hazard Rate Cosine P

aP 0 2 - -

Hazard Rate Simple Polynomial 0 2 - - Uniform Cosine 0.98 2 - - Half Normal Cosine 1.32 2 - - Half Normal Hermite 3.14 1 - - Uniform Simple Polynomial 3.59 3 - - Note: For each model the AIC∆ values and the number of parameters are presented.

AIC∆ is the difference in the AIC (Akaike’s Information Criterion) values between each model and the model with the lowest AIC value. P

a PMost parsimonious model

Table 1-2. Overall summary of estimates of abundance of gopher tortoise burrows for each abundance estimation method in two strata (G5 and C3/C7), Ordway-Swisher Biological Station, Florida

ˆMethod D ˆ ( )N tot Cost

G5 Line transecta

Obs 1 8.58 (6.87 - 10.73) 946.40 0.52 Obs 2 8.49 (6.73 - 10.71) 936.25 - Sample count 50%b 8.00 - 14.66c 882.21 - 1616.66c 1.19 66%b 9.00 - 13.50c 992.49 - 1488.74c 1.57 83%b 10.00 - 12.40c 1102.77 – 1367.43c 1.98 100%b 11.33 1249.44 2.38 Double observer 11.33 1249.44 2.38 C3/C7 Line transecta,d

Obs 1 11.32 (9.19 - 13.94) 1318.31 0.46 Sample count 50%b 10.67 - 15.33c 1246.21 – 1781.97c 1.04 66%b 11.50 - 14.50c 1339.39 – 1688.79c 1.38 83%b 12.20 - 13.80c

1420.92 – 1607.27c 1.73

Total count (100%b) 13.00 1514.09 2.08 Double observer

ˆ13.04 1518.75 2.08

Note: D is the estimated burrow density (with 95% confidence interval) in burrows ha-1, and ) is the estimated number of burrows in the stratum. “Cost” are presented in terms of time (person-hours) needed to sample 1 ha.

ˆ (N tota Results are based on the most

parsimonious model (Table 1-1). b Proportion of plots sampled. c Range of estimates d I did not analyze line transect data for Observer 2 for stratum C3/C7 because Observer 2 did not collect data independently of Observer 1.

32

Table 1-3. Estimated number of gopher tortoises in stratum C3/C7, Ordway-Swisher Biological Station, Florida Burrow abundance Gopher tortoise abundance Method

ˆBN (Active)

ˆBN (Inactive)

ˆ ˆGTN (Active) GTN (Inactive) ˆ ( )GTN tot

C3/C7a,b

Line transect Obs1 582.62 735.69 291.31 29.43 320.74 Sample count 50% 447.36 - 639.68 798.85 - 1142.92 223.68 - 319.84 31.95 - 45.72 255.63 - 365.56 66% 480.81 - 606.23 858.58 - 1082.56 240.40 - 303.12 34.34 - 43.30 274.74 - 346.42 83% 510.07 - 576.97 910.84 - 1030.30 255.04 - 288.49 36.43 - 41.21 291.47 - 329.70 Total count 100% 543.52 970.57 271.76 38.82 310.58 Double observer

ˆ 545.19 973.56 272.60 38.94 311.54

Note: (Active) and (Inactive) are the estimates for the total number of active and inactive burrows in the stratum, ˆ (Active) and ˆ (Inactive) are the estimated numbers of gopher tortoises in active and inactive burrows,

respectively, and )t is the estimated total number of gopher tortoises in all burrows in the stratum.

BN ˆBNGTN GTN

ˆ (GTN to a Burrow occupancy surveys were conducted only in management unit C3 (estimated burrow occupancy rates were 0.50 for active burrows and 0.04 for inactive burrows), therefore I estimated gopher tortoise abundance for stratum C3/C7 only. b For stratum C3/C7, the proportion of active and inactive burrows detected using the line transect method for Observer 1 was 0.44 and 0.56, respectively. The proportion of active and inactive burrows detected using the total count methods was 0.36 and 0.64, respectively.

33

Figure 1-1. Map of Ordway-Swisher Biological Station in north-central Florida, USA, showing stratum G5 and stratum C3/C7, and locations of line transects and plots.

34

Proportion Sampled

50% 66% 83% 100%

No.

of B

urro

ws

40

50

60

70

80

90A)

Proportion Sampled

50% 66% 83% 100%

No.

of B

urro

ws

60

65

70

75

80

85

90

95B)

Figure 1-2. Effects of proportion of plots sampled using sample count method on estimates of

abundance in two strata (G5 and C3/C7), Ordway-Swisher Biological Station in north-central Florida. Extrapolated range of total number of burrows are plotted against the proportion of plots sampled. A) In stratum G5. B) In stratum C3/C7.

35

CHAPTER 3 ACCURACY OF ESTIMATES OF ABUNDANCE BASED ON THE LINE TRANSECT METHOD: INFLUENCE OF SPATIAL DISTRIBUTION OF OBJECTS, AND LENGTH,

LAYOUT, AND NUMBER OF TRANSECTS

Introduction

Estimates of abundance are necessary for monitoring population status and for assessing

the impacts of management actions. Obtaining these estimates is notoriously difficult (Seber

1982). Several methods have been developed to estimate abundance, including line transect,

mark-recapture, and double observer (Krebs 1999, Seber 1982, Williams et al. 2002).

Line transect is a distance-based method and is statistically robust for estimating

abundance (Buckland et al. 2001, Krzysik 2002, Williams et al. 2002). Implementation of the

line transect method involves laying out transects either randomly or systematically at

predetermined distances, walking along the line transects detecting objects, and recording

sighting angles and sighting distances, or perpendicular distances of objects to the line. If

assumptions are met, the line transect method is efficient, cost-effective and provides rigorous

estimates of abundance. Consequently, this method has been used to estimate abundance for

many species of birds (Jarvinen and Vaisanen 1975, Hanowski et al. 1990), terrestrial and marine

mammals (Jefferson 1996, Plumptre 2000, Ruette et al. 2003, Calambokidis and Barlow 2004),

reptiles (Lewis et al. 1985, Krzysik 2002), amphibians (Lewis et al. 1985, Donnelly and Guyer

1994), and plants (Abrahamson 1984, Gentry and Emmons 1987). Additionally, line transect

method has been used to estimate abundance of many inanimate objects including nests

(Hashimoto 1995), dung (Marques et al. 2001, Ellis and Bernard 2005), and burrows

(Lohoefener 1990, Swann et al. 2002) as an index of animal abundance (Borchers et al. 1998,

Buckland et al. 2001).

36

The accuracy of estimates of abundance obtained from the line transect method may vary

depending upon the spatial distribution and density of objects, and the length, layout, and

number of line transects. Researchers cannot change the spatial distribution and density of

objects, but it is possible to design a study by varying the length, layout, and number of transects

in order to maximize accuracy and precision of estimates of abundance for a given spatial

distribution and density of objects.

My objectives were to address the following questions: 1) Which spatial distribution

pattern of objects is the line transect method most appropriate for? 2) For a given spatial

distribution, does the line transect method depend on object density? 3) For a given spatial

distribution and density of objects, how can one optimize the study design by varying total

transect length, transect layout pattern, and number of transects in order to maximize accuracy of

estimates of abundance?

Given the large number of factors involved and due to limitations of time and resources,

questions such as these can only be addressed effectively using simulations. Thus I used a

simulation-based approach to achieve my objectives.

The methodology and results in this study could be applied to a number of objects or

organisms, including invertebrates, plants, and nests (Buckland et al. 2000), provided some of

the basic assumptions of line transect abundance estimation (Burnham et al. 1980, Buckland et

al. 2001) are not violated.

