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Analysis of larval trematode communities.

INTRODUCTION

Considerable debate centers around whether communities are more than just random assemblages of species (Strong et al. 1984, Sih et al. 1985, Sale 1991). Although disturbance, physical stress, recruitment dynamics, predation, and competition all might alter the distribution and composition of species in a community, the role of interspecific competition is at the center of the community structure debate (e.g., Diamond 1975, Connor and Simberloff 1979, Connell 1980, 1983, Schoener 1983, Gurevitch et al. 1992). To resolve this issue, we must explicitly and consistently define "community structure," find tractable systems for study, and use analytical approaches that can detect nonrandom structure and distinguish the relative importance of potential structuring forces. For this, we and others have chosen a model system to address questions of community structure: guilds of larval trematodes in their first intermediate host snails. We will describe methods specifically developed for this system, use them, and then discuss how our approach applies to the study of other communities. Our goals are to specify the major hypotheses concerning what structures larval trematode guilds, refine testable predictions that stem from these hypotheses, and provide tests to determine whether our observations are consistent with predictions. To do the latter, we applied our approaches to data on larval trematodes that parasitize the horn snail, Cerithidea californica.

We see "community structure" as the pattern of distribution and abundance of species in a community. Following May (1984), we will term a group of species lacking statistical association to be an "unstructured" community. Hence, the more a community differs from a random association of species, the more "structured" it is. Likewise, forces may "structure" a community if they cause the association of species to depart from a null model of species abundance and distribution. We have found it useful to separate structuring forces that affect patterns of recruitment from those forces that occur after recruitment. It is of particular interest to examine how patterns in recruitment can affect the importance of postrecruitment structuring forces. A truly null model would spatially and temporally homogenize intraspecific recruitment rates, allow inter-specific coexistence, and not allow species to partition the habitat. In reality, recruitment of a species will usually exhibit spatial and temporal variation, and species may interact or vary in their habitat preferences. These forces can add structure to an assemblage.

Communities of parasites are a valuable model for the analysis of such questions because hosts represent well-defined and replicated habitats (Esch et al. 1990). Although most studies of parasite communities have focused on helminths in the guts of vertebrates or the gills of fishes, ecological parasitologists have recently begun to investigate the structure of larval trematode guilds (e.g., Kuris 1990, Sousa 1990, 1993, Fernandez and Esch 1991a, b). Guild, sensu Root (1973), is the term that best describes an assemblage of such trematodes (Kuris 1990). Snails serve as first intermediate hosts for trematodes that, as adults, are parasites of vertebrates. Larval trematodes typically castrate their snail hosts; asexual reproduction of larvae from even a single infection substantially increases the worm population in an infected snail such that trematode tissue largely replaces the gonads and digestive glands of the snail. Thus, each snail represents a limited resource for a trematode infection and competition is, therefore, a potentially important structuring force operating within trematode guilds (Kuris 1990, Sousa 1992). Consistent with this logic are well-documented observations of interference competition between trematode species (reviewed by Lim and Heyneman 1972). Competition between two species of trematodes within individual snails, herein termed the "infracommunity" (Holmes and Price 1986), often results in losses of subordinate species (reviewed in Lie et al. 1973, Combes 1982, Sousa 1992). It is not clear, however, that interactions are frequent enough to significantly affect attributes of community structure at the level of the trematode community within a host population (the "component community" sensu Holmes and Price 1986) (Holmes 1990, Sousa 1990, 1992, 1993, Fernandez and Esch 1991b). Here, we introduce methods to determine whether competition at the infracommunity level significantly affects the proportion of interacting trematodes in the component community. In addition, we are able to estimate the proportion of individuals excluded from the metapopulation of each species. Our approach is more sensitive than alternative approaches that compare diversity indices to assess the importance of competition (Sousa 1990) as these are only likely to be useful in the limiting case where competition leads to the exclusion of some species (Kuris 1990, Kuris and Lafferty 1994).

