Predicting the relationship between local and regional species richness from a patch occupancy dynamics model

Transcription

1 Ecology 2000, 69, Predicting the relationship between local and regional species richness from a patch occupancy dynamics model B. HUGUENY* and H.V. CORNELL{ *ORSTOM, Laboratoire d'ecologie des eaux douces, Universite Lyon I, 43 Bld du 11 Novembre 1918, Villeurbanne cedex, France; and {Department of Biology, University of Delaware, Newark, DE USA Summary 1. A linear relationship between the number of species in ecological communities (local richness) and the species pools from which the communities are drawn (regional richness) suggests that species interactions are not su cient to limit local richness and that communities are not saturated with species. Instead, this relationship implies that communities are open to regional in uences and are interlinked by dispersal. 2. Here we show how the linear relationship between local and regional richness in real, noninteractive, assemblages of cynipid gall wasps on California oaks, can be predicted from a simple patch-occupancy model. 3. One cynipid assemblage has been surveyed for 3 years, allowing for crude estimates of colonization and extinction rates per patch. Using the mainland/island model of patch occupancy dynamics, these rates are combined with the observed number of cynipid species associated with each oak species (regional richness) to predict the expected local species richness in each patch. Assuming that species are independently distributed among localities, the expected variance in species richness among localities is also computed. 4. The model is then tested on an independent data set. When di erences in sampling e ort (number of surveyed trees per locality) were accounted for, the regression equation relating observed (n = 41) to predicted local species richness does not di er statistically from the line of perfect agreement. The residuals are also distributed according to the predicted variance. 5. Although not statistically signi cant, the variance in local richness appears to be slightly underestimated by the model. One explanation may be that cynipid species display some positive covariance in their distribution among localities, that is, groups of species occur together in given localities more frequently than would be expected by chance. Variance ratio tests identi ed statistically positive covariance within cynipid assemblages for three oaks species. 6. The close t of the model to the data supports the theoretical scenario for noninteractive communities, that the slope of the local±regional richness relationship and patch-occupancy processes are di erent expressions of the same phenomenon. Key-words: cynipid wasps, extinction and colonization rates, island biogeography, metapopulation, species associations. Ecology (2000) 69, Correspondence: B. Hugueny, ORSTOM, Laboratoire d'ecologie des eaux douces, Universite Lyon I, 43 Bld du 11 Novembre 1918, Villeurbanne cedex, France. hugueny@biomserv.univ-lyon1.fr

2 195 B. Hugueny & H.V. Cornell Introduction The conventional wisdom in ecology over the past 30 years has been that interactions among populations operating within small areas over relatively short periods of time are, in the main, responsible for regulating the numbers of species in ecological communities (local richness). However, it has become increasingly clear that this view is too simplistic, and, as a result, there has been a broadening of the spatial and temporal scales over which community processes are studied (Ricklefs 1987; Cornell & Lawton 1992). This broadening of perspective has been driven in part by the frequent occurrence of linear relationships between local and regional species richness (Cornell & Karlson 1997). Such linear relationships, which have been termed proportional sampling (Cornell & Lawton 1992), suggest that species interactions are not su cient to limit local richness and that communities are not saturated with species. Instead, proportional sampling implies that communities are open to regional in uences and are interlinked by dispersal. Regional dispersal is also a key component of metapopulation or patch occupancy models (Hanski 1994a). In these models a region is subdivided into a nite number of homogeneous habitat patches, and each patch is able to support a local population. If more than one species occupies this patchy universe, then each patch can support local populations of any of the species that comprise the regional pool (e.g. Caswell & Cohen 1993). The pool of species occupying this universe has been termed the metacommunity (Hanski & Gilpin 1991). A key provision of patch occupancy models is that local populations of any species can be driven to extinction by disturbance or demographic stochasticity. However, these models also allow populations to be regionally connected via dispersal so that, despite local extinction, persistence is possible at the regional scale. The equilibrium proportion of occupied patches is determined by the balance between local extinction within a patch and patch-to-patch dispersal rates of each species. Regional dispersal in a spatial context thus links two previously independent theoretical frameworks in ecology: patch occupancy dynamics and the regional regulation of local species richness (e.g. Caswell & Cohen 1993). The purpose of this paper is develop this synthesis further by showing how the relationship between local and regional richness in a real assemblage can be predicted from a simple island/mainland patch occupancy model (Gotelli 1991). Toward this end, we have reanalysed data collected by Cornell (1985, 1986) on species richness of cynipine gall wasps on California oaks. California oaks display patchy distributions as a result of habitat heterogeneity