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Interspecific Competition and Species Co-Occurrence Patterns on Islands: Null Models and theEvaluation of EvidenceAuthor(s): Edward F. Connor and Daniel SimberloffReviewed work(s):Source: Oikos, Vol. 41, No. 3, Island Ecology (Dec., 1983), pp. 455-465Published by: Wiley on behalf of Nordic Society OikosStable URL: http://www.jstor.org/stable/3544105 .

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OIKOS 41: 455-465. Copenhagen 1983

Interspecific competition and species co-occurrence patterns on islands: null models and the evaluation of evidence

Edward F. Connor and Daniel Simberloff

Connor, E. F. and Simberloff, D. 1983. Interspecific competition and species co-occurrence patterns on islands: null models and the evaluation of evidence. - Oikos 41: 455-465.

Several recent studies have adduced non-overlapping geographic ranges as evidence that two species competitively exclude one another. We have previously pointed out that to show that a particular pattern of species' co-occurrence is unusually exclusive (for whatever reason), one must contrast the observed pattern with that expected were species placed independently of one another, and one must consider all species, not only those that appear a priori to have unusually exclusive ranges. Furthermore, even when one is able to show that an unusually large number of species' distributions are improbably exclusive, in the absence of independent non-distributional evidence capable of eliminating other reasonable explanations for these odd distributions, one cannot infer that competition or any other specific cause is responsible for the observed pattern. Other workers have critized our methods, suggested alternative procedures, and damned the use of null models in ecology. We respond to these criticisms and illustrate problems that beset these alternative procedures. We also reaffirm our view that null hypotheses in ecology are useful.

E. F. Connor, Dept of Environmental Sci., Clark Hall, Univ. of Virginia, Charlottes- ville, VA 22903, USA. D. Simberloff, Dept of Biological Sci., Florida State Univ., Tallahassee, FL 32306, USA.

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Accepted 3 March 1983 ? OIKOS

29* OIKOS 41:3 (1983) 45 5



1. Introduction

Although sound experimental evidence exists that interspecific competion occurs in nature (Wilbur 1972, Neill 1975, Coen et al. 1981, Crowell and Pimm 1976, Munger and Brown 1981, and others), the inference that it is of overwhelming importance in structuring ecological communities is based primarily on ambigu- ous indirect evidence (e.g., Diamond 1975, 1978). For example, Terborgh (1971) and Terborgh and Weske (1975) estimate that between 37% and 71% of the elevational limits of birds along the Vilcabamba of Peru are determined by interspecific competition. They ar- rive at this estimate solely by inspection of known vegetation discontinuities and each species' elevational frequency distribution. Abutting distributions that are not coincident with vegetation changes are inferred to be maintained by competitive exclusion. Wider species ranges on another nearby mountain range are also attri- buted to competitive release. Evidence of aggressive encounters between species or range expansions after removal of a putative competitor is not presented. Nor is it shown that individual species' habitat preferences do not account for the observed degree of elevational exclusivity (cf. Dueser and Hallett 1980). Is this kind of indirect evidence a sufficient basis to infer that species' distributions are determined by competition? Have we in any instance eliminated other biologically reasonable hypotheses? Could not abutting distributions reflect independently evolved habitat preferences, interaction with a predator or parasite, or pure chance? In earlier papers (Connor and Simberloff 1979, 1983, Simberloff and Connor 1979, 1981), we have attempted to answer these questions by examining one class of indirect evidence that is often adduced as evidence of interspecific competition: data on geographical patterns. Our goals were first, to develop a procedure to determine if a particular geographical pattern was indeed odd; second, to determine if these unusual patterns could best be explained by an hypothesis of interspecific competition, or whether other reasonable explanations were equally plausible; and third, to illustrate what we believe to be the pitfalls of making causal inferences from indirect pattern evidence.

Common wisdom holds that if interspecific competition is an important force shaping geographical distribution, then competitive exclusion should tend to produce non-overlapping species' distributions. Diamond (1975) suggests that this is in fact true, and particularly well exemplified by what he terms "checkerboard" distributions of bird species among islands. He presents three examples (Figs 20, 21, 22) involving two species in each of three genera of birds (Pachycephala, Ptilinopus, and Macropygia) in the Bis- marck Islands. He contends that the geographical pattern within each genus is improbably exclusive and therefore prima facie evidence that competition is responsible for the exclusivity.

We disagree with these conclusions. First, by isolating these three examples from a large group of possible examples (Diamond (1975) reports 141 species of birds or 9870 pairs of species in the Bismarck Islands) he has failed to control the "experiment wide error rate" and therefore has grossly inflated the probability of making a Type I error, rejecting the null hypothesis that these distributions are not unusual when in fact it is true. This is analogous to concluding that the probability of obtaining five heads in a row from the toss of a fair coin is (0.5)5 = 0.0313, when if the event is embedded in a longer series of coin tosses, say 10, the probability of obtaining at least one run of five heads is actually 0.1875 (6 X (0.5)5). The point is that, yes, these arrangements isolated post facto are improbably exclusive, but one would expect by chance alone to find a few improbable pairwise arrangements when inspecting 9870 pairs of species. Second, to state that a particular geographic pattern is unusually exclusive and therefore competitively produced, one must contrast the observed distribution with that expected were species independently placed on islands subject only to constraints that incorporate other relevant biologically and environmentally determined structure. Lastly, even were we able to show that an unusually large number of species' geographic patterns are improbably exclusive, in the absence of independent non-geographical evidence capable of eliminating other reasonable explanations for these odd distributions, one cannot infer that competition or any other specific cause is responsible for the observed pattern (Pielou and Pielou 1968, Simberloff and Connor 1981).