Determining structure with a null model

To determine if a given community is structured, it is necessary to test whether it is significantly different from a random assemblage of species. The degree to which a community departs from a null model represents a quantitative measure of community structure (Grant and Schluter 1984). For example, certain species combinations may occur more or less frequently than expected by chance. A null model that uses a species combination approach (analysis of species co-occurrences) can serve to construct "null communities" for comparison with observed communities. This approach is particularly appropriate for parasite studies because the opportunity to sample large numbers of hosts provides sufficient statistical power to detect structure (Simberloff 1990). Several authors have proposed methods for constructing and testing null models of species combinations (see reviews in Harvey et al. 1983, Jackson et al. 1992). Because hosts are much less variable than other habitat units such as islands or lakes, constraints on column totals (the number of trematode species in each snail individual) used to account for habitat heterogeneity (see Gilpin and Diamond 1984) are often unnecessary. For a null model used in past studies (e.g., Cort et al. 1937, Bourns 1963, Vernberg et al. 1969, Werding 1969, Combescot-Lang 1976, Vaes 1979, Rohde 1981, Kuris 1990, Fernandez and Esch 1991a), the expected number of double infections of trematode species i and j is [E.sub.ij]: [E.sub.ij] = N[p.sub.i][p.sub.j], where N is the number of hosts (infected and uninfected) and [p.sub.i] and [p.sub.j] represent the prevalences (where prevalence is the proportion of hosts infected, Margolis et al. 1982) of species i and j. Summing [E.sub.ij] over all species pairs gives the expected number of double infections in a sample ([Sigma][E.sub.ij]). The difference between the expected ([Sigma][E.sub.ij]) and observed ([Sigma][O.sub.ij]) number of double infections indicates the degree of structure.

Unfortunately, it is often difficult to distinguish a null model from a hypothetically structured assemblage (Colwell and Winkler 1984). Therefore, it is prudent to opt for sensitive statistical analyses. It is common to compare expected frequencies of double infections with observed frequencies of double infections using a chi-square or G test, separately testing each species pair in a 2 x 2 table (Kuris 1990, Fernandez and Esch 1991a). Each test, however, is not strictly independent, violating the assumptions of the heterogeneity test (Schluter 1984). The likelihood of obtaining a false positive (Type 1 error: rejecting the null hypothesis when it is true) increases with the number of statistical tests conducted (Pielou 1974, Sousa 1993). Type 2 error is also a potentially serious problem because the small sample size for each comparison of a pair of species makes it difficult to statistically detect a biologically significant effect (e.g., Fernandez and Esch 1991a). An alternative approach is to conduct a single test for the entire guild (e.g., Sousa 1990). Although such an approach loses species-specific information (Harvey et al. 1983), it has considerably more power than pairwise comparisons and is much less likely to produce a false significant result.

Null parameters

Because observed species abundances and distributions used to parameterize null models may have been shaped by interspecific interactions, the expected values generated are not truly what we would expect if species did not interact or vary in their ecological requirements (Grant and Abbott 1980, Gilpin and Diamond 1984). The following is an example for two species, dominant a and subordinate b. Assuming that the probability of recruitment to a host is independent of whether that host is infected, we can try to determine how many b individuals species a eliminated. Out of a population of 100 snails that have all shared the same risk of infection, imagine that a recruits to 80 snails and b to 50 snails. By independent assortment, we would expect 40 snails were infected at some point with both a and b, 40 by a only, and 10 by b only (leaving 10 snails uninfected). We might expect that a has displaced some of the b in the 40 double infections. Let's say we find 70 snails with a only, 10 with a and b, and 10 with b only (30 individuals orb lost to competition). Here, the observed overall prevalence of a is 0.8 and the overall prevalence of b is 0.2. Using the general random model, N[p.sub.i][p.sub.j], we would expect 100 x 0.8 x 0.2 = 16 double infections. Since we observed 10 double infections, this suggests that we have lost six individuals of b to competition (a gross underestimate compared with the 30 individuals actually lost to competition), and competition does not seem very important. This null model nearly always underestimates expected co-occurrences. Gilpin and Diamond (1984) argue that this obstacle is the most intractable difficulty of using "null" models. To avoid this requires parameterizing the null model with the prevalence that each species would have obtained if no interactions occurred. We can calculate these "null parameters" (in this case, prevalence) if we know certain aspects of the biology of the interacting species. In the Appendix, we derive formulae that estimate the null prevalence of a species from observed values. These formulae vary depending on assumptions about how species interact.