I hypothesized that: 1) Estimates of abundance obtained from the line transect method

would be more accurate when objects were randomly or uniformly distributed in space; 2) For a

given spatial distribution pattern, precision of estimates of abundance would increase with

increasing object density; 3) increasing transect length would increase the accuracy of estimates

37

of abundance for all spatial distribution patterns and density levels; 3) for a clumped distribution

of objects, a random transect layout and several short transects would provide more accurate

estimates of abundance because such a study design would provide greater spatial coverage; 4)

for a uniform distribution of objects, a random transect layout would provide more accurate

estimates of abundance; and 5) for a random distribution of objects, transect layout and transect

number would not have a substantial effect on the accuracy of estimates of abundance.

Methods

Simulation Inputs

I considered three spatial distributions of objects: clumped, random and uniform. Within

each spatial distribution I used three levels of object densities: low (2 objects ha-1), medium (6

objects ha-1), and high (10 objects ha-1). For each combination of spatial distribution and density

level, I used a) three transect lengths: 10 m ha-1, 20 m ha-1, and 30 m ha-1, d) two types of

transect layout patters: random transect layout and systematic transect layout, e) and two levels

of total number of transects: few long and several short transects. There were a total of 216

unique combinations of input variables.

Spatial Distribution and Density of Objects

Using MATLAB I designed an 800 ha study area and simulated locations of objects within

the study area using the following spatial distributions: uniform grid (hereafter, uniform),

uniform random (hereafter, random), and clumped (Krebs 1999). For a uniform distribution, I

evenly spaced the objects throughout the study area (Zollner and Lima 1999) (Figure 2-1C). For

a random distribution, each object was distributed independently of all other objects (Figure

2-1B). I implemented this by generating the x and coordinates for the object using a uniform

random distribution throughout the study area (Zollner and Lima 1999). For a clumped

distribution, objects were aggregated in groups or patches (Figure 2-1A). To implement this I

y

38

39

randomly distributed parent objects throughout the study area, and using a random Gaussian

distribution with the parent object as the mean, and variance v (ranging from 2 to 5) depending

upon the density of objects, I generated “offspring” around each parents object (Zollner and

Lima 1999, Conradt et al. 2003). The number of parent objects was selected randomly from a

range of 25 to 50. I divided the total population size by the number of parent objects to determine

the number of “offspring” around each parent. Offspring that fell outside the borders of the study

area were deleted and the overall object density was readjusted.

To evaluate the effect of object density on estimates of abundance obtained from the line

transect method I varied the object densities from 2 objects haP

-1P to 10 objects haP

-1P in increments

of 4 objects ha P

-1 Pfor each spatial distribution.

Layout Pattern of Line Transects

I laid out line transects in two different patterns: systematic and random. For a systematic

transect layout (Figures 2-2C and 2-2D), x and y coordinates and the angle θ for the first

transect were predetermined. The coordinates were chosen to ensure that all line transects would

fall inside the study area. I used 0, 45 and 90 degrees for θ in order to provide an adequate

representation of systematic transect layouts. Subsequent transects were then placed at 90 m

intervals so as to prevent double-counting of objects from two adjacent transects. For a random

transect layout (Figures 2-2A and 2-2B) several different sets of transects were laid out

throughout the study area. The x and y coordinates and the angle θ for the first transect of

each transect set was chosen at random. Subsequent transects were then placed at 90 m intervals

parallel to the first transect. I ensured that all transect sets were located inside the study area and

did not overlap each other.

Total Length of Line Transects

The total transect length was determined using transect density in m ha-1. For instance, a

transect density of 10 m ha-1 would result in a total transect length of 8000 m in an 800 ha study

area. I used transect densities ranging from 10m ha-1 to 30m ha-1 in increments of 10m ha-1. The

lengths of all transects were equal within each simulation run. Based on the transect density used

I chose the total number of transect sets in the study area as well as the number of transects in

each set.

Number of Transects

The number of transect sets and the number of transects in each set varied with transect

density and were chosen to meet either of two conditions: a few long transects, or several short

transects in each transect set (Figures 2-2A, 2-2B, 2-2C, and 2-2D).

For a random transect layout with few long transects (Figure 2-2A) the number of transect

sets for a transect density of 10 m ha-1 was 2, and for transect densities of 20 m ha-1 and 30 m

ha-1 the number of transect sets was a randomly chosen number between 3 or 4. The number of

transects in each transect set was a randomly chosen number between 4 and 6. For a systematic

transect layout with few long transects (Figure 2-2C) the number of transect sets was 1 for all

transect densities. The number of transects for a transect density of 10 m ha-1 was 7, and for

transect densities of 20 m ha-1 and 30 m ha-1 the number of transects was a randomly chosen

number between 8 and 14.

For a random transect layout with several short transects (Figure 2-2B) the number of

transect sets for a transect density of 10 m ha-1 was 3, and for transect densities of 20 m ha-1 and

30 m ha-1 the number of transect sets was a randomly chosen number between 4 or 5. The

number of transects in each transect set was a randomly chosen number between 7 and 10. For a

systematic transect layout with several short transects (Figure 2-2D) the number of transect sets

40

41

was 1 for all transect densities. The number of transects for a transect density of 10 m haP

-1P was

10, and for transect densities of 20 m ha P

-1P and 30 m ha P

-1P the number of transect was a randomly

chosen number between 11 and 19.

Data Collection and Analysis

I set the transect strip width ( w ) at 30 m. This was the width of the area searched on each

side of the line transect; objects beyond 30 m were not considered. I used the half normal

detection function to determine whether objects within 30 m were detected. The half normal

detection function is often a good choice as a key function in line transect sampling (Buckland et

al. 2001). This took the form

2 2( ) exp( / 2 )g x x σ= − (2-1) Where ( )g x = probability of detecting an object at perpendicular distance x from the line, and σ = scale parameter, which I estimated following Brown and Cowling (1998)

1 22 (2 )wσ π −= (2-2) For each object within the strip width I generated a uniform random number between 0 and

1. If the random number was greater than or equal to the detection probability obtained from the

half normal detection function, the object was marked as detected. If the random number was

less than the detection probability, the object was considered undetected. I measured the

perpendicular distance of every object detected within the transect strip width of 30 m. I called

Program DISTANCE (Thomas et al. 2003) from within MATLAB to analyze the data using a

half normal cosine detection function to estimate the density of objects as:

ˆ (0)ˆ2

nfDL

= (2-3)

Where D̂ = estimate of density, n = number of objects detected, L = total transect length, ˆ (0)f = estimated probability distribution function at the line and was determined as

0

1ˆ (0)( )

wfg x dx

=

∫. (2-4)

42

I also calculated the number of objects detected as a percentage of the total number of

objects in the study area. I ran 100 simulations for each combination of spatial distribution of

objects and density of objects, and the layout, density and number of transects. The total number

of simulation runs was 21,600 for 216 different combinations of input variables. I then compared

the estimated density obtained from the line transect method ( D̂ ) with the actual ‘true’ density

( TD ) for each combination of spatial distribution, transect layout pattern, transect density, and

number of transects. To measure accuracy of estimates of abundance I calculated the root mean

squared error between D̂ and TD (RMSE) following Williams et al. (2002).

2

1

1 ˆ( )1

n

i Ti

RMSE D Dn =

= −− ∑ (2-5)

Where n = number of samples I also calculated RMSE as a percentage of TD (RMSE%).

To measure bias of the estimates I calculated the mean of the difference between D̂ and

TD as a percentage of TD (Bias%). Precision of estimates was quantified as the coefficient of

variation of D̂ (CV( D̂ )). I also calculated the percentage of times the 95% CI of estimates of

density computed by Program DISTANCE contained TD . I performed all statistical analyses

using SAS® software (SAS Institute, 2004).

Results

Overall Results

Detailed results are provided in the Appendix (Table A-1). The estimated scale parameter

(σ ) for all simulation runs was 0.24. Ignoring all factors (spatial distribution and density of

objects, and length, layout, and number of transects) RMSE% was 26.8%, Bias% was 3.9%,

CV( D̂ ) was 60.4%, and the 95% CI of D̂ contained TD 83.2% of the time, 11.3% of the time it

was underestimated (below the lower limit of CI), and 5.5% of the time it was overestimated

(above upper limit of CI) (Table 2-1). Accuracy, as well as bias and precision, of estimates of

density varied among spatial distribution patterns and densities of objects depending upon the

length, layout, and number of transects (Table 2-1).