Previously (Connor and Simberloff 1979), we outlined a procedure to assess the null probability of observing a particular amount of exclusivity in species co-occurrence patterns. Based upon the analyses performed with this procedure, we concluded that adducing a role for competition in shaping species' co-occurrence patterns, over and above whatever role competition may play in determining how many species an island has or how many islands a species occupies, is very difficult since many non-overlapping distributions are expected for non-competitive reasons. Recently, Diamond and Gilpin (1982, 1983), Gilpin and Diamond (1982) and Wright and Biehl (1982), have criticized our procedures. We would like to reiterate our points and our analytical procedure in an attempt to relieve what we perceive to be the considerable confusion that has arisen over our interpretation of these issues, and to respond to our critics.

2. The Connor and Simberloff procedure

Connor and Simberloff (1979) represented the dis- tributon of species among islands as binary 0-1 matrices in which each column represented an island and each row a species. A species' presence on an island was

456 OIKOS 41:3 (1983)



indicated by a 1 and an absence by a 0. Exclusive or partially exclusive distributions could then be recog- nized as pairs or groups of species (rows) in which no, or just a few, matches of l's occur across the columns. Determining the actual number of species pairs, trios, quartets, etc. that share 0, 1, 2, 3, . . . N islands is then simply a counting problem (albeit not a small one for large speciose archipelagos). From these counts the actual frequency distribution of levels of exclusivity can be generated for pairs or larger groups of species for any archipelago.

At issue, however, is to what expected amount of exclusivity should the observed amount be compared? One could generate an expected distribution of exclusivity simply assuming independent placement of species (a totally unconstrained matrix). Such a distribution would be "truly null" with respect to species co-occurrences, but would lack realism. The fact that small islands have fewer species than do large islands is well established (Connor and McCoy 1979). That some species are restricted to just a few islands and some are widely distributed is also well known (Darlington 1957, Cain 1944). To generate an expected distribution of exclusivity that ignores such ubiquitous patterns leads only to a further confounding of the causes of any apparent odd geographic pattern, and a marked tendency to find that ranges of species pairs overlap more than expected.

Alternatively, one can generate an expected distribution of exclusivity that accounts for species-area relationships and/or species occurrence distributions, To generate an expected distribution of exclusivity that is null with respect to species co-occurrences, yet posses- ses other relevant biologically and environmentally determined structure (such as species/area relationships and species occurrence distributions), Connor and Sim- berloff (1979) generated a series of binary matrices with row and column sums identical to those of the actual matrix. However, to assure that the expected matrices were null with respect to species co-occurrence patterns, presences of species (l's) were placed independently and uniform randomly subject only to row and column sum constraints. This procedure was performed repeatedly to generate the expected frequency of species pairs or trios and its variance for each level of exclusivity, i.e., how many pairs or trios are expected to share 0, 1, 2, . . . islands. The actual and expected distributions of exclusivity were then compared using a x2 statistic.

Employing such a procedure, Connor and Simberloff (1979) examined three faunas. They observed for the New Hebrides birds a close agreement between observed and expected distributions of exclusivity and for the West Indies birds and bats an excessive number of exclusive arrangements. However, in the latter two examples a very large number of allopatric arrangements was expected, even though the expected was significantly lower than the actual level of allopatry. Con-

nor and Simberloff (1979) suggested several possible causes for the excessive exclusivity observed, among them competitive exclusion, predation, geographical speciation, and unsettled taxonomy. We concluded by stating that adducing a role for competition in shaping species' co-occurrence patterns over and above whatever role competition may play in determining how many species an island has or how many islands a species occupies, is very difficult since many exclusive patterns are expected for non-competitive reasons.

3. Criticisms of the Connor and Simberloff approach

3.1. Owls and hummingbirds

Both Diamond and Gilpin (1982, 1983) and Wright and Biehl (1982) claim that the Connor and Simberloff (1979) procedure tends to dilute the effect of competitive exclusion by ".... submerging instances of competitors with exclusive distributions in an irrelevant mass of data from ecologically remote pairs of species

." (Diamond and Gilpin 1983). Wright and Biehl (1982) feel that one should ".... restrict the analysis to species which are potential competitors". While the assembly rules proposed by Diamond (1975) to which we were responding were not restricted to guilds or "potential competitors", we agree that it will be difficult to discern the effects of competition on biogeographic patterns from a community-wide analysis. In fact, we said exactly that ". . . statistical tests of properly posed null hypotheses will not easily detect such competition, since it must be embedded in a mass of non-competitively produced distributional data" (Connor and Sim- berloff 1979).