It is possible to estimate the prevalence at which a species had recruited by using its present observed prevalence. For our previous example, we assume that, since a is dominant, it should not have lost any members to competition. Therefore, its null prevalence is the same as its postinteractive prevalence (0.8). By the same reasoning, we also know that single infections of species b were never doubly infected with species a. To find the null prevalence of b, we return to the rules for independent assortment. Twenty uninfected snails were available to b for single infections (a infected the other 80). Species b only infected 10 of these; this is a 50% infection rate. As we assume that b infects parasitized snails with the same probability as uninfected snails, we estimate that the null prevalence of species b was 50%. Now, using the null prevalence to estimate the initial overlap between a and b, 100 x 0.8 x 0.5 = 40 expected double infections. This leaves 40 - 10 = 30 individuals of b lost to competition with a (the correct value). The difference between this approach and using observed prevalences in the null model can be substantial for cases where competitively dominant species are common.

Interpretation of structure

Often, many fewer double infections occur than are expected from a null model (reviewed by Sousa 1992). Two general mechanisms could reduce the number of double infections and structure the guild. First, the opportunity for co-occurrences may be less frequent than expected because of spatial or temporal heterogeneity in recruitment or the differential distribution of parasite species among host phenotypes. Second, co-occurring trematodes might not survive because (1) hosts with multiple-species infections suffer higher mortality rates than do hosts with single infections or (2) interspecific competition among trematodes could reduce the number of multiple-species associations that persist. None, some, or all of these factors might influence an assemblage.

In previous analyses of expected infections, investigators often pooled temporal (e.g., Kuris 1990) or spatial (e.g., Fernandez and Esch 1991a) collections, making it impossible to interpret the potential effects of heterogeneity in recruitment. Other studies have assumed (without testing specifically) that spatial (or temporal) heterogeneity in recruitment explains the occurrence of fewer double infections than expected (e.g., Fernandez and Esch 1991a). However, although spatial (or temporal) variation in recruitment can hypothetically reduce interspecific interactions (Cort et al. 1937, Kuris 1990, Sousa 1990, 1992, Fernandez and Esch 1991a), it can also intensify their frequency (Robson and Williams 1970, Kuris 1990, this paper). For heterogeneity to affect community structure, there must be intraspecific variation in recruitment. If this variation is negatively correlated among species, there will be fewer co-occurrences than expected and species will be isolated. On the contrary, a positive association among species will intensify interactions. For example, if trematode species a recruits mostly to site 1 while trematode species b recruits mostly to site 2, they will rarely co-occur. Conversely, if the prevalence of both species is disproportionately high at site 1, there will be more co-occurrences between the two species than if there was no intraspecific variation in recruitment among sites.

The analysis of heterogeneity in recruitment requires obtaining several samples of hosts that each have experienced uniform risks of infection. That is, each sample should consist of individuals of similar age, collected at the same time from an area in which they are likely to mingle. Host mobility increases the likelihood that a sample from a given area will represent a homogeneous unit (Fernandez and Esch 1991a). It is also important to sample from a narrow host age class as older hosts will have a greater cumulative risk than young hosts. Although trematode species might isolate themselves if they specialized among various host phenotypes, or more readily infected unparasitized than parasitized snails, there is no evidence that this occurs in our host-parasite system with the possible exception of size selectivity (Sousa 1990, 1993). In experimental studies of other snail-trematode systems, if miracidia (searching stages hatched from trematode eggs) were selective, they were more likely to penetrate snails infected with other trematode species than uninfected snails (Heyneman et al. 1972, Kuris 1973, Lie et al. 1973, 1976, Boss 1977, Jourdane 1980, Lie 1982). The propensity of trematode miracidia to penetrate infected hosts would increase the incidence of parasite co-occurrences and make our analysis of structure conservative. If the probability of infecting a host is strongly dependent on whether the host is already parasitized, both the null model and the method for determining null prevalence will require modification.