The Bias% across all three spatial distributions (clumped, random and uniform) was less

than 10%. RMSE% ranged from 8.5% to 36.4%, and CV( D̂ ) ranged from 55.0% to 63.4%

depending upon the spatial distribution of objects (Table 2-1). The probability of detecting an

object in the strip of area (2wL p̂ ) was 79.5%, 79.4%, and 83.8% for clumped, random, and

uniform distributions respectively and did not vary substantially within spatial distributions.

Clumped Distribution

Ignoring all other factors, RMSE% was 36.4%, Bias% was 6.1%, CV ˆ( )D was 63.4%, and

95% CI of D̂ contained 67.9% of the time, 20.0% of the time it was underestimated, and

12.1% of the time it was overestimated (Table 2-1). The number of objects detected as a

percentage of the total number of objects simulated was 4.9%, 9.9% and 14.8% when using a

transect density of 10 m ha

TD

-1, 20 m ha-1, and 30 m ha-1 respectively.

Effects of object density

Estimates of density were less biased when object density was the highest. Bias% ranged

from 9.6% when object density was 2 objects ha-1 to 5.6% when object density was 10 objects

ha-1. RMSE% ranged from 37.3% when object density was 2 objects ha-1 to 31.9% when object

density was 10 objects ha-1, with no clear trend. CV ˆ( )D ranged from 33.0% when object density

was 2 objects ha-1 to 30.1% when object density was 10 objects ha-1, with no clear trend (Table

2-1). Surprisingly, the percentage of times 95% CI of D̂ contained was only 64.3% to 72.6%

depending upon object density, with no clear trend (Table 2-1). The percentage of times it was

TD

43

underestimated ranged from 18.5% to 21.5%, and the percentage of times it was overestimated

ranged from 8.8% to 13.3% (Table 2-1).

Effects of object density and transect length

Accuracy of estimates of density increased with increasing transect density for all object

densities with RMSE% ranging from 22.7% to 49.7% depending upon object density and

transect density (Figure 2-3A). When object density was low, Bias% decreased from 13.7% to

6.4% with increasing transect density, however, when object density was medium or high, Bias%

ranged from 5.3% to 6.8%, with no clear trend (Table A-1). Precision ranged from 21.2% to

42.1% depending upon object density and transect density (Table A-1). For all object densities,

the percentage of times 95% CI of D̂ contained increased with increasing transect density.

The range of values was 59.4% to 76.5% (Figure 2-4A) depending upon object density and

transect density.

TD

Effects of object density and transect layout

RMSE% ranged from 28.1% to 40.4% depending upon object density and transect layout,

with no clear trend (Figure 2-5A). For all object densities the bias of estimates of density was

less for a systematic transect layout, however precision was lower. Bias% ranged from 5.0% to

17.6%, and CV ˆ( )D ranged from 25.7% to 33.4% (Table A-1) depending upon object density and

transect layout. The percentage of times 95% CI of D̂ contained ranged from 61.3% to

73.7% with no clear trend (Figure 2-6A).

TD

Effects of object density and transect number

RMSE% ranged from 31.5% to 37.5% depending upon object density and transect layout,

with no clear trend (Figure 2-7A). For all object densities the bias of estimates of density when

using few long transects was less than when using several short transects, however, the precision

44

was lower. Bias% ranged from 4.9% to 11.0%, and CV ˆ( )D ranged from 29.4% to 33.6% (Table

A-1) depending upon object density and transect number. The percentage of times 95% CI of D̂

contained ranged from 63.0% to 73.1% and there was no clear trend (Figure 2-8A). TD

Effects of object density, and transect length, layout, and number

Taking into account all factors for a clumped object distribution, the lowest RMSE% was

17.8% for an object density of 6 objects ha-1, a transect density of 30 m ha-1, a random transect

layout, and few long transects. Bias% was 2.8%, CV ˆ( )D was 17.5%, and 95% CI of D̂

contained 78.0% of the time. TD

Random Distribution

Ignoring all other factors, RMSE% was 8.5%, Bias% was 0.7%, CV ˆ( )D was 55%, and the

95% CI of D̂ contained 94.0% of the time, 3.6% of the time it was underestimated, and

2.4% of the time it was overestimated (Table 2-1). The number of objects detected as a

percentage of the total number of objects simulated was 4.7%, 9.5% and 14.2% when using a

transect density of 10 m ha

TD

-1, 20 m ha-1, and 30 m ha-1 respectively.

Effects of object density

Accuracy of estimates of density increased with increasing object density. RMSE%

decreased from 14.3% when object density was 2 objects ha-1 to 6.6% when object density was

10 objects ha-1 (Table 2-1). Precision of estimates of density increased with increasing object

density. CV ˆ( )D decreased from 14.1% when object density was 2 objects ha-1 to 6.5% when

object density was 10 objects ha-1 (Table 2-1). Bias% ranged from 0.5% to 1.7% depending upon

object density with no clear trend (Table 2-1). The percentage of times 95% CI of D̂ contained

ranged from 93.5% to 94.4% with no clear trend (Table 2-1). The percentage of times it was TD

45

underestimated ranged from 3.0% to 4.1%, and the percentage of times it was overestimated

ranged from 2.1% to 2.7% (Table 2-1).

Effects of object density and transect length

Accuracy of estimates of density increased with increasing transect density for all object

densities. RMSE% ranged from 5.0% to 17.7% depending upon object density and transect

density (Figure 2-3B). Bias% ranged from 0.2% to 1.9% depending upon object density and

transect density with no clear trend (Table A-1). Precision of estimates of density increased with

increasing transect density with CV ˆ( )D ranging from 4.9% to 17.5% depending upon object

density and transect density (Table A-1). The percentage of times 95% CI of D̂ contained

ranged from 93.1% to 95.1% with no clear trend (Figure 2-4B).

TD

Effects of object density and transect layout

Accuracy of estimates of density was slightly higher when using a systematic transect

layout for all object densities. RMSE% ranged from 6.5% to 14.5% depending upon object

density and transect layout (Figure 2-5B). Bias% ranged from 0.3% to 1.6% depending upon

object density and transect layout with no clear trend (Table A-1). Precision of estimates of

density was slightly higher when using a systematic transect layout for all object densities.

CV ˆ( )D ranged from 6.5% to 14.2% depending upon object density and transect layout (Table

A-1). The percentage of times 95% CI of D̂ contained ranged from 93.2% to 94.8% with no

clear trend (Figure 2-6B).

TD

Effects of object density and transect number

For all object densities there was no clear trend in the effect of transect number on

accuracy of estimates of density. RMSE% ranged from 6.5% to 14.6% (Figure 2-7B), Bias%

ranged from 0.3% to 2.0%, and CV ˆ( )D ranged from 6.4% to 14.2% depending upon object

46

density and transect number (Table A-1). The percentage of times 95% CI of D̂ contained D

ranged from 93.1% to 94.8% with no clear trend (Figure 2-8B).

Effects of object density, and transect length, layout, and num

T

ber

lowes SE% was 4.8%

for

Taking into account all factors for a random object distribution, the t RM

an object density of 10 objects ha-1, a transect density of 30 m ha-1, a systematic transect

layout, and several short transects. Bias% was 0.4%, CV ˆ( )D was 4.8%, and 95% CI of D̂

contained TD 94.7% of the time.

Uniform Distribution

For a uniform distribution, ignoring all other factors, RMSE% was 28.1%, Bias% was

5.0%, CV ˆ( )D was 62.1%, and 95% CI of D̂ contained TD 87.5% of the time, 10.4% of the t

it was underestimated, and 2.1% of the tim it was overestimated (Table 2-1). For a uniform

distribution the number of objects detected as a percentage of the total number of objects

simulated was 4.7%, 9.5%, and 14.1% when using a transect density of 10 m ha

ime

e

-1, and

-1

y

end in the effect of object density on accuracy of estimates of density.