However, restricting the analysis to guilds or "potential competitors" is not a simple matter, since to do so requires assigning species to guilds or a determination of which species are in fact "potential competitors". Partitioning all the species in a community into guilds is no easy task and requires data on resource use for each species (Root 1967). Krebs (1978) contends that "no one has yet been able to analyse all the guilds in a community". Those studies that have delineated guilds have relied on massive amounts of field data (Root 1967, Feinsinger 1976, Alatalo and Alatalo 1979). For no single guild, much less the entire avian community, have Diamond and Gilpin (1982, 1983) either delineated the guild or presented the evidence necessary to justify the guild boundaries. Furthermore, even were one able to delineate a single guild satisfactorily, its geographic pattern of species co-occurrence could tell us little about competition in general. Not only could different guilds be structured by different forces, but also one would need to know the null probability that, of the N guilds examined, one or more guilds would produce a pattern that would have been statistically odd had only that single guild been examined. If a few guilds are chosen randomly, and not selected because of the

OIKOS 41:3 (1983) 457



likelihood of detecting a competitive effect, stronger inferences can be made.

Restricting the analysis to only "potential competitors" is equally problematic, since one must determine a priori which of the total possible set of species pairs involve "potential competitors". While an accu- rate assessment of this is apt to be as laborious as de- lineating guilds, one could examine groups arbitrarily defined by taxonomy, body size, bill morphology, or any other easily observed characteristic. In fact we did so for taxonomic families in all three examples we examined, and Vuilleumier and Simberloff (1980) performed a similar analysis for taxonomic, ecological, and randomly partitioned paramo bird faunas. In any event, one cannot focus solely on the group of "potential competitors" since to conclude that a particular level of exclusivity among "potential competitors" is odd, one must show that such a pattern is odd relative to the level of exclusivity observed for species not considered to be "potential competitors".

We agree that an analysis based on guilds or "potential competitors" would be interesting. In either instance, to determine the correct null probability of a particular pattern of species co-occurrences requires one to examine the entire fauna, not merely those species thought most likely to be competitors.

3.2. Hidden structure in the marginal constraints

Diamond and Gilpin (1982, 1983) claim that by con- straining the expected rearrangements of species distributions to satisfy the observed marginal totals (row and column sums), one builds "hidden structure" into the null expectation of exclusivity. In other words, they feel that competition has already affected the number of species found on an island and the number of islands a species occupies. Although Diamond and Gilpin (1982, 1983) present no evidence that competition has affected the marginal totals or the pattern of species co-occurrences, it is surely possible that competition does affect the species richness of an island or the geographic range of a species, as we clearly stated (Connor and Simber- loff 1979: 1136). This need not necessarily translate into altered co-occurrence patterns, however. The marginal distributions of the row and column sums, not single marginal totals, set the constraints for rearranging the patterns of species co-occurrences. One must show that the shape or locations of the marginal distributions are affected by competition to conclude that fixing the margins to equal the observed values builds in "hidden structure".

Grant and Abbott (1980) raise the specter that fixing the marginal totals for the expected rearrangements to equal the observed is always circular. Either this is not true, or the entire premise of contingency table analysis is wrong, since, in a manner analogous to contingency table analysis, we are asking if the co-occurrence as- pects of the observed pattern of species' presences and

absences can be explained by the joint distribution of the marginal totals. However, just as in contingency table analysis, for certain fixed margins the number of possible rearrangements can be so small that statistical significance cannot be achieved. We have already shown that the possible patterns of species co-occurrences achievable subject to a fixed set of marginal totals can include instances that are statistically odd. The observed patterns of exclusivity for the West Indies birds and bats (Connor and Simberloff 1979) are statistically surprising. Statistically unusual arrangements are also achievable for the row and column sums observed for the New Hebrides birds (Connor and Simberloff 1983), but the observed pattern of species co-occurrences in the New Hebrides birds is not one of these odd patterns.

Were one able to demonstrate that competition had affected the marginal distributions, then fixing the mar- ginals to equal the observed totals would be at least somewhat circular. As we mentioned above, without fixing some of the marginal totals (row sums, for example), it is impossible to generate a reasonable null expectation of exclusivity for any particular archipelago. If we must conclude that the marginal totals are affected by competition, and therefore cannot fix the totals, then it becomes impossible to test the null hypothesis that a particular pattern of species co-occurrence is not statistically odd. If this is what Grant and Abbott (1980) intend, then they are arguing that it is impossible to test an hypothesis concerning the causes of geographical arrangements solely from data on geographical arrangements. But this is our very point! One cannot from geographical data alone easily determine the causes of a geographical pattern.