within natural landscapes and habitat fragmentation in human-altered landscapes. Moreover, the cynipids associated with these oaks exhibit a linear relationship between local and regional species richness and thus provide a clear example of proportional sampling, the earmark of an unsaturated community that is open to regional in uences (Cornell & Lawton 1992). Materials and methods Patch occupancy models provide the equilibrium fraction of localities occupied by a species within a region (p) as a function of colonization and extinction rates per locality. If localities are homogeneous, p is also the probability of the presence of the species in one locality. The expected species richness of a locality (local species richness, LSR) is given by the sum of species-speci c probabilities of presence: E LSR ˆS RSR iˆ1 p i eqn 1 (regional species richness, RSR) where p i is the expected proportion of patches occupied at equilibrium by species i given by some single-species patch-occupancy model. Some multispecies patch occupancy models assume that the extinction probability of a species increases if competitively dominant species are already present in the patch (Caswell & Cohen 1993) producing negative covariances among species. However, because cynipid wasp communities are considered noninteractive (Cornell 1985), we focus on patch occupancy models that assume no interspeci c interactions among species within a patch. Thus, assuming that species distributions among patches are statistically independent, the variance of LSR is given by: V LSR ˆS RSR iˆ1 p i 1 p i : eqn 2 Equations 1 and 2 can be rewritten as: E LSR ˆpRSR eqn 3 and V LSR ˆp 1 p RSR eqn 4 where RSR is the size of the regional pool. The average of p i over all species in the metacommunity is given by p which becomes the average proportion of regional species richness found in a local patch. Spatially implicit metapopulation models can be classi ed into four categories based, in part, upon whether colonization and/or extinction rates per patch are a function of regional occurrence (Gotelli 1991). The simplest of these models, the island/ mainland model, assumes that colonization and extinction rates are constant and not a ected by regional occurrence. The island/mainland model is the single species/several patches analogue of MacArthur & Wilson's (1963) equilibrium model of island biogeography in which p i =c i /(c i +e i ), where

3 196 Local species richness and patch occupancy dynamics c i and e i denote, respectively, the colonization and extinction probabilities of species i in one unit of time in the patch. The underlying assumptions of the model are as follows: (i) well mixed assemblages; (ii) homogeneous patches; and (iii) independence between the number of occupied patches and the per species colonization and extinction probabilities in a patch. In addition, because the communities are not interactive, average c and average e are unaffected by the size of the regional species pool. Given these assumptions, the model predicts a linear, proportional sampling relationship between regional and local species richness. Thus, if a real species assemblage exhibits a proportional sampling curve, its slope might be predicted from observed colonization and extinction rates of the constituent species. A good match between predicted and observed slopes would suggest that this simple model is an adequate description of the patch dynamics of the metacommunity. A major advantage of using the island/mainland model is that colonization and extinction rates can be estimated from temporal surveys of communities within representative localities. Cornell (1986) surveyed one locality (locality 7) for 3 years, generating crude estimates of colonization and extinction rates in the cynipid wasp assemblage. However the sampling protocol did not provide enough data for estimating colonization and extinction rates per species. We thus had to pool species and assume that p 1 =p 2 =...=p n = p in equations 1 and 2. Colonization rate was computed as the ratio of the number of observed colonizations to the number of possible colonizations. The number of possible colonizations between two years is the number of species not present in the locality in the rst year (regional richness minus local richness at year one). The total number of possible colonizations is the sum of the possible colonizations between years one and two and between years two and three. We proceeded similarly to estimate extinction rates (i.e. observed extinctions/possible extinctions). The number of possible extinctions between two years is the number of species present in the locality the rst year. Because only four trees were surveyed in each of the three years, these calculations produced an estimate for p(n = 4), the probability that a given cynipid species will appear in a locality where four trees have been surveyed. However, this estimate cannot be used directly to predict the slope of the LSR± RSR relationship. Sample sizes used to estimate local richness in each locality varied (range 4 ± 15 trees). Thus, the observed local richness at each locality and the predicted slope of the LSR±RSR curve must both be corrected for di erences in sampling e ort. Suppose that, in a given locality, sr obs species have been observed by sampling n samp trees. Assuming that species are randomly placed on trees, the number of species expected on n trees is given by: sr N ˆ n ˆ1 1 sr obs =RSR Š n=nsamp : eqn 5 Although cynipid species do not actually occur at random on individual trees with respect to their height (Cornell 1986), we estimated extinction and immigration rate by pooling data for four trees of varying heights (range 1 ± 10 m). This size range encompasses most of the tree size gradient observed in all other localities so