RMS

-1, 20 m ha

30 m ha respectively.

Effects of object densit

There was no clear tr

E% ranged from 8.8% to 28.4%, Bias% ranged from 3.7% to 10.1%, and CV ˆ( )D ranged

from 8.3% to 24.6% depending upon object density (Table 2-1). The percentage of es 95% C

of ˆ

tim I

D contained TD ranged from 88.0% to 92.8% with no clear trend (Table 2-1). The

per ntage of tim it was underestimated ranged from 4.0% to 15.3%, and the percenta

times if was overestimated ranged from 0.3% to 3.3% (Table 2-1).

ce es ge of

47

Effects of object density and transect length

estimates of density increased with increasing

transe

%

n

f

When object density was low, accuracy of

ct density, however for medium or high object densities, there was no clear trend in the

effect of object density on accuracy of estimates of density. RMSE% ranged from 7.2% to 47.8

depending upon object density and transect density (Figure 2-3C). Bias% ranged from 1.0% to

24.7% depending upon object density and transect density with no clear trend (Table A-1). Whe

object density was low, precision of estimates of density increased with increasing transect

density, however for medium or high object densities, there was no clear trend in the effect o

object density on the precision of estimates of density. CV ˆ( )D ranged from 5.4% to 32.7%

depending upon object density and transect density (Table A-1). The percentage of times 95%

of ˆ

CI

D contained TD ranged from 62.0% to 98.6% with no clear trend (Figure 2-4C).

Effects of object density and transect layout

For all object densities the accuracy of estimates of density was significantly higher when

using a random transect layout. RMSE% ranged from 4.9% to 32.6% (Figure 2-5C), Bias%

ranged from 0.1% to 13.5%, CV ˆ( )D ranged from 4.9% to 27.0% (Table A-1), and the

percentage of times 95% CI of D̂ contained TD ranged from 77.2% to 99.3% dependin

object density and transect layout (Figure 2-6C).

Effects of object density and transect number

g upon

ates of density was higher when using several

short

cision

For all object densities the accuracy of estim

transects with RMSE% ranging from 8.5% to 28.8% depending upon object density and

transect number (Figure 2-7C). Bias% ranged from 3.3% to 12.2% depending upon object

density and transect number with no clear trend (Table A-1). For all object densities the pre

of estimates of density was higher when using several short transects with CV(D) ranging from

48

8.1% to 25.4% depending upon object density and transect number (Table A-1). The percentage

of times 95% CI of D̂ contained TD ranged from 79.8% to 93.3% and was slightly higher when

using several short transects (Figure 2-8C).

Effects of object density, and transect length, layout, and number

lowest RMSE% was

2.6

Taking into account all factors for a uniform object distribution, the

% for an object density of 6 objects ha-1, a transect density of 30 m ha-1, a random transect

layout, and several short transects. Bias% was 0.2%, CV ˆ( )D was 2.6%, and 95% CI of D̂

contained TD 100.0% of the time.

Discussion

Accuracy of estimates of abundance this method may vary with respect to

spatia

er of

ary

, and number of

transe l

) For a

influence accuracy of density estimates?

obtained from

l distribution and density of objects, but it is typically not possible to alter the spatial

distribution or density study objects. However, it might be possible to improve accuracy of

estimates of density through study design, for example, by altering layout, length, and numb

transects. This, however, requires an understanding of how layout, length, and number of

transects influence accuracy of estimates of densities, and of how these influences might v

depending upon the spatial distribution pattern and density of study objects.

I conducted a simulation study to determine the effect of length, layout

cts on estimates of density and the precision of these estimates for different object spatia

distributions and densities. Specifically, I asked the following questions: (1) How does accuracy

and of estimates of abundance obtained from the line transect method vary across spatial

distribution patterns? (2) How might these patterns be influenced by density of objects? (3

given spatial distribution and density level, how does the layout, length, and number of transects

49

Overall, density estimated using the line transect method was within 3.9% of the true

density, but it varied substantially depending upon spatial distribution pattern of objects (Table

2-1). this

y

ightly

ensity

n of objects was clumped. Bias of estimates of density increased

with i

ere

ias,

The line transect method was most accurate when objects were distributed randomly; in

case root mean squared error (RMSE) between estimated density and true density was 8.5% of

the true density (Table 2-1). Consequently, this method may be most appropriate for objects or

organisms that exhibit a random distribution pattern. In contrast, the line transect method was

least accurate when object were distributed in a clumped pattern; in this case the root mean

squared error (RMSE) between estimated density and true density was 36.4% of the true densit

(Table 2-1). The spatial distribution of objects did not seem to substantially influence the

precision of estimates of density (Table 2-1). The percentage of times 95% CI of estimated

density contained true density was highest for a random distribution of objects (94.0%), sl

less for a uniform distribution of objects (87.5%), and lowest for a clumped distribution of

objects (67.9%) (Table 2-1).

There was no clear trend for the effect of object density on accuracy of estimates of d

when the pattern of distributio

ncreasing object density, but there was no clear trend for precision of estimates of density.

When objects were distributed randomly, accuracy of estimates of density increased with

increasing object density. Precision of estimates of density increased with increasing object

density; however, there was no clear trend in bias of estimates of density. When objects w

distributed uniformly, there was no clear trend for the effect of object density on accuracy, b

or precision of estimates of density. The percentage of times 95% CI of estimated density

contained the true density did not seem to be affected by object density for any object

distribution.

50

The results of my study were consistent with most of my hypotheses. The line tra

method worked well for a random

nsect

distribution of objects (RMSE% was 8.5% of the true

densi

density;

effect

y was

ed

rovide a basis for adequate variance

estim al

ty). However, accuracy of estimates of density was less than desired for a uniform

distribution of objects (RMSE% was 28.1% of the true density) (Table 2-1). For a random

distribution of objects, precision of estimates of density increased with increasing object

however, when object distribution was clumped or uniform, there was no clear trend in the

of object density on precision of estimates of density. Consistent with my hypothesis, accuracy

of estimates of density increased with an increasing transect length for random and clumped

distributions. However, for a uniform distribution of objects with medium and high object

density, there was no clear trend in the effect of transect length on accuracy of estimates of

density (Figures 2-3A, 2-3B, and 2-3C). Consistent with my hypothesis, for a clumped

distribution of objects, a random transect layout worked better than when using a systematic

transect layout when object density was medium and high, however, when object densit

low, a systematic transect layout provided slightly greater accuracy (Figure 2-5A). Transect

number did not seem to have a substantial effect on accuracy of estimates of density for all

object densities (Figure 2-7A). Consistent with my hypothesis, a random transect layout work

very well when objects were distributed uniformly (Figure 2-5C), and when objects were

distributed randomly, transect layout and transect number did not have a substantial effect on the

accuracy of estimates of density (Figures 2-5B and 2-7B).

Buckland et al. (2001) note the importance of replication of transects and stress that a

minimum of 10 to 20 replicate lines should be surveyed to p

ation. In my study, the average number of transects simulated for each of the three spati

distributions (clumped, random, and uniform) was approximately 11 and 18 when using few long

51

transects and several short transects respectively. Additionally, Buckland et al. (2001) note that a

systematic placement of lines provides better spatial coverage and has superior precision to lines

that are randomly and independently distributed. In my study, transect layout did not seem to

affect the spatial coverage of transects, and the number of objects detected as a percentage of the

total number of objects simulated ranged from 9 to 10% for both random and systematic transe

layouts for all spatial distributions. However, transect layout did have an influence on the

precision of estimates of abundance. For a clumped distribution, a random transect layout

provided greater precision than using a systematic transect layout for all object densities. F

random distribution, using a systematic transect layout provided slightly greater precision f

object densities. For a uniform distribution, using a random transect layout provided substantiall

greater precision for all object densities (Table A-1).