Wright and Biehl (1982) feel that fixing the row sums, the number of islands on which each species occurs, is a reasonable approach to generating a null expectation of species co-occurrence patterns (see discussion of alternative procedures below). However, they point out that by also fixing the number of species on an island, as we did, our procedure fails to detect significant aggregation in species co-occurrence patterns. Once again, but for a different reason, it is suggested that our procedure is not "truly null". But, the intent of our analysis was not to determine if there was any evidence for non-randomness in species distributions among islands. We firmly believe there is! A visual inspection of a presence-absence matrix of species in almost any archipelago will reveal that species are aggregated. This is largely because the physical conditions and habitats necessary for the establishment of species in particular taxa are also aggregated. This very aggregation is at least partially responsible for species-area relationships. Our procedure was designed to examine the pattern of species co-occurrences after such aggregation had been factored out by accounting for species-area relationships, not to ask merely if any non-randomness is evident in species co-occurrence

458 OIKOS 41:3 (1983)



patterns. It is interesting to note that the procedures advocated by Diamond and Gilpin (1982, 1983) and by Wright and Biehl (1982) fail to factor out this aggregation, and that they therefore conclude that species are non-randomly distributed among islands. But, the observed non-randomness is a tendency towards aggregation, not exclusion. Where in this result is there evidence of competition?

3.3. Checkerboards

Diamond and Gilpin (1982, 1983) question the power of our test by claiming that it fails to recognize as non- random ". . . the simplest, clearest, and most non-random pattern caused by interspecific competition . . .", namely a perfect checkerboard. On the contrary, perfect checkerboards are not necessarily caused by competition, nor are the samples of checkerboards presented by Diamond and Gilpin (1982, 1983) unusual. They compute the probability of observing a particular checkerboard distribution subject only to fixed row sums. This, however, allows degenerate rearrangements of species presences and absences that involve sites with no species (Connor and Simberloff 1983). Why should the null expectation of species co-occurrence patterns for a specific group of islands count rearrangements that include only a subset of the actual sites? When expecta- tions of exclusivity are computed subject to fixed row and column sums, no degenerate rearrangements are allowed, and the examples of checkerboards presented by Diamond and Gilpin (1982, 1983) are shown not to differ from expectation (Connor and Simberloff 1983).

3.4. Technical flaws The remaining criticisms lodged by Diamond and Gilpin (1982, 1983) against our procedure concern the technical details of our analysis rather than the approach to generating the null expectation of exclusivity. They chastize us for using Monte Carlo procedures rather than employing an explicit solution to generate the null distribution of exclusivity. While we agree that this would be desirable, it is certainly not necessary. Fur- thermore, no explicit solution exists even to count the number of possible matrix rearrangements for fixed row and column sums, much less for the null distribution of exclusivity from this population of rearrangements.

They contend that our test cannot detect the direction of any observed non-randomness. But this can certainly be accomplished by an inspection of the deviations between observed and expected, and by an inspection of the individual cell contributions to the x2 statistic. In those instances where we concluded that the observed and expected distributions differed, we indicated the direction of the difference (Connor and Simberloff 1979). Their test can do no better. The last point raised by Diamond and Gilpin (1982,

1983) in criticism of our procedure is that it considers

all pairs of species equally rather than weighting each pair by the probability that a random arrangement of that pair would have produced a distribution as exclusive as that observed. Essentially they contend that a pair of widely distributed allopatric species is less likely to have arisen by independent placement than is a pair of narrowly distributed allopatric species. Again, we were responding to Diamond's (1975) assembly rules, which state nothing about weighting certain species groups, only that exclusive distributions occur, and do so for competitive reasons. One can weight as Diamond and Gilpin (1982, 1983) suggest using our procedure, but performing the bookkeeping chores associated with counting the number of exclusive pairs or trios slightly differently. For each rearrangement of species presences and absences generated subject to the fixed marginal totals, one can count not only the expected number of pairs, trios, etc. with 0, 1, 2, 3, . . . N co-occurrences, but also record similar information as a function of the combined distributional breadth of the species in a group. For example, one can generate the expected number of species pairs whose combined occurrence totals (row sums) are 2, 3, 4, .. . 2N that display each level of co-occurrence. As an example we have performed such an analysis for the West Indies bats (Fig. 1). While once again by x2 analysis the observed and expected distributions are significantly different (x2 = 105.16, df = 57, p < 0.0005, cells lumped so that no expected values are less than 1 and less than 20% are less than 5) one can also see that certain categories of combined occurrence breadth have an excessive number of exclusive pairs. Determining which of these demand some causal explanation and the nature of the cause requires evidence other than that on geographical distribution.

4. Alternative procedures

4.1. The Diamond and Gilpin procedure

To overcome what they believe to be the shortcomings of our procedure Gilpin and Diamond (1982) and Diamond and Gilpin (1983) have suggested their own 4-step procedure:

1) Compute the probability that the i'th species occurs on the j'th island as pij = Ri Cj/T where Ri is the i'th column sum, Cj is the j'th row sum, and T is the grand sum (number of l's in the matrix). 2) Compute the expected overlap between each pair of species and its standard deviation from the above probabilities. The expected overlap between species i and k is Eik = Ij pij Pki and its standard deviation is SDik = V PH Pkj (1-pj Pkj)- 3) Standardize the observed values by substracting the expected and dividing by the standard deviation of the expected (dik = (Pik- Eik/SDik)), where dik is

OIKOS 41:3 (1983) 459



4~~~~~~~4

16~~~~

Fig. 1. Deviation of observed from expected number of islands shared for pairs of bat species in the West Indies as a function of the combined occurrence frequency of each species pair. The plotted values are the individual cell contributions ([0 - E]2/E) to the overall x2 statistic reported in the text. Data are from Baker and Genoways (1978).

the observed overlap expressed as standard deviates of the expected, and Oik is the observed overlap. 4) Compare the frequency distribution of standar- dized observations to a (0,1) standard normal distribution via x2, and a graphical representation.