After recruitment patterns determine which species will interact, host or parasite mortality related to multiple infections may further structure the trematode guild by eliminating some double infections. Although host mortality induced by multiple infections occurs in some host-parasite systems (Anderson and May 1978), multiple infections of parasitic castrators, such as trematodes, usually do not increase host mortality rates (Kuris 1974, Sousa 1992). Instead, experiments reveal the regular occurrence of predation by dominant species (with mouthed redial larval stages) on subordinate species and that certain species with only sporocyst larval stages (mouthless) are able to indirectly suppress the development of other subordinate species in a largely linear dominance hierarchy (Lie et al. 1968, Lira and Heyneman 1972, Kuris 1973, 1990, Combes 1982, Sousa 1993) (although in some cases this can be described as asymmetric omnivorous intraguild predation [Polls et al. 1989], we will simply refer to all interactions where one species negatively affects another species as competition). Preemption, where the first species to arrive is able to stave off subsequent recruits, is rare (Lie et al. 1968, Kuris 1990, Sousa 1992). If competition structures the trematode guild, the expected number of double infections in a sample should be greater than the observed number of double infections. Facilitation among species, on the other hand, could lead to more observed double infections than expected (Kuris 1990).

METHODS

To illustrate our method of analysis, we used the guild of larval trematodes that parasitize the marine snail, Cerithidea californica. This snail and its associated larval trematodes have been the subject of numerous studies (Martin 1955, 1972, Yoshino 1975, Sousa 1983, 1990, 1993, Kuris 1990, Lafferty 1991, 1993a, b). We sampled five sites (spatially separated by [approximately equal to] 50 m or more) at Carpinteria Salt Marsh (California, USA) over 20 d in May 1991. At each sample site, we collected snails within a 10-m stretch of tidal channel. Mark and follow experiments indicate that infected and uninfected snails mix randomly within a site over a period of 1 wk (I. Davila-Marcano, unpublished data). We therefore assumed the movements of individual snails effectively eliminated spatial heterogeneity within a site. Because the movement of a single snail was rarely consistent in a single direction, we do not expect that movement among sites was frequent.

We collected snails between 25 and 30 mm in length to minimize variation among sites that was not due to spatial separation and to reduce the effects of host size on infection by trematode species. Snails in this size class were abundant. Restricting the size class and spatial scale limited the intraspecific heterogeneity in recruitment within each site. From each site, we dissected snails until we found a total of 100 that were infected. We identified the trematodes found in single and double infections after Martin (1972).

For the trematodes studied here, dominants either coexist with or kill subordinates. Note that this scenario does not assume that competition occurs; rather, it assumes that if competition does occur the outcome is predictable. In this case, the null prevalence of species i, [e.sub.i], is the expected prevalence of species i without competition. This is the proportion of "competitor-free" hosts that species i occupies. In other words, [e.sub.i] = ([p.sub.i] - [o.sub.id])/(1 - [p.sub.d]) where [p.sub.d] represents the prevalence of all species (d) that are dominant to species i, and [o.sub.id] is the prevalence of double infections observed between i and d (although we observed none, we would have counted triple infections as three observed double infections). From this, the expected number of double infections between species i and j is N[e.sub.i][e.sub.j]. Using a dominance hierarchy proposed by Kuris (1990) and Sousa (1993), we determined [e.sub.i] for each species.

We used heterogeneity chi-square tests to determine whether overall prevalence was the same at each of the five sites and whether the relative prevalence of each species was the same at each site (lumping the prevalence of the six rarest species). Next, we investigated the five samples for the structuring effect of spatial heterogeneity. To do this, we compared the number of double infections expected if there was no intraspecific variation in recruitment among sites with the number of double infections expected from the actual recruitment regime among sites. The expected number of double infections from a group of k samples is the sum of the number of expected double infections calculated separately for each sample ([Sigma][E.sub.ij]). This equals [[Sigma].sub.k][[Sigma].sub.i][[Sigma].sub.j][N.sub.k][p.sub.ki][p.sub.kj] and can be referred to as the sum of the expected. The expected number of double infections if there was no intraspecific variation in recruitment is calculated directly from the pooled samples (E[[Sigma].sub.i][[Sigma].sub.j]). This equals [

k][N.sub.k][p.sub.kj])/([[Sigma].sub.k][N.sub.k]) and can be referred to as th expected of the pooled. Going back to our previous example, by sampling 100 snails from an additional site where a recruited to 40% and b to 90% the sum of the expected (over both sites) would be 100 x 0.9 x 0.4 + 100 x 0.5 x 0.8 = 76 and the expected of the pooled would be 200 x 0.65 x 0.65 = 84.5 (spatial heterogeneity isolates the species). The "expected of the pooled" will equal the "sum of the expected" if heterogeneity does not structure the community. Likewise, the sum of the expected will be equal to the observed double infections if interactions do not structure the community. For each prediction, we estimated the expected frequency of double infections with observed ([p.sub.i]) and null ([e.sub.i]) prevalences. We compared the results from each approach in our analysis.