Williams et al. (2002) note that systematic positioning of transects is acceptable if the

animal or object locations are random, else random tra

ct

or a

or all

y

nsect placement is necessary to ensure

accur

ties

e

,

found that transect lengths did not

ate statistical inferences. My results were consistent with this observation. I found that

when objects followed a random distribution, results from the line transect method using a

systematic transect layout and a random transect layout were very similar for all object densi

(Figures 2-5B and 2-6B, and Table A-1). However, for uniformly distributed objects, the lin

transect method worked better when using a random transect layout than a systematic transect

layout (Figures 2-5C and 2-6C, and Table A-1). When objects followed a clumped distribution

results from the line transect method using a systematic transect layout and a random transect

layout were similar (Figures 2-5A and 2-6A, and Table A-1).

Fowler (1986) conducted a study to assess the effect of transect length on estimates of

density and precision for species of coral reef fish. The study

52

signif

y

d

f

icantly affect estimates of density; however, precision was variable with the smallest

transect length providing the least precise estimates of density. In my study, for a clumped

distribution, accuracy of estimates of density (Figure 2-3A), precision of estimates of densit

(Table A-1), and 95% CI coverage of TD (Figure 2-4A) increased with increasing transect

density for all object densities. For a random distribution, accuracy of estimates of density

(Figures 2-3B), and precision of estima of density (Table A-1) increased with increasing

transect density for all object densities. However increasing transect density did not seem to

significantly influence the 95% CI coverage of TD for any object density (Figure 2-4B). For a

uniform distribution with low and object density, increasing the transect density increased the

accuracy and precision of estimates of density (F ure 2-3C and Table A-1). However, there

seemed to be a contradictory effect on estimates of density when object density was medium an

high (Figures 2-3C and 2-4C). One reason for this could be the relatively poor performance o

the line transect method for a uniform distribution with an object density of 10 objects ha-1, a

transect density of 20 m ha-1, and a systematic transect layout (RMSE% = 55.1%, Bias% =

32.7%, CV ˆ( )

tes

ig

D = 33.3%, and 95% CI coverage of TD = 50.7%).

Conclusion

For objects that are distributed in a clumped distribution, there was no clear trend in the

effect of object density on accuracy of esti dance. Bias of estimates of density

decre

f

mates of abun

ased as object density was increased; however, there was no clear trend in the effect of

object density on precision of estimates of abundance. The percentage of times the 95% CI o

estimated density contained true density was very low for a clumped distribution of objects

which is troubling because most organisms occur in clumped distributions. There was no

significant effect of transect layout on estimates of abundance. I recommend using a higher

53

transect length as this increased the accuracy of estimates of density, and the 95% CI cove

true density. The number of transects did not have a significant effect on accuracy of estimat

abundance.

For objects that are distributed in a random distribution, accuracy of estimates of

abundance in

rage of

es of

creased with increasing object density. I recommend using a systematic transect

layou dom

ial.

of

or all object densities, I recommend using a random transect layout as

this p

t

cts.

t as accuracy of estimates of abundance was slightly greater than when using a ran

transect layout. I also recommend using a higher transect length as accuracy of estimates of

abundance increased with increasing transect density; however, this increase was not substant

The number of transects (few long, or several short) did not significantly affect the accuracy

estimates of abundance.

For objects distributed in uniform distribution, the line transect method worked best for a

medium object density. F

rovided significantly greater accuracy than when using a systematic transect layout. When

using a random transect layout, total transect length increased the accuracy of estimates of

abundance and I recommend using a higher transect length. I also recommend using several shor

transects as accuracy of estimates of abundance was higher than when using few long transe

54

Table 2-1. Density estimates by object spatial distribution and density

Input TD D̂ 95% CI( D̂ ) RMSE% CV( D̂ ) Bias% 95% DCI Under Over

Overall 5.94 6.17 6.12 – 6.22 26.8% 60.4% 3.9% 83.2% 11.3% 5.5%

Clumped

5.79 6.14 5.72 – 5.86 36.4% 63.4% 6.1% 67.9% 20.0% 12.1%

2 objects ha-1 1.97 2.13 2.13 – 2.19 37.3% 33.0% 9.6% 72.6% 18.5% 8.8%

6 objects ha-1 5.75 6.08 6.01 – 6.16 31.6% 29.7% 5.8% 64.3% 21.5% 14.2%

10 objects ha-1 9.65 10.19 10.07 – 10.32 31.9% 30.1% 5.6% 66.9% 19.8% 13.3%

Random 6.00 6.04 5.92 – 6.08 8.5% 55.0% 0.7% 94.0% 3.6% 2.4%

2 objects ha-1 2.00 2.03 2.02 – 2.04 14.3% 14.1% 1.5% 93.5% 4.1% 2.4%

6 objects ha-1 6.00 6.03 6.01 – 6.05 8.4% 8.4% 0.5% 94.3% 3.0% 2.7%

10 objects ha-1 10.00 10.07 10.05 – 10.10 6.6% 6.5% 0.7% 94.4% 3.5% 2.1%

Uniform 6.02 6.32 5.94 – 6.09 28.1% 62.1% 5.0% 87.5% 10.4% 2.1%

2 objects ha-1 2.00 2.20 2.19 – 2.22 21.5% 17.2% 10.1% 88.0% 11.8% 0.3%

6 objects ha-1 6.04 5.81 5.80 – 5.83 8.8% 8.3% 3.7% 92.8% 4.0% 3.3%

10 objects ha-1 10.01 10.94 10.83 – 11.05 28.4% 24.6% 9.2% 81.9% 15.3% 2.8%

Note: is the true object density, TD D̂ is the estimated object density, 95% CI( D̂ ) is the 95% confidence interval of D̂ , RMSE% is the root mean squared error between D̂ and as a percentage of , CV( ˆ

TD TD D ) is the coefficient of variation of D̂ , Bias% is the mean difference between D̂ and TD as a percentage of TD , 95% DCI is the percentage of times that the 95% CI computed by Program DISTANCE for D̂ contained , ‘Under’ is the percentage of times that was below the lower limit of TD TD 95% DCI , and ‘Over’ is the percentage of times that D was above the upper limit of 95%T DCI .

55

0 5 10 15 20 250

5

10

15

20

25

A)

0 5 10 15 20 250

5

10

15

20

25

B)

Figure 2-1. Examples of simulated spatial distributions of objects with a density of 2 objects ha-1. A) For a clumped distribution. B) For a random distribution. C) For a uniform distribution.

56

0 5 10 15 20 250

5

10

15

20

25

C)

Figure 2-1. Continued

57

0 5 10 15 20 250

5

10

15

20

25

A)

Figure 2-2. Transect layout patterns with objects simulated in a random spatial distribution with a density of 2 objects ha , and a transect density of 10 m ha-1 -1. For the systematic layouts the starting x and y coordinates for the first transect line were chosen as 10 and 10 respectively to ensure that all transects fell inside the study area. A) Random transect layout with ‘few long transects’. B) Random transect layout with ‘several short transects’. C) Systematic transect layout with ‘few long transects’. D) Systematic transect layout with ‘several short transects’.

58

0 5 10 15 20 250

5

10

15

20

25

B)

0 5 10 15 20 250

5

10

15

20

25

C)

Figure 2-2. Continued

59

0 5 10 15 20 250

5

10

15

20

25

D)

Figure 2-2. Continued

60

A)

0

10

20

30

40

50

60

10 m ha-1

20 m ha-1

30 m ha-1

Object density (Objects ha-1)2 6 10

Transect Density

RM

SE%

Figure 2-3. Effect of transect length on accuracy of estimates of density for a given object spatial

distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The root mean squared error between estimated object density ( D̂ ) and true object density ( ) as a percentage of (RMSE%) is plotted against transect density (m haTD TD -1) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution.