If the null hypothesis of independent species placement is true, the histogram of standard deviates should follow a (0,1) normal distribution. An excessive number of species pairs in the upper tail of the distribution would indicate significant aggregation, and an excess in the lower tail significant exclusivity.

Although we applaud the spirit of this method, inas- much as it represents an attempt to test the null hypothesis of independent species placement among islands, several technical problems beset this technique.

4.2. Expected or fixed marginal distribution

The computational procedure used by Gilpin and Diamond (1982) and Diamond and Gilpin (1983) to generate the expected overlap between species effec- tively sets the row and column sums for the expected species co-occurrence pattern to be on average equal to the observed row and column sums, rather than equal to the observed sums, as we did. In doing so, the Gilpin and Diamond (1982) procedure counts degenerate rearrangements with species occurring nowhere and/or sites with no species as possible null rearrangements. This, in essence, allows more degrees of freedom in rearranging the matrix of species presence and absences, but many of these additional rearrangements are

degenerate. This practice lowers the null probability of observing any specified level of exclusivity and biases their test in favor of rejecting the null hypothesis of independent species placement (Connor and Simberloff 1983). Furthermore, those arrangements that are not degenerate may possess marginal distributions quite different from the observed marginal distributions, so that the expected pattern of species co-occurrences is confounded with this variation in the marginal distributions.

Gilpin and Diamond's (1982) motivation for this as- pect of their procedure is to remove the "hidden structure" they feel is built in by fixed marginal distributions. However, this approach fails to remove such "hidden structure"; rather it merely obscures any relationship between the marginal distributions and the observed pattern of species' co-occurrences since it obliterates the marginal distributions. Our procedure admits that "hidden structure" could affect the marginal distributions, so we proceed by testing the null hypothesis that above and beyond whatever "hidden structure" is imparted by the marginal totals, the pattern of species co-occurrences can be explained to result from independent placement. Were the Gilpin and Diamond (1982) procedure capable of removing the so-called "hidden structure", then we suggest the term "hidden structure" to be a misnomer. Rather, "hidden structure", if it exists, will remain hidden. Whatever structure is imparted to the pattern of species co-occurrences, hidden or otherwise, by the marginal distributions should be clearly attributable to the marginal distributions. This can only be achieved if the marginal distributions are fixed and therefore known.

460 OIKOS 41:3 (1983)



4.3. Cell probabilities

The procedure for computing the probability that the i'th species occurs on the j'th island (step 1) does not compute probabilities. It computes expected frequencies. As mentioned by Gilpin and Diamond (1982) these values can exceed 1, and often do (Connor and Simberloff 1983). Gilpin and Diamond (1982) adopt several ad hoc methods to deal with this problem. They further claim that their procedure follows the traditional log-linear model of contingency table analysis. How- ever, such an analysis is appropriate for frequency data, not binary presence-absence data. It is not possible to fit a log-linear or a logistic model to these "probabilities" (Bishop et al. 1975). Of the several ways suggested by Gilpin and Diamond (1982) to estimate cell probabilities only the Monte Carlo procedure is correct. We have already pointed out Diamond and Gilpin's (1982) aversion to Monte Carlo methods.

4.4. Asymptotic normality The last step in the procedure outlined by Gilpin and Diamond (1982) is to compare the observed frequency of standard deviates (step 4) to a (0,1) normal distribution. This comparison is predicated on the assumption that, given no species association, the observed frequency distribution of standard deviates would be asymptotically (0,1) normal. We ask, asymptotic with respect to what? We have no analog of sample size in this problem, so one cannot observe the behavior of the distribution of standard deviates for larger samples to determine if it is, in fact, asymptotically normal. Why assume normality? Could the null distribution be skewed or leptokurtic? Obviously, the outcome of the X2 test is very sensitive to the shape assumed for the expected distribution of standard deviates. If the true expected distribution is skewed, then the conclusions reached by Gilpin and Diamond (1982) for the New Hebrides and Bismarcks avifaunas may be wrong. However, without a means of assessing the asymptotic behavior of the expected distribution of standard deviates it is impossible to tell. This renders rigorous hypothesis testing based on the Gilpin and Diamond (1982) procedure rather tenuous.