Since we sampled more snails from low prevalence sites, we weighted observed values according to sample size so that sites with low prevalence were not disproportionately overrepresented. The weighted frequency of a species = F x 170/N, where F is the observed frequency of a species, 170 is the average number of snails sampled, and N is the number of snails in a subsample. Our analysis did not account for variation in snail density among sites.

We report expected and observed numbers of co-occurrences. Although it is possible to compare expected and observed double infections, we found it more biologically meaningful to compare (using 95% confidence limits) the proportion of trematodes expected to interact before and after the effects of competition. Fig. 2 illustrates the statistical power of this approach for cases with no double infections. Although this approach detects the net effects of structure, non-random structure can act in opposite directions, leading to a nonsignificant net effect. For this reason, we also suggest comparing the distribution of the standard deviate (standardized difference between observed and expected values) with a normal distribution having a mean of zero and standard deviation of one (e.g., Jackson et al. 1992). The standard deviation for the estimates of [E.sub.ij]/N over all n(n - 1)/2 species combinations is [SD.sub.ij] = [[[Sigma]([E.sub.ij]/N)(1 - [E.sub.ij]/N)].sup.1/2]. The standard deviate between the observed and expected number of double infected hosts is [d.sub.ij]: [d.sub.ij] = ([O.sub.ij]/N - [E.sub.ij]/N)/[SD.sub.ij]. We then compared the distribution of [d.sub.ij] for all species with a standard normal distribution to determine structure within the observed guild. We report two-tailed probabilities for all tests.

RESULTS

Prevalence at the sites ranged from 42 to 83%. Out of 500 infected snails, we identified nine trematode species and found seven snails with double infections. This was similar to other studies that have found double infections in only 2.5% of infected snails (Sousa 1993). Table 1 shows the observed number of double infections and the numbers estimated from the null models.

Prevalence ([[Chi].sup.2] = 75.8, df = 4, P [is less than] 0.01) and guild composition ([[Chi].sup.2] = 63.8, df = 11, P [is less than] 0.01) varied among sites. Thus, at Carpinteria Salt Marsh, spatial heterogeneity might significantly affect community structure. The simple null model, N[p.sub.i][p.sub.j], indicated little difference in the expected number of double infections between the pooled sites (71) and the sum of the sites (74). This suggested no significant effect of spatial heterogeneity on the potential number of double infections. There was no difference between the distributions of the standard deviates (Kolmogorov-Smirnov, P = 0.64). After using N[e.sub.i][e.sub.j], however, there was a significant difference between the expected number of double infections for pooled sites (111) and the sum of the expected double infections calculated for each site separately (133, see Fig. 3). In this case, the distributions of the standard deviates differed significantly (Fig. 4, Kolmogorov-Smirnov, P = 0.028). Therefore, spatial heterogeneity caused more, not fewer, co-occurrences.

For both null models, the difference between 8.7 observed double infections and the sum of the expected double infections (N[p.sub.i][p.sub.j] = 74, N[e.sub.i][e.sub.j] = 133) was considerable TABULAR DATA OMITTED and highly significant (Figs. 3 and 4, Kolmogorov-Smirnov, P [is less than] 0.001). Thus, we infer that competition resulted in the elimination of most of the expected co-occurrences. Table 2 presents the estimated proportion of each species lost to competition. Over all, interspecific competition apparently resulted in an estimated 16% loss of the trematodes that recruited to 25 to 30 mm snails.

DISCUSSION

The structuring effect of heterogeneity results from the interplay of isolating and intensifying factors. The relative prevalences of each trematode species varied among subsamples, acting to isolate species. In addition, however, variation in the absolute total prevalence among subsamples intensified the likelihood of double infections. Although both factors acted significantly in our study, the net effect was to intensify interactions. This finding is contrary to assertions that variability in recruitment reduces interactions (Sousa 1990, Fernandez and Esch 1991a, Esch and Fernandez 1993, Rohde 1993). As available evidence suggests that doubly infected snails did not suffer higher mortality than did hosts with single infections, competitive exclusion apparently eliminated most of the subordinate species in these co-occurrences. Using null parameters in the null model (N[e.sub.i][e.sub.j]) gave a different indication of the magnitudes of the structure imparted by both spatial heterogeneity and competition than did standard observed parameters. The notable differences between estimates derived from these models would have been even more pronounced had dominant species been common.