61

0

2

4

6

8

10

12

14

16

18

20

10 m ha-1

20 m ha-1

30 m ha-1

Object density (Objects ha-1)2 6 10

Transect Density

RM

SE%

B)

0

10

20

30

40

50

60

10 m ha-1

20 m ha-1

30 m ha-1

Object density (Objects ha-1)2 6 10

Transect Density

RM

SE%

C)

Figure 2-3. Continued

62

95%

CI o

f den

sity

est

imat

e

0

20

40

60

80

100

10 m ha-1

20 m ha-1

30 m ha-1

Object density (Objects ha-1)2 6 10

Transect density

A)

Figure 2-4. Effect of transect length on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The percentage of times that the 95% CI computed by Program DISTANCE for each density estimate ( D̂ ) contained true object density ( ) is plotted against transect density (m ha

TD-1) for different object densities. A) In a clumped distribution. B) In a

random distribution. C) In a uniform distribution.

63

95%

CI o

f den

sity

est

imat

e

0

20

40

60

80

100

10 m ha-1

20 m ha-1

30 m ha-1

Object density (Objects ha-1)2 6 10

Transect density

B)95

% C

I of d

ensi

ty e

stim

ate

0

20

40

60

80

100

120

10 m ha-1

20 m ha-1

30 m ha-1

Object density (Objects ha-1)2 6 10

Transect density

C)

Figure 2-4. Continued

64

0

10

20

30

40

50

RandomSystematic

Object density (Objects ha-1)2 6 10

Transect layout

RM

SE%

A)

Figure 2-5. Effect of transect layout on accuracy of estimates of density for a given object spatial

distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The root mean squared error between estimated object density ( D̂ ) and true object density ( ) as a percentage of (RMSE%) is plotted against transect layout (random, and systematic) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution.

TD TD

65

0

2

4

6

8

10

12

14

16

RandomSystematic

Object density (Objects ha-1)2 6 10

Transect layout

RM

SE%

B)

0

5

10

15

20

25

30

35

RandomSystematic

Object density (Objects ha-1)2 6 10

Transect layout

RM

SE%

C)

Figure 2-5. Continued

66

95%

CI o

f den

sity

est

imat

e

0

20

40

60

80

RandomSystematic

Object density (Objects ha-1)2 6 10

Transect layout

A)

Figure 2-6. Effect of transect layout on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The percentage of times that the 95% CI computed by Program DISTANCE for each density estimate ( D̂ ) contained true object density ( ) is plotted against transect density (m ha

TD-1) for different object densities. A) In a clumped distribution. B) In a

random distribution. C) In a uniform distribution.

67

95%

CI

of d

ensi

ty e

stim

ate

0

20

40

60

80

100

RandomSystematic

Object density (Objects ha-1)2 6 10

Transect layout

B)

95%

CI

of d

ensi

ty e

stim

ate

0

20

40

60

80

100

120

RandomSystematic

Object density (Objects ha-1)2 6 10

Transect layout

C)

Figure 2-6. Continued

68

0

10

20

30

40

Few longSeveral short

Object density (Objects ha-1)2 6 10

Transect number

RM

SE%

A)

Figure 2-7. Effect of transect number on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The root mean squared error between estimated object density ( D̂ ) and true object density ( ) as a percentage of (RMSE%) is plotted against transect layout (random, and systematic) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution.

TD TD

69

0

2

4

6

8

10

12

14

16

Few longSeveral short

Object density (Objects ha-1)2 6 10

Transect number

RM

SE%

B)

0

5

10

15

20

25

30

35

Few longSeveral short

Object density (Objects ha-1)2 6 10

Transect number

RM

SE%

C)

Figure 2-7. Continued

70

Dis

tanc

e 95

% C

I

0

20

40

60

80

FewlongSeveralshort

Object density (Objects ha-1)2 6 10

Transect number

A)

Figure 2-8. Effect of transect number on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The percentage of times that the 95% CI computed by Program DISTANCE for each density estimate ( D̂ ) contained true object density ( ) is plotted against transect density (m ha

TD-1) for different object densities. A) In a clumped distribution. B) In a

random distribution. C) In a uniform distribution.

71

95%

CI o

f den

sity

est

imat

e

0

20

40

60

80

100

FewlongSeveralshort

Object density (Objects ha-1)

2 6 10

Transect number

B)

95%

CI o

f den

sity

est

imat

e

0

20

40

60

80

100

FewlongSeveralshort

Object density (Objects ha-1)2 6 10

Transect number

C)

Figure 2-8. Continued

72

CHAPTER 4 CONCLUSION

The overall goal of my research was to analyze abundance estimation methods using real

and simulated data. I field-tested the efficacy and cost-effectiveness of line transect, total count,

sample count, and double observer methods for estimating gopher tortoise burrow abundance. I

applied these methods to estimate burrow abundance in two strata in the Ordway Swisher

Biological Station, Florida. Additionally, I also addressed the issue of gopher tortoise burrow

occupancy, and used estimates of burrow abundance and occupancy rates to estimate abundance

of gopher tortoises. I then further analyzed the line transect method using a simulation-based

approach in MATLAB.

The results of my field study indicated that habitat type of the study area, and available

time and resources should be taken into consideration when selecting an abundance estimation

method. The line transect method is perhaps the most efficient method for estimating gopher

tortoise burrow abundance because it is less costly than total and sample count methods, and it is

more likely to capture a wider range of spatial variation in the distribution and abundance of

burrows, while providing statistically robust estimates of precision. However, a good

understanding of the method as well as some understanding of underlying theory and working

knowledge of Program DISTANCE is needed for effective implementation of this method.

If one wishes to implement the total count or sample count method, I recommend using

multiple observers in order to obtain estimates of detectability. The total count and sample count

methods are relatively straightforward to implement, and require no sophisticated software for

data analyses. However, these methods are costly, particularly when a substantial proportion of

the sites needed to be sampled. Moreover, these methods do not offer rigorous estimates of

73

74

precision. The double observer method partially addressed some of these concerns by providing

estimates of precision (when detectability is less than one), but is costly to implement.

My estimates of burrow occupancy rates (active: 0.50 ± 0.09; inactive: 0.04 ± 0.04) were

substantially lower than Auffenberg and Franz’s ‘correction factor’ of 61.4% (Auffenberg and

Franz 1982). Some studies have used this or a similar correction factor (e.g., Ashton and Ashton

(in press)) for converting estimates of burrow abundance to tortoise abundance (Kushlan and

Mazotti 1984, Doonan 1986, Doonan and Epperson 2001, FFWCC 2006, Gregory et al. 2006).

However, this approach ignores the spatial, temporal or habitat-specific variation in occupancy

rate and can cause estimates of gopher tortoise abundance to be unreliable (Burke and Cox 1988,

Breininger et al. 1991, McCoy and Mushinsky 1992, Moler and Berish 2001). I recommend that

burrow cameras (or similar technologies) should be used, along with a patch occupancy

modeling approach for data analysis, to estimate habitat-specific burrow occupancy rates.

The results of the simulation study provided valuable information about the influence of

length, layout and number of transects on the accuracy of estimates of abundance for different

spatial distribution patterns and density levels of objects. The accuracy of estimates of abundance

obtained from the line transect method varied substantially depending upon spatial distribution

pattern of objects. The line transect method was most accurate when objects were distributed

randomly. Consequently, this method may be most appropriate for objects or organisms that

exhibit a random distribution pattern. In contrast, the line transect method was least accurate

when object were distributed in a clumped pattern, which is troubling because most organisms

occur in clumped distributions. Increasing transect length had a positive effect on the accuracy of

estimates of abundance for random and clumped spatial distributions of objects, and I

recommend that researchers use, at a minimum, a transect length that will provide 60 to 80

observations as recommended by Buckland et al. (2001). For a clumped distribution of objects,

the positive effect of an increasing transect length on accuracy of estimates of abundance was

greater, as this likely captured the greater spatial variation in distribution of objects, and I

recommend that researchers try to maximize the total transect length when determining study

design.

Transect layout pattern had a significant effect for a uniform distributions of objects; in

this case, accuracy and precision of estimates of abundance were substantially higher, and bias

was lower when using a random transect layout. Furthermore, when using a random transect

layout, increasing transect length increased the accuracy of estimates of abundance. For a

random distribution of objects, using a systematic transect layout provided slightly greater

accuracy than when using a random transect layout. For a clumped distribution, there was no

significant effect of transect layout on estimates of abundance.