4.5. The Wright and Biehl procedure

Wright and Biehl (1982) feel that our procedure (Con- nor and Simberloff 1979) and others we have outlined (Connor and Simberloff 1978, Simberloff 1978) are "not appropriate to determine whether island colonization is random". They suggest an alternative approach that they feel is "better able to detect the effect of competitive exclusion on insular distributions". While we agree that the procedures we have developed to compute an expectation of the number of species shared between sites are not particularly informative nor pow-

erful regarding questions concerning the pattern of species' co-occurrences (Connor and Simberloff 1978, Simberloff 1978), they were not intended primarily to test such hypotheses. These procedures were designed to test hypotheses concerning the similarity of sites in their species composition, not the similarity of species distributions among sites. Similar procedures have been developed for and applied to paleobiogeographic and biostratigraphic applications (Raup and Crick 1979, Harper 1978). Once again the tested hypotheses concern similarity between sites or within sites over time.

The procedure suggested by Wright and Biehl (1982) to supplant ours (Connor and Simberloff 1979) for examining how many sites a group of species shares, starts by computing the probability of obtaining a pattern of species co-occurrence as exclusive as or more exclusive than that observed. The computation is performed for each species pair and follows the hypergeometric distribution suggested by Connor and Simberloff (1979: 1133). An expectation of the number of sites shared between species can also be computed (Wright and Biehl 1982).

Using this procedure, Wright and Biehl (1982) examined four pairs of species, the three avian examples adduced by Diamond (1975) as evidence of competitive exclusion, and Lacerta lizards in the Adriatic. They also examined the New Hebrides birds and the West Indies bats.

The Wright and Biehl (1982) procedure essentially fixes the row totals of the expected species' presence-absence matrix to equal the observed, but lets the column totals vary freely. As we stated above, this fails to constrain the expected pattern of species co-occurrences to account for the omnipresent species-area relationship and therefore tends to bias their test toward rejecting the null hypothesis. Again, the question of interest is whether or not the observed pattern of species co-occurrence is consistent with a hypothesis of independent placement, given the observed species-area relationship and species occurrence distribution. This is the hypothesis our procedure was designed to test. Had we been interested in asking simply whether there is evidence of non-randomness in species' distributions, as Wright and Biehl (1982) appear to be, we would have fixed neither the row nor the column sums. However, such a test would not be particularly interesting since we know species to be non-randomly distributed with respect to the physical environment, particularly at a geographic scale.

In fact, we used the very procedure suggested by Wright and Biehl (1982) to compute the probabilities of obtaining by independent placement the levels of exclusivity observed for Macropygia and Pachycephala as presented by Diamond (1975), (Connor and Sim- berloff 1979: 1133). For Macropygia we calculated identical probabilities, but Wright and Biehl (1982) appear for Pachycephala to have erred in two ways. First, using their species frequencies, we find their published

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Tab. 1. Hypergeometric tail probabilities that independent species placement would have resulted in exclusivity as extreme as that observed for four selected species pairs.

Number of islands with Hypergeometric Data source Neither Species Species Both probability species 1 only 2 only species

Ptilinopus 3 18 9 2 0.0003 Diamond (1975), Fig. 22 21 18 9 2 0.0903 Diamond (1975), Figs 22,8,15 and text, p.357

Pachycephala 17 14 12 0 0.0034 Wright and Biehl (1982), Tab. 1 21 18 18 0 0.0035 Diamond (1975), p. 390 17 15 11 0 0.0037 Diamond (1975), Fig. 21

Macropygia 13 14 6 0 0.0245 Diamond (1975), Fig. 20 30 14 6 0 0.1226 Diamond (1975), Figs 20, 6, 25 and text, p. 357

Lacerta 11 28 18 0 0.0000001 Nevo et al. (1972)

value (their Tab. 1) too low by a factor of 10. Second, Diamond (1975) states in his text that 11 islands support P. pectoralis, 18 support P. melanura dahlia and 21 support neither. His figure 21 has, for analogous totals, 11, 15, and 17, respectively. Wright and Biehl have used 12, 14, and 17, respectively. Tab. 1 depicts the correct hypergeometric probabilities for all three con- figurations, as well as for the other examples given in Tab. 1 of Wright and Biehl (1982). A second point of interest arises for the other two examples, Macropygia and Ptilinopus, in their Tab. 1 from Diamond (1975). From Diamond's Figs 6, 8, 15, and 25, and his text on p. 357, it is apparent that his Figs 20 and 22 greatly under- estimate the number of islands with neither species of Macropygia and Ptilinopus, respectively. When the data from the full 50 surveyed islands are included, the null probabilities (our Tab. 1) are insignificant.

In any event, as we noted earlier, these four pairwise examples of Wright and Biehl's Tab. 1 are culled from a mass of biogeographic data precisely because they ap- peared, a priori, to constitute unusual exclusivity. Un- less all available data are analyzed simultaneously, one cannot assess the statistical significance of some particular subset. For the three avian examples from the Bismarck Archipelago neither the matrix simulation method nor the pairwise hypergeometric method (but expanded to all pairs) can be applied since the biogeographic data described by Diamond (1975) as "given by Mayr and Diamond 1975" have never been published. Consequently one cannot tell whether three such exclusively arranged pairs could have arisen by independent placement. For Lacerta, Nevo et al. (1972) have performed introduction experiments that buttress their conclusion of competitive exclusion between L. sicula and L. melisellensis.