We conclude that competition is the best explanation for the fewer than expected double infections observed within these infracommunities. Even the seven double infections that we did observe could represent competitive events in progress (Kuris 1990, Fernandez and Esch 1991a). This conclusion is consistent with the findings of Sousa (1990, 1993) and Kuris (1990) for the same host-parasite system, as well as for studies of larval trematode assemblages in other molluscan hosts where double infections were less frequent than expected (Fernandez and Esch 1991 a, references in Kuris 1990 and Sousa 1992, Kuris and Lafferty 1994). We envision a three-step process determining the species composition of a guild of larval trematodes. First, the diversity and abundance of species that recruit to an area will determine the potential for co-occurrences (Kuris 1990, Sousa 1992). Then, spatial and temporal heterogeneity in recruitment will determine whether the initial number of co-occurrences is higher or lower than the potential number of co-occurrences. Finally, with time, competition, according to a hierarchy of dominance, will reduce the number of multiple-species infections that persist.

The importance of competition in structuring the trematode community is directly dependent on the proportion of hosts experiencing multiple infections. In the present case, overall prevalence was 61.6%, and competition appears to have displaced 16% of all trematode individuals. However, because we restricted our analysis to a narrow size class of hosts, we have only accounted for structure in a portion of the trematode guild. In an experimental mark--recapture study where overall prevalence at the study site was only 30%, Sousa (1993) found that annual replacement of one trematode by another eliminated 72% of Euhaplorchis californiensis (by far the most common trematode in our system), 11% of Acanthoparyphium spinulosum, 8% of Echinoparyphium sp., 8% of Himasthla rhigedana, and 1% of Parorchis acanthus (the most dominant species). These results are consistent with a highly interactive system. The vast majority of replacements were by the dominant species, P. acanthus and H. rhigedana (Sousa 1993), demonstrating the importance of the competitive hierarchy.
TABLE 2. An estimation, using prevalence pooled over all sites ([e.sub.i] vs.
[p.sub.i]), to estimate the effects of competition on the relative abundance
of trematode species. Numbers represent occurrences (double and single
infections) of each species. Estimated numbers before competition were
rounded to the nearest whole integer. Percentage losses were calculated from
the unrounded estimation.

Trematode            Before            After
species            competition       competition          Change

                                                              0%
PARO                    9.6                9.6             -1.7%
HIMA                   55.0               54.0            -11.6%
ECHI                   42.9               37.9            -16.1%
ACAN                    9.7                8.1            -13.1%
EUHA                  455.9              396.1            -20.6%
RENB                    2.7                2.1            -51.8%
SMST                   20.5                9.9            -60  %
LGXI                    2.7                1.1            -63.4%
SMXI                   35.4               13.0            -16.2%

Total                 634.3              531.8


General applications

Although developed to study larval trematodes, our approach applies to the general study of communities. Granted, communities of parasites are somewhat easier to study than free-living organisms because the scale at which we determine the presence or absence of a parasite species, the host, is unambiguous and biologically meaningful (Esch et al. 1990). Analogous, though more arbitrary, spatial scales for quantifying the presence-absence of free-living organisms would be the area of a home range, territory, or, for sessile species, the area covered by an individual. To use our methodology to determine the structure of a community of two free-living species, a and b, would require determining areas used by individuals, pairs, or other logical groups of each species. Then, as we have done for host snails, one could calculate the proportion of those areas occupied by species a, b, a and b, or neither a nor b. Although simply quantifying the presence or absence of a species leads to the easiest analysis, it may be more powerful to incorporate species densities in some cases (Rahel 1990). To test for structure, it is necessary to compare the observed frequency of overlapping areas with the frequency expected if the two species were randomly distributed and did not interact. Determining the expected frequency of overlap would require choosing and developing the appropriate null model (Strong et al. 1979). To generate a truly null expected value requires using null parameters in the null model. In the Appendix, we derive null prevalences for displacement or mortality associated with dominance or preemption. Where the observed overlap is different from expected, the community is structured. In some cases, it may not be possible to predict the position of every species in a postulated hypothetical linear dominance hierarchy. The exclusion of species with questionable dominance ranks from calculations of the expected prevalence of other species is appropriate yet carries the potential price of underestimating expected prevalences.