that our estimate of p should not be biased as long as a representative sample of trees is surveyed at each locality. With this expression, we can compute species richness standardized for any sample size. Most of the local richness estimates (20) were based on sample sizes of 10 trees, so we chose this as the standard sample; all other estimates of local richness were standardized to 10 trees. Similarly, the expected slope between local and regional species richness, provided that 10 trees have been sampled at each locality, is given by: p N ˆ 10 ˆ1 1 p N ˆ 4 Š 10=4 : eqn 6 The value for p(n = 10) can be substituted for p in equation 1 and predicted local species richness can be compared with observed local richness, both values having been standardized to samples of 10 trees. If local richness is adequately predicted by the simple island/mainland patch occupancy model, and the predictions are not overly sensitive to our simplifying assumptions, then a regression of observed values on predicted values should not di er signi cantly from a line of slope = 1 crossing the origin. However, conventional least-squares procedures cannot be used to estimate this regression equation because, according to equation 4, the expected variance of LSR is proportional to RSR (and hence to the predicted LSR value). Thus, the assumption of homoscedasticity is violated. A way to circumvent this problem is to use a weighted least-squares procedure. In our case the weight is the inverse of the square root of the predicted value (Draper & Smith 1966, p. 81). In other words, the observed and predicted values are divided (weighted) by the square root of the predicted values before performing regression analysis. See SYSTAT (1992) for more details on the weighting procedure. If variance in local richness is adequately predicted by the patch occupancy model, then there should be agreement between the observed variance and that predicted by equation 2. This equation was used to generate standardized residuals (observed value minus predicted value divided by predicted standard deviation). Agreement with the model was tested by comparing the variance of the standardized residuals to unity, the predicted value. This procedure is most e ective when RSR is large, such that the sum of independent random variables (p i )

4 197 B. Hugueny & H.V. Cornell approximates a normal distribution. Because RSR is sometimes small (less than 30) in our study, the results should be interpreted with caution. Equation 2 assumes that species are independently distributed among localities. If this assumption is not met then the predictions of equation 2 must be modi ed to take into account any covariance in species' distributions. If there is an excess of positive covariance, that is, if groups of species occur together and/or are together absent from given localities more frequently than would be expected by chance, then equation 2 underestimates the true variance in local richness. Conversely, the true variance is overestimated if there is an excess of negative covariance where some species occur in the absence of other species more frequently than expected. To test the null hypothesis of independent distributions, we used a variance ratio test proposed by Schluter (1984). This test is based on the ratio (V) of the variance in total species number per locality to the sum of the variances of individual species. If V > 1 then there is net positive covariance in species distributions and if V < 1 then net covariance is negative. V was calculated for cynipid communities associated with four California oak species and signi cant deviations from the null hypothesis (V =1) were tested with the W statistic (W = N*V). W is approximately chi-square distributed with N degrees of freedom, where N is the number of localities. Results Table 1. Observed and possible number of extinction and immigration events of cynipid species in locality 7 Given the estimated extinction and immigration rates from locality 7 (Table 1) the patch occupancy model predicts that p(n = 4) = Standardizing to a sample size of 10 trees by applying equation 6, p(n = 10) = This standardized value was then used to generate the predicted relationship between local and regional species richness. The predicted relationship is in good agreement with the data (Fig. 1). This agreement is con rmed by the regression of observed local richness on predicted local richness which does not di er signi cantly from a line of unitary slope crossing the origin (H 0 : origin = 0, t = 0 89, 0 3 < p < 0 5; H 0 : slope = 1, t = 1 46, 0 1 < p < 0 2). Locality 7 was not included in the analysis in order that the data used to test the model be kept independent of those used to estimate the model parameters. The observed variance in local species richness is somewhat higher than that predicted by the patch occupancy model: the variance of standardized residuals is 1 34 instead of 1. However this value does not di er statistically from unity (95% CL: 0 90± 2 19). At least some of this excess variance is probably because the cynipid species are not independently distributed among localities. The variance test (Table 2) identi ed signi cant excess positive covariance in cynipid species distributions on three of the four California oak species surveyed. On the fourth oak species, the test for positive covariance was nearly signi cant. Discussion Extinctions Immigrations Observed Possible Rate Despite crude estimates of extinction and colonization rates, the patch occupancy model accurately predicts mean local species richness from measure- Fig. 1. Relationship between local species richness (standardized for 10 sampled trees) and regional species richness. The local species richness predicted from patch-occupancy dynamics (2 2 SD predicted) is shown.