Even when the data for all species in a pool are available, the Wright and Biehl (1982) method - assessing the null hypergeometric probabilities for all species pairs in the species pool - is defective. The species pairs are not independent of one another and this may easily inflate the observed numbers of species pairs whose

exclusivity appears extraordinary. We cannot present a general treatment of the bias that this non-indepen- dence will likely produce, but the following simple example should demonstrate the problem. Wright and Biehl (1982) choose to call a biogeographic arrangement not predominantly interactive if the null hypergeometric probability of independent placement is less than 0.05 for at least 5% of the pairs. Suppose there were 12 species in a species pool, arranged over 10 islands. Suppose further that species 1, 2, 3, and 4 were each found on 5 islands, and that strict competitive exclusion existed between species 1 and 2, 2 and 3, and 3 and 4. Finally suppose that there were no interactions between any other species. That is, exclusive pairs com- prise 3/(1') = 4.5% of all pairs. Now, let A, B, C, D, and E be the islands occupied by species 1. Then F, G, H, I, and J must be the islands occupied by species 2, so that species 3 must occupy A, B, C, D, and E. Then species 4 must occupy islands F, G, H, I, and J, and 1 and 4 are thus exclusively arranged even though there is no interaction between them. The null hypergeometric probability for each of the 4 exclusive pairs is 0.004, and there are thus at least 4/(12) = 6.1% of the species pairs exclusive at this level. There may be others, produced by chance alone in the uniform random placement of the remaining 8 species, but just these 4 pairs would cause the system to be classified as interactive by Wright and Biehl (1982), even though the actual number of interactions is too low by their stated criterion.

One can conceive of other simple situations produc- ing spurious associations, either positive or negative. If species 1 and species 2 were obligate mutualists, for example, and species 1 and species 3 competitively excluded one another, species 2 and 3 (given an appropriate number of islands and occurrences) would be improbably exclusive by the pairwise hypergeometric test, even though they do not interact. One can say in general that looking at all pairs, as Wright and Biehl (1982) suggest, will likely lead to overestimation of the degree of biological structure. The Gilpin and Diamond (1982) procedure which also examines all pairs, al-

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though not using hypergeometric probabilities, suffers from this same problem. Our matrix simulation method does not produce this artifact. An exactly analogous problem was recently noted by Meagher and Burdick (1980) with respect to nearest neighbor analysis. To determine if individuals of two species or sexes are arranged independently in space, since pairs of individuals are not independent of one another (if one knows that A is B's nearest neighbor, one's prior assessment of A's nearest neighbor is modified), the traditional x2 contingency analysis is invalid; the test statistic is not distributed as x2. Meagher and Burdick (1980) use a re- peated simulation to generate the distribution.

5. Discussion

Our message is simple and short, so we reiterate.

1) In order to infer that some pattern of species co-occurrence is odd, one must know what is expected. Therefore, some hypothesis contrasting observed and expected patterns of co-occurrence must be stated and tested. This hypothesis can involve either a comparison of the observed pattern of co-occurrence with that expected given independent placement of species subject to fixed marginal distributions, or a comparison of the co-occurrence pattern for species within arbitrarily defined groups of "potential competitors" with that co-occurrence pattern expected of non-competitors. Other comparisons are possible, but there must be some null hypothesis. 2) The expectation of species' co-occurrence should account for species-area relationships and species' occurrence distributions. 3) An excessive number of exclusively distributed species is consistent with an hypothesis of competition, but can also be explained as resulting from several other causes, i.a., geographical speciation, multiple colonization routes, predation, parasitism, and independently evolved habitat preferences. 4) Since a unique cause cannot be associated with a particular class of co-occurrence patterns, it is impossible based solely on biogeographical evidence to infer that competition or any other specific cause is responsible for a particular geographic pattern. Evidence of active replacement or colonizations that failed because of active exclusion is necessary to infer that competition causes and maintains an exclusive geographic pattern. Therefore, evidence on geographical patterns, per se, is no basis for inferring a role for competition. 5) Failure to reject the null hypothesis of independent species placement does not constitute its acceptance, nor does it imply that competition or any other causal processes do not occur. It does imply that there is no evidence in the pattern of species co-occurrences, per se, that compels one to posit some effect of one species on another species' geography.

6) All this is to say that not only will it be difficult to conclude that a pattern of species co-occurrence is statistically odd, but also that data on geographical patterns alone are an insufficient basis to determine the causes of those patterns.

Although we feel that Gilpin and Diamond's (1982) and Wright and Biehl's (1982) procedures are incorrect and inappropriate, their intent is to test null hypotheses against alternatives. This we applaud. It is certainly a refreshing change from the common practice of invok- ing, post hoc, competition as the cause of exclusive species ranges (Diamond 1975, 1978, Terborgh 1971, Terborgh and Weske 1975). However, in the view of Diamond and Gilpin (1982, 1983) and Wright and Biehl (1982), competitive exclusion still holds a paramount position relative to the other possible causes of exclusive arrangements. Available evidence does not seem to us to support this view.