Structure, if found, could be a result of heterogeneity or interaction. Two spatial scales for sampling these areas would allow the determination of the relative role of spatial heterogeneity. The smaller spatial scale should be one in which there is little intraspecific variation in recruitment. Replicates of these small-scale samples should then be taken over the entire community of interest. This scale could be as large as the geographic distributions of the species. Wiens (1989) recommends investigating several spatial scales to determine the effects of scaling processes on the determinants of community structure. Comparing the sum of expected values of overlap on small spatial scales with the expected overlap calculated by pooling over a single large spatial scale would indicate whether heterogeneity acted to isolate the species, intensify their overlap, or did not affect their relative distributions. Samples taken over time would generate a similar analysis for temporal heterogeneity.

As we have tried to give the most general examples possible, one might have to modify our approach to suit the biology of the community under study. Here, we have concentrated solely on methods used to analyze patterns that we can observe in nature. The use of appropriate descriptors of a community, stratified samples, appropriate null models, and powerful statistical comparisons will make it easier to determine community structure from such observations. We feel strongly that this approach can lead to valuable insight but recognize that experimental approaches, though often difficult, are necessary to further investigate these patterns.

ACKNOWLEDGMENTS

A University of California President's Undergraduate Fellowship helped finance the field work conducted by D. Sammond. W. Sousa provided an invaluable preprint. A. Bush, S. Cooper, T. Huspeni, R. Schmitt, T. Stevens, A. Stewart-Oaten, and R. Warner provided helpful comments on the manuscript. T. Case, M. Cody, B. Downs, T. Price, and several others participated in helpful discussions. I. Davila-Marcano gave us access to his unpublished data.

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APPENDIX

Here, we derive the number of individuals of a species, i, expected to have recruited to a sample of territories (for parasites, these territories are hosts). For five biological scenarios, we describe an equation for the observed frequency of a species as a function of its pre-interactive frequency, solve for the pre-interactive frequency, and then calculate the pre-interactive frequency using hypothetical observed values. These equations are the equivalent of performing a series of binomial trials on each territory. A subordinate (according to dominance or preemption) that recruits to the same territory as a dominant could coexist, be killed, move to a conspecific territory, move to an empty territory, or move to a nonheterospecific territory. Scenario 1 fits what we expect most often happens for the larval trematodes in our system. Kuris (1990) used a similar approach to calculate the pre-interactive prevalence of trematode species by incorporating information from a proposed dominance hierarchy.

Scenario 1. -- Dominants either coexist with or kill subordinates, e.g., parasitic castrators or parasitoids (or the subordinate species moves to a conspecific territory). The observed prevalence of a species i will be equal to its initial prevalence minus the initial prevalence of double occurrences with dominant species plus the fraction of those double occurrences observed at the time of sampling. This is expressed as [p.sub.i] = [e.sub.i] - [p.sub.d][e.sub.i] + [O.sub.id], where [p.sub.i] is the observed prevalence of species i, [e.sub.i] is the prevalence of species i that recruit and would in isolation survive to the sampling date, [p.sub.d] is the combined prevalence of all species that are dominant to i, and [O.sub.id] is the proportion of double occurrences observed between i and d. Solving for [e.sub.i] yields [e.sub.i] = ([p.sub.i] - [o.sub.id])/(1 - [p.sub.d]). In this case, the prevalence of species i expected at recruitment is the portion of available hosts times the proportion of "competitor-free" hosts that species i occupies. Using hypothetical values of [p.sub.i] = 0.2, [p.sub.d] = 0.8, and [O.sub.id] = 0.1, [e.sub.i] = 0.5.

Scenario 2. -- Subordinates coexist with dominants or move to an empty territory, e.g., nesting song birds, hermit crabs, pontonean shrimps in penn shells. The observed prevalence of a species will be equal to the initial prevalence minus the initial prevalence of double occurrences with dominant species plus the prevalence of those double occurrences observed at the time of sampling plus the prevalence of double occurrences that move. This is expressed as [p.sub.i] = [e.sub.i] - [p.sub.d][e.sub.i] + [o.sub.id] + ([p.sub.d][e.sub.i] - [o.sub.id]). Solving for [e.sub.i] yields [e.sub.i] = [p.sub.i]. For the same hypothetical observed values, [e.sub.i] = 0.2.