5 198 Local species richness and patch occupancy dynamics Table 2. Variance test for cynipid species associations on four oak (Quercus) species (positive association: *P < 0 05, **P < 0 01, NS: not signi cant) Oak species S variances of species occurrences Variance of species richness Q. chrysolepis * Q. lobata ** Q. douglasii * Q. agrifolia (NS) W ments of the regional species pool. Moreover, the model only slightly underestimates the dispersion of observed values around the prediction line. The close t of the model to the data supports the theoretical scenario for noninteractive communities, that the slope of the proportional sampling curve and temporal turnover within a locality are di erent expressions of the same patch-occupancy processes. However, in other systems, proportional sampling may be observed without temporal turnover as is the case for insect herbivore species on bracken (J. H. Lawton, personal communication). In these cases, patch occupancy dynamics models are clearly not helpful either in explaining the local±regional richness relationship or in explaining patterns of species occurrence (Gaston & Lawton 1989). The island/mainland patch dynamic model was chosen for the analysis because it is conceptually simple and is easy to test with presence-absence data from several time intervals. However, the model's strength is also its weakness; simplicity demands that some unrealistic assumptions have to be made. The major ones are that colonization and extinction rates are constant through time and space. In other words, each patch in a particular place experiences the same colonization and extinction rates over time, and all patches at a given time are homogeneous with respect to these rates over space. Violation of these assumptions can result in a distorted prediction of both the mean and the variance in local richness among metacommunities. Although there is no direct evidence that the assumption of temporal constancy is violated in the cynipid system, circumstantial evidence raises the possibility that it might be; for example, several metapopulation models predict that colonization rates are unlikely to be constant if the number of occupied colonization sources uctuates through time (Gotelli 1991). Because potential colonization sources for any cynipid assemblage are multiple (other trees, patches, oak species), the availability of colonists in these potential sources at any given time should vary on probabilistic grounds alone. Similarly, the core-satellite hypothesis predicts that extinction rates should also be inconstant and should vary inversely with the number of occupied patches (Hanski 1982) because of the rescue e ect (Brown & Kodric-Brown 1977). This inverse relationship generates bimodality in species distributions among patches. For some species of oak, there is a clear bimodality in the distribution of cynipid occurrences (Cornell 1985), lending support to the hypothesis. However bimodality may result from causes other than rescue e ect (Gotelli & Simberlo 1987; Nee, Gregory & May 1991), thus rm conclusions about variable extinction rates will require that these alternatives be tested. Other evidence suggests that the assumption of spatial constancy might also be violated. Notably, several sampled cynipid assemblages exhibited extreme LSR/RSR ratios that seemed to correlate with the spatial location of the sampled localities (Cornell 1985). Those with excessively low ratios occurred at the edges of host ranges and those with unexpectedly high ratios occurred in mixed associations of several host species at the same locality. Host populations at the edge of the species range may be subjected to low colonization rates because of isolation from other host individuals, and higher extinction rates because of extreme ecological conditions. Those in mixed associations may experience reduced extinction rates and/or increased colonization rates as a result of increases in total host density for those cynipids that can colonize multiple host species. Spatiotemporal variability in colonization and extinction rates per patch cannot be incorporated into the simple island/mainland model. However, spatially explicit metapopulation models (Hanski 1994b) can generate such variability as a function of percentage patch occupancy, patch isolation and patch quality. These models have been successfully applied to butter y populations (Thomas & Hanski 1997) which are similar in crucial ways to cynipid populations. The larval stages of both groups are closely associated with one or a few plant species, so that the presence or absence of these plants provides an easy way to identify patches of suitable quality. In addition, the dynamics of both butter y and cynipid populations are faster than patch (host) dynamics. Thus, the application of spatially explicit models to cynipid assemblages may prove e ective