In this respect, we point out that in spite of the strik- ing concordance in results between our procedure and those of Gilpin and Diamond (1982) and Wright and Biehl (1982), these authors persist in their view that a case for competitive exclusion can be built on biogeographic data alone. For the New Hebrides birds Gilpin and Diamond (1982) found, as did we, no excess of exclusive species ranges over that expected from independent placement. Wright and Biehl (1982) found only a slight excess of aggregative arrangements over that expected for both the New Hebrides birds and the West Indies bats, while we found significantly more exclusive pairs of species than expected in the West Indies bats. For the Bismarck Island avifauna, Gilpin and Diamond (1982) also found an excess of exclusive distributions over expected, but the excess is vanishingly small (Gilpin and Diamond 1982: Fig. 4). Since the Bismarck data are unpublished, we cannot apply either our matrix simulation approach or the hypergeometric calculations. The pattern strikingly evident from both Gilpin and Diamond's (1982) and Wright and Biehl's (1982) analysis is one of a significant tendency towards aggregation in species co-occurrences. Where in this result is there evidence of an overwhelming pattern even consistent with competitive exclusion, much less caused by competition?

6. Postscript on null hypotheses Diamond and Gilpin (1982, 1983), Schoener (1982), and Harvey et al. (1983), labor to discredit the use of null hypotheses in ecology. They claim that not only are those we have discussed above ill conceived, weak, circular, difficult to test, and of course unsuccessful, but that other null hypotheses posed and tested by various authors (Connor and Simberloff 1978, Connor and McCoy 1979, Strong et al. 1979, Simberloff and Boecklen 1981) are equally reprehensible. By implica-

OIKOS 41:3 (1983) 463



tion one could add to this list a growing body of similar literature equally deserving of this disdain (Williams 1964, Poole and Rathcke 1979, Ricklefs and Travis 1980, Rabinowitz et al. 1981, Dillon 1981, Coleman et al. 1982, Malanson 1982, DeVita et al. 1982, and others). We, of course, believe that these null hypotheses have been useful, startlingly informative, and, in specific instances, vindicated by further analysis (Strong and Simberloff 1981, Connor et al. 1983, Connor and Simberloff 1983, Simberloff 1983).

We believe it would be informative here to set out the role we envision for null hypotheses and our motivation for using them in ecology and biogeography. Strong (1980) similarly discusses the virtues of using null hypotheses in these two disciplines.

In a strict statistical sense a null hypothesis is an hypothesis of no effect. It is merely a conjecture that nothing in the data at hand would lead one to posit an explanation other than chance for the observed result. While a null hypothesis is not the only kind of hypothesis that can serve as the "tested hypothesis", it is certainly the most common in conventional statistical usage.

In experimental research, the results derived from specific treatments or manipulations applied to subjects are compared with untreated or control subjects. The tested hypothesis is usually the null hypothesis of no difference between treatments and controls. Unfortu- nately much ecological research is non-experimental. Large sets of observations concerning the morphology, distribution, abundance, behavior, and resource use of plants and animals are collected primarily for descrip- tive purposes, but are also examined in reference to a wide array of ecological and evolutionary theories. If particular portions of these data are found to be consistent with a particular theory, then they are adduced as support for that theory. Traditionally one does not ask if some alternative theory might explain the available evidence equally well or even if the data are statistically consistent with the theory they are said to support.

Why is this so? Unlike in experimental research where an explicit "tested hypothesis" is evaluated by use of a variable with known distributional properties, in non-experimental research, the distributional properties of the variable of interest are often unknown. For an example we return again to data on the geographical distribution of species. From an analysis of the distribution of birds in the Bismarck Islands, Diamond (1975) developed his "assembly rules". These rules state, in sum, that competition is a major force determining the arrangement of species among islands. The evidence adduced in support of this idea is the observed pattern of which bird species are on which islands. However, if competition is the "experimental effect" for which we must test, to what "control" do we compare the observed species' geographies? How do we assess what effects competition has?

The variable of interest is the exclusivity of species'

ranges. We can determine the value of this variable for the observed species' geographies by an inspection of the data. But, how can we determine the value of this variable for the "control" instance where competition has played no role? What range of values could this variable assume, were competition of no importance? This question must be answered in order to test an hypothesis concerning the role of competition in determining biogeography.

We suggest that a null hypothesis and a null model, contrived to generate the expected distributions of the variable of interest under the null hypothesis, can use- fully approximate the role of the "control" in order to test an hypothesis involving non-experimental evidence. However, from such an analysis one can conclude only either that species' independent biologies suffice to explain the data at hand, or that some additional causal explanation must be invoked. Without further evidence, probably of an experimental nature, one can neither eliminate any particular causal mechanism, nor conclude that a particular mechanism has operated.

We conclude by pointing out that we have consis- tently used null models as a means to challenge inferences drawn from non-experimental evidence. We feel that this is the proper and useful role for null models. As long as the practice of inferring cause from non-experimental evidence continues to flourish among ecologists, then we expect null models also to flourish.

Acknowledgements - We would like to thank George Horn- berger for his comments on this manuscript and Betsy Blizard for preparing the figure. This research was supported by a grant from the Academic Computing Center of the Univ. of Virginia.

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