The number of transect used did not significantly affect the accuracy of estimates of

abundance when the object distribution pattern was random or clumped. However, for a uniform

distribution of objects, accuracy of estimates of abundance was higher when using several short

transects than when using few long transects.

75

APPENDIX OVERALL RESULTS

76

Table A-1. Simulation study results Dist ODens TDens TL TNum TD D̂ 95% CI( D̂ ) RMSE RMSE% CV( D̂ ) Bias% 95% DCI Sim Runs - - - - - 5.94 6.17 6.12 – 6.22 1.59 26.8% 60.4% 3.9% 83.2% 21600

clumped

- - - - 5.79

6.14

5.72 – 5.86

2.11

36.4%

63.4%

6.1%

67.9%

7200

random

- - - - 6.00

6.04

5.92 – 6.08

0.51

8.5%

55.0%

0.7%

94.0%

7200

uniform

- - - - 6.02

6.32

5.94 – 6.09

1.69

28.1%

62.1%

5.0%

87.5%

7200

clumped

2 - - - 1.97

2.16

2.13 – 2.19

0.73

37.3%

33.0%

9.6%

72.6%

2400

clumped

6 - - - 5.75

6.08

6.01 – 6.16

1.82

31.6%

29.7%

5.8%

64.3%

2400

clumped

10 - - - 9.65

10.19

10.07 – 10.32

3.08

31.9%

30.1%

5.6%

66.9%

2400

random

2 - - - 2.00

2.03

2.02 – 2.04

0.29

14.3%

14.1%

1.5%

93.5%

2400

random

6 - - - 6.00

6.03

6.01 – 6.05

0.51

8.4%

8.4%

0.5%

94.3%

2400

random

10 - - - 10.00

10.07

10.05 – 10.10

0.66

6.6%

6.5%

0.7%

94.4%

2400

uniform

2 - - - 2.00

2.20

2.19 – 2.22

0.43

21.5%

17.2%

10.1%

88.0%

2400

uniform 6 - - - 6.04 5.81 5.80 – 5.83 0.53 8.8% 8.3% 3.7% 92.8% 2400Note: Dist is the spatial distribution of objects, ODens is the density of objects in objects ha-1, TDens is the transect density in m ha-1, TL is the transect layout (‘r’ is random, and ‘s’ is systematic), TNum is the transect number (‘f’ is few long, and ‘s’ is several short), TD is the true object density in objects ha-1, D̂ is the estimated object density in objects ha-1, 95% CI( D̂ ) is the 95% confidence interval of D̂ , RMSE is the root mean squared error between D̂ and TD , RMSE% is RMSE as a percentage of TD , CV( D̂ ) is the coefficient of variation of D̂ , Bias% is the mean of the difference between D̂ and TD as a percentage of TD , 95% DCI is the percentage of times that the 95% CI computed by Program DISTANCE for D̂ covered TD , and ‘Sim runs’ indicates the total number of simulation runs upon which the associated results are based.

77

Table A-1. Continued Dist ODens TDens TL TNum TD D̂ 95% CI( D̂ ) RMSE RMSE% CV( D̂ ) Bias% 95% DCI Sim Runs uniform

10

- - - 10.01

10.94

10.83 – 11.05

2.85

28.4%

24.6%

9.2%

81.9%

2400

clumped

- 10 - - 5.79

6.17

6.00 – 6.34

2.70

46.6%

68.1%

8.4%

64.0%

2400

clumped

- 20 - - 5.79

6.17

6.01 – 6.32

1.92

33.2%

62.2%

6.9%

68.4%

2400

clumped

- 30 - - 5.79

6.09

5.95 – 6.24

1.55

26.7%

59.4%

5.5%

71.4%

2400

random

- 10 - - 6.00

6.05

5.92 – 6.19

0.65

10.8%

55.5%

0.9%

93.9%

2400

random

- 20 - - 6.00

6.03

5.90 – 6.17

0.46

7.7%

54.9%

0.8%

93.8%

2400

random

- 30 - - 6.00

6.04

5.91 – 6.17

0.37

6.2%

54.6%

1.0%

94.4%

2400

uniform

- 10 - - 6.02

5.97

5.84 – 6.10

0.61

10.1%

53.5%

2.0%

95.5%

2400

uniform

- 20 - - 6.02

6.87

6.68 – 7.07

2.79

46.4%

71.2%

10.7%

77.8%

2400

uniform

- 30 - - 6.02

6.11

5.98 – 6.25

0.64

10.6%

55.7%

3.0%

89.3%

2400

clumped

- - r - 5.79

6.27

6.09 – 6.44

1.90

32.8%

60.3%

10.4%

72.8%

1800

clumped

- - s - 5.76

6.10

6.00 – 6.21

2.18

37.6%

64.4%

5.8%

66.3%

5400

random

- - r - 6.00

6.04

5.88 – 6.19

0.53

8.8%

55.0%

0.9%

93.8%

1800

random

- - s - 6.00

6.05

5.96 – 6.11

0.50

8.4%

55.0%

0.9%

94.1%

5400

uniform

- - r - 6.01

6.02

5.88 – 6.19

0.48

8.0%

55.3%

0.1%

97.9%

1800

uniform

- - s - 6.02

6.41

6.30 – 6.52

1.93

32.1%

63.9%

6.9%

84.1%

5400

clumped - - - f 5.79 6.11 5.98 – 6.21 2.11 36.4% 63.5% 6.1% 68.2% 3600

78

Table A-1. Continued Dist ODens TDens TL TNum TD D̂ 95% CI( D̂ ) RMSE RMSE% CV( D̂ ) Bias% 95% DCI Sim Runs clumped - - - s 5.79 6.18 6.06 – 6.31 2.11 36.5% 63.2% 7.7% 67.7% 3600

random

- - - f 6.00

6.05

5.94 – 6.16

0.52

8.6%

55.1%

0.8%

94.1%

3600

random

- - - s 6.00

6.04

5.93 – 6.15

0.50

8.3%

54.8%

1.0%

94.0%

3600

uniform

- - - f 6.02

6.30

6.17 – 6.42

1.72

28.5%

61.8%

5.5%

86.1%

3600

uniform

- - - s 6.02

6.34

6.21 – 6.47

1.67

27.7%

62.4%

4.9%

88.9%

3600

clumped 2 10 - - 1.97 2.24 2.17 – 2.30 0.98 49.7% 42.1% 13.7% 68.4% 800clumped 2 20 - - 1.97 2.14 2.09 – 2.18 0.65 33.1% 29.5% 8.8% 73.0% 800clumped

2 30 - - 1.97

2.09

2.06 – 2.13

0.49

24.7%

22.8%

6.3%

76.5%

800

clumped 6 10 - - 5.75 6.12 5.96 – 6.28 2.35 40.9% 38.2% 6.3% 59.4% 800clumped 6 20 - - 5.75 6.05 5.94 – 6.17 1.65 28.7% 27.1% 5.2% 64.8% 800clumped

6 30 - - 5.75

6.08

5.99 – 6.17

1.30

22.7%

21.2%

5.6%

68.8%

800

clumped 10 10 - - 9.64 10.16 9.89 – 10.43 3.92 40.6% 38.5% 5.3% 64.4% 800clumped 10 20 - - 9.66 10.31 10.12 – 10.51 2.82 29.2% 26.9% 6.7% 67.5% 800clumped

10 30 - - 9.66

10.11

9.95 – 10.27

2.29

23.8%

22.6%

4.6%

68.9%

800

random 2 10 - - 2.00 2.02 2.00 – 2.05 0.35 17.7% 17.5% 1.2% 93.4% 800random 2 20 - - 2.00 2.03 2.01 – 2.05 0.27 13.4% 13.1% 1.5% 93.1% 800random