Scenario 3. -- Subordinates coexist with dominants or move to a territory that does not contain a dominant, e.g., anemone fishes, ungulates. The prevalence of individuals of a species will be equal to the prevalence of initial individuals minus the proportion that moves to a conspecific territory. Assuming that two subordinates do not move to the same open territory, this is expressed as [p.sub.i] = [e.sub.i] - ([p.sub.d][e.sub.i] - [o.sub.id])([e.sub.i] - [p.sub.d][e.sub.i])/(1 - [p.sub.d]) or [p.sub.i] = [e.sub.i](1 - [p.sub.d][e.sub.i] + [o.sub.id]). Solving for [e.sub.i] yields [e.sub.i] = (1 + [o.sub.id] - [[([o.sub.id] + 1).sup.2] - [4[p.sub.d][p.sub.i]].sup.1/2])/2[p.sub.d]. For the same hypothetical observed values, [e.sub.i] = 0.22.

Scenario 4 (preemption). -- The first species to arrive coexists with or kills the second species to arrive, e.g., sessile, filter-feeding invertebrates (or the second species to arrive moves to a conspecific territory, e.g., barnacles with selective, gregarious settlement). Assuming each species has a 50% chance of being the first to arrive, the observed number of individuals of a species will be equal to the total number of initial individuals minus half the initial amount of double occurrences with other species plus half the number of those double occurrences observed at the time of sampling. This is expressed as [p.sub.i] = [e.sub.i] - [e.sub.i][e.sub.h]/2 + [o.sub.ih]/2, where [e.sub.h] is the fraction of heterospecific individuals expected at recruitment. The observed number of heterospecific individuals, [p.sub.h], will be equal to the total number of initial heterospecific individuals minus half the initial amount of double occurrences with species i plus half the number of those double occurrences observed at the time of sampling. This is expressed as [p.sub.h] = [e.sub.h] - [e.sub.i][e.sub.h]/2 + [o.sub.ih]/2. Using both equations to solve for [e.sub.i] yields [e.sub.i] = 1 + {[p.sub.i] - [p.sub.h] - [([[[p.sub.h] - [p.sub.i] - 2].sup.2] - 4[[2[p.sub.i] - [o.sub.ih]].sup.1/2]}/2. For the same hypothetical observed values, and for [p.sub.h] = 0.8, [e.sub.i] = 0.26.

Scenario 5 (preemption). -- The second species to arrive coexists with the first species to arrive or moves to an empty territory, e.g., mantis shrimps. The observed number of individuals of a species will be equal to the total number of initial individuals minus the initial amount of double occurrences plus the number of those double occurrences observed at the time of sampling plus the number of double occurrences that move. This is expressed as [p.sub.i] = [e.sub.i] - [e.sub.i][e.sub.h] + [o.sub.ih] + ([e.sub.i][e.sub.h] - [o.sub.ih]). Solving for [e.sub.i] yields [e.sub.i] = [p.sub.i]. For the same hypothetical observed values, [e.sub.i] = 0.2.

It is not possible to explicitly calculate [e.sub.i] for the scenario where the second species to arrive coexists with the first species or moves to a nonheterospecific territory. This may not be a likely pattern of interaction for preemption because if recruitment order determines dominance, early recruiting individuals should be able to exclude members of their own species.

The goal of these formulae is to provide values for null models that are free from the effects of competition. Although the scenarios incorporate assumptions about interactions, they do not assume that competition occurs; they only assume that if competition does occur its outcome is predictable. Only by determining the number of each species that recruit, is it possible to estimate the number of territories with co-occurring species that would be expected were structuring forces such as competition or variation in habitat selection not operating. For two species, the expected null frequency of co-occurrences equals N[e.sub.i][e.sub.j]. This may vary strongly from the more generally used null model N[p.sub.i][p.sub.j] in scenarios where species kill or move to conspecific territories, especially if dominants are common. For situations where subordinate species may move to another habitat, it may be justifiable to modify our equations to account for certain percent loss of those individuals that move.
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Author:Lafferty, K.D.; Sammond, D.T.; Kuris, A.M.
Publication:Ecology
Date:Dec 1, 1994
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