6 199 B. Hugueny & H.V. Cornell in re ning the expected values for the mean and variance in local richness. Nevertheless, the island/mainland model provided a good approximation to slope of the proportional sampling curve, suggesting that its predictive power for expected local richness is robust to the simplifying assumptions. The possible reasons for this robustness are twofold. First, the cynipid species may have been close to its patch occupancy equilibrium. As a result, the proportion of patches occupied may have been relatively constant through time, resulting in roughly constant colonization and extinction rates. Secondly, although there is between-patch heterogeneity in the cynipid system, the same level of heterogeneity may have occurred in each region with respect to key habitat features. Between-patch heterogeneity does not a ect the prediction of the LSR±RSR slope under these circumstances. However it can still a ect variance in local richness if groups of species prefer similar habitats and/or reject other similar habitats in the heterogeneous matrix; in other words, there is species covariance in patch occupancy. Variance ratio tests con rm that there is signi cant positive covariation of this nature in the cynipid system and this covariation probably accounts for the variance underestimate (although it is not signi cant) in the prediction model. Diamond & Gilpin (1980) reached a similar conclusion in trying to predict variance in island species richness from immigration and extinction rates. In testing the island/mainland model, we assumed that the cynipid communities were noninteractive. This assumption is plausible in the light of evidence from previous studies (Cornell 1985) and is further supported in the current study by the absence of negative covariance among species distributions. Nevertheless, it is useful to consider the e ects of species interactions on the LSR±RSR relationship in patch occupancy models. The simplest way to deal with species interactions in the island/mainland model is to assume that di use competition (or other negative interactions) increases the extinction rate when more species are locally present, generating a concave extinction curve (MacArthur & Wilson 1963). The model then predicts a convex curvilinear relationship between LSR and RSR. However proportional sampling might still occur in the presence of intense competition, as shown by Caswell & Cohen (1993), provided that the disturbance rate is high enough. Hanski & Simberlo (1997) pointed out that the underpinnings of conservation biology have undergone a paradigm shift from island biogeography theory to metapopulation theory. This shift has occurred despite the fact that `fundamentally, the theory of island biogeography can be construed as just a multispecies version of an analogous metapopulation theory, so it is hard to imagine objective scienti c reasons for accepting one while rejecting the other' (Hanski & Simberlo 1997). One possible explanation for this shift derives from historical differences in the spatial scales for which these two theoretical perspectives were developed. The dynamic theory of island biogeography was originally developed to explain patterns at island and continental scales, whereas metapopulation theory was restricted to habitat fragments at the landscape scale. By placing the LSR±RSR relationship within the framework of patch-occupancy dynamics we have demonstrated how local species richness can be regulated by processes operating at the metapopulation scale. Moreover, by basing our analysis on the island/mainland model, we have demonstrated the application of island biogeography theory to scales traditionally reserved for metapopulation approaches. Just as the metapopulation concept provided novel insights into population dynamics in a spatial context, so the metacommunity concept applied here should increase our understanding of the spatial processes a ecting species diversity in communities. Acknowledgements We would like to thank S. Harrison and J. H. Lawton for helpful comments on an earlier version of the manuscript. H. V. Cornell was supported by the National Science Foundation and the NERC Centre for Population Biology, Imperial College, Silwood Park. References Brown, J.H. & Kodric-Brown, A. (1977) Turnover rates in insular biogeography: e ect of immigration on extinction. Ecology, 58, 445±449. Caswell, H. & Cohen, J.E. (1993) Local and regional regulation of species-area relations: a patch-occupancy model. 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