2 30 - - 2.00

2.04

2.02 – 2.05

0.22

11.2%

10.8%

1.9%

93.9%

800

random 6 10 - - 6.00 6.04 6.00 – 6.09 0.65 10.8%

10.7%

0.7% 94.6% 800random 6 20 - - 6.00 6.01 5.98 – 6.05 0.47 7.8% 7.8% 0.2% 93.3% 800random

6 30 - - 6.00

6.03

6.00 – 6.05

0.35

5.9%

5.9%

0.4%

95.0%

800

random 10 10 - - 10.00 10.09 10.04 – 10.15 0.84 8.4% 8.3% 0.9% 93.8% 800random 10 20 - - 10.00 10.06 10.02 – 10.10 0.60 6.0% 5.9% 0.6% 95.1% 800random

10 30 - - 10.00

10.06

10.03 – 10.10

0.50

5.0%

4.9%

0.6%

94.3%

800

79

Table A-1. Continued Dist ODens TDens TL TNum TD D̂ 95% CI( D̂ ) RMSE RMSE% CV( D̂ ) Bias% 95% DCI Sim Runs uniform 2 10 - - 2.00 2.23 2.20 – 2.26 0.46 23.0% 17.9% 11.5% 91.5% 800 uniform 2

20 - - 2.00 2.18 2.15 – 2.20 0.42 21.1% 17.7% 8.7% 86.1% 800uniform

2 30 - - 2.00

2.20

2.18 – 2.23

0.40

20.1%

15.8%

10.2%

86.3%

800

uniform 6 10 - - 6.04 5.76 5.73 – 5.79 0.54 8.9% 8.0% 4.6% 98.6% 800uniform 6 20 - - 6.04 5.95 5.91 – 5.99 0.61 10.0%

10.1%

1.5% 85.3% 800

uniform

6 30 - - 6.04

5.73

5.71 – 5.76

0.44

7.2%

5.4%

5.0%

94.4%

800

uniform 10 10 - - 10.01 9.92 9.86 – 9.97 0.78 7.8% 7.8% 1.0% 96.4% 800uniform 10 20 - - 10.01 12.49 12.77 – 12.21 4.78 47.8% 32.7% 24.7% 62.0% 800uniform

10 30 - - 10.01

10.41

10.35 – 10.47

0.93

9.3%

8.1%

3.9%

87.4%

800

clumped 2 - r - 1.97 2.31 2.26 – 2.37 0.79 40.4% 31.0% 17.6% 71.3% 600clumped

2 - s - 1.97

2.10

2.07 – 2.14

0.71

36.3%

33.4%

6.9%

73.1%

1800

clumped 6 - r - 5.75 6.10 5.97 – 6.23 1.62 28.1% 26.0% 6.0% 73.3% 600clumped

6 - s - 5.75

6.08

5.99 – 6.16

1.88

32.8%

30.9%

5.6%

61.3%

1800

clumped 10 - r - 9.66 10.39 10.17 – 10.60 2.75 28.5% 25.7% 7.6% 73.7% 600clumped

10 - s - 9.65

10.13

9.98 – 10.28

3.19

33.0%

31.4%

4.9%

64.7%

1800

random 2 - r - 2.00 2.03 2.01 – 2.06 0.29 14.5% 14.2% 1.7% 93.7% 600random

2 - s - 2.00

2.03

2.02 – 2.04

0.29

14.3%

14.0%

1.5%

93.4%

1800

random 6 - r - 6.00 6.02 5.97 – 6.06 0.54 9.0% 8.9% 0.3% 94.5% 600random

6 - s - 6.00

6.03

6.01 – 6.05

0.49

8.2%

8.2%

0.5%

94.2%

1800

random 10 - r - 10.00 10.07 10.01 – 10.12 0.68 6.8% 6.7% 0.7% 93.2% 600random

10 - s - 10.00

10.08

10.05 – 10.11

0.65

6.5%

6.5%

0.8%

94.8%

1800

uniform 2 - r - 2.00 2.00 1.99 – 2.01 0.16 8.1% 8.1% 0.1% 99.3% 600uniform

2 - s - 2.00

2.27

2.25 – 2.29

0.49

24.3%

17.9%

13.5%

84.2%

1800

uniform 6 - r - 6.04 6.01 5.99 – 6.03 0.30 4.9% 4.9% 0.5% 98.5% 600

80

Table A-1. Continued Dist ODens TDens TL TNum TD D̂ 95% CI( D̂ ) RMSE RMSE% CV( D̂ ) Bias% 95% DCI Sim Runs uniform 6 - s - 6.04 5.75 5.73 – 5.77 0.59 9.8% 8.9% 4.8% 90.8% 1800

uniform 10 - r - 10.01 10.08 10.02 – 10.14 0.76 7.6% 7.5% 0.7% 96.0% 600uniform

10 - s - 10.01

11.22

11.08 – 11.36

3.26

32.6%

27.0%

12.1%

77.2%

1800

clumped 2 - - f 1.97 2.13 2.09 – 2.17 0.73 37.1% 33.6% 8.3% 72.2% 1200clumped

2 - - s 1.96

2.18

2.14 – 2.22

0.74

37.5%

32.5%

10.9%

73.1%

1200

clumped 6 - - f 5.75 6.06 5.96 – 6.17 1.83 31.8% 30.1% 5.4% 65.6% 1200clumped

6 - - s 5.75

6.10

6.00 – 6.20

1.81

31.5%

29.4%

6.0%

63.0%

1200

clumped 10 - - f 9.65 10.12 9.95 – 10.29 3.07 31.8% 30.3% 4.8% 66.8% 1200clumped

10 - - s 9.65

10.26

10.09 – 10.44

3.10

32.1%

29.9%

6.3%

67.0%

1200

random 2 - - f 2.00 2.02 2.00 – 2.04 0.28 14.1% 13.9% 1.0% 93.8% 1200random

2 - - s 2.00

2.04

2.02 – 2.06

0.29

14.6%

14.2%

2.0%

93.1%

1200

random 6 - - f 6.00 6.03 6.00 – 6.06 0.52 8.6% 8.6% 0.6% 94.5% 1200random

6 - - s 6.00

6.02

5.99 – 6.05

0.49

8.2%

8.2%

0.3%

94.1%

1200

random 10 - - f 10.00 10.09 10.05 – 10.13 0.67 6.7% 6.6% 0.9% 93.9% 1200random

10 - - s 10.00

10.06

10.02 – 10.09

0.65

6.5%

6.4%

0.6%

94.8%

1200

uniform 2 - - f 2.00 2.24 2.22 – 2.27 0.49 24.3% 18.7% 12.2% 86.3% 1200uniform

2 - - s 2.00

2.16

2.14 – 2.18

0.36

18.2%

15.1%

8.1%

89.6%

1200

uniform 6 - - f 6.04 5.79 5.76 – 5.82 0.55 9.1% 8.5% 4.1% 92.3% 1200uniform

6 - - s 6.04

5.84

5.81 – 5.86

0.51

8.5%

8.1%

3.3%

93.3%

1200

uniform 10 - - f 10.01 10.85 10.70 – 11.01 2.88 28.8% 25.4% 8.4% 79.8% 1200uniform 10 - - s 10.01 11.02 10.88 – 11.17 2.82 28.1% 23.9% 10.1% 84.0% 1200

LIST OF REFERENCES

Abrahamson, W. G. 1984. Species response to fire on the Florida Lake Wales Ridge. American Journal of Botany 71:35-43.

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BIOGRAPHICAL SKETCH

Saif Z. Nomani was born in 1978 in Karachi, Pakistan. He graduated from Karachi

Grammar School in 1996 and attended college at the Lahore University of Management Science,

Lahore, Pakistan. He transferred to Rutgers University, New Brunswick, NJ, in January 1998.

Upon graduating in January 2002 with his B.S. in computer science he worked as a physical

security consultant at Constantin Walsh-Lowe LLC. After 4 years of working as a consultant he

was admitted to the Master of Science program at the Department of Wildlife Ecology and

Conservation at University of Florida, Gainesville, FL, in 2005.

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