Species co-occurrences and neutral models: reassessing J. M. Diamond s assembly rules

OIKOS 107: 603/609, 2004 Species co-occurrences and neutral models: reassessing J. M. Diamond s assembly rules Werner Ulrich Ulrich, W. 2004. Species co-occurrences and neutral models: reassessing J. M. Diamond s assembly rules. / Oikos 107: 603/609. The question whether species co-occurrence patterns are non-random has intrigued ecology for more than two decades. Recently Gotelli and McCabe used meta-analysis to show that natural assemblages indeed tend to have non-random species cooccurrence patterns and that these patterns are in line with the predictions of Diamond s assembly rule model. Here I show that neutral ecological drift models are able to generate patterns in line with Diamond s assembly rules and very similar to the empirical results in Gotelli and McCabe. Ecological drift shifted species co-occurrence patterns (measured by C-scores, checkerboard scores and species combination scores) of model species placed into a grid of the 25 cells (sites; metacommunity sizes 5 to 25 species with 100 individuals each) significantly from an initial random pattern towards a pattern predicted by the assembly rule model of Diamond. These findings imply that instead of asking whether natural communities are structured according to some assembly rules we should ask whether these non-random patterns are generated by species interactions or by stochastic drift processes. W. Ulrich, Nicolaus Copernicus Univ. Toruń, Dept of Animal Ecology, Gagarina 9, PL-87-100 Toruń, Poland (ulrichw@uni.torun.pl). One of the fundamental questions in ecology is whether ecological communities are structured according to a set of general rules. But this is also one of the most controversial issues in ecology (Strong et al. 1984, Weiher and Keddy 1999). Especially the assembly rule model of Diamond (Diamond 1975) has stirred an intensive debate over the past three decades (Connor and Simberloff 1979, 1983, 1984, Diamond and Gilpin 1982, Gilpin and Diamond 1982, Manly 1995, Sanderson et al. 1998, Weiher and Keddy 1999). Diamond (1975) claimed to have identified a set of fundamental rules that determine species co-occurrence pattern in natural communities. As the main structuring force he identified interspecific competition. The debate about Diamond s model focused mainly on two questions: whether the model is logically sound (Connor and Simberloff 1979) and how to construct adequate null models for testing it (Manly 1995, Gotelli and Graves 1996, Sanderson et al. 1998, Gotelli and Rhode 2002). This debate resulted in improved statistical techniques and in the development of software for testing non-randomness in presence absence or abundance matrices (Schluter 1984, Gotelli et al. 1997, Shenk et al. 1998, Gotelli 2000, Gotelli and Entsminger 2001, 2002). These efforts clarified the performance of certain null model algorithms and their ability to detect nonrandom species co-occurrence patterns (Gotelli 2000, 2001, Gotelli and Entsminger 2003). A major drawback in the discussion about the assembly rule model was the restricted data base. The original formulation of the model rested on presence absence data of bird species of the Bismarck Archipelago (Diamond 1975). Since then, only a few additional studies were used to test the model (Gotelli and Graves 1996). In this respect, the recent publication of Gotelli and McCabe (2002) is a major step forward. They Accepted 15 May 2004 Copyright # OIKOS 2004 ISSN 0030-1299 OIKOS 107:3 (2004) 603

undertook a meta-analysis of 96 studies on the distribution of species among replicated sites and found significant deviations from the null model of random species associations towards the direction predicted by the assembly rule model of Diamond. However, even this result does not decisively answer the question what causes the observed deviations from random patterns. The classical interpretation points to species interactions, especially to competition, as the main force for shaping community structure (Connell 1980, Tilman 1982, Weiher and Keddy 1999). Instead, Schoener and Adler (1991) and Bell (2001) pointed to habitat heterogeneity as a source for non-random species spatial distributions. However, it is also possible that pure stochastic processes generate non-randomness. Recently, Bell (2000, 2001) and Hubbell (2001) argued for random processes that shape local and regional community structure. Their neutral community models treat all species as being identical and local community structures being the result of single random birth, death, immigration, and emigration events inside a regional metacommunity of fixed population size. Their approach has gained wide interest (Whitfield 2002, Ulrich 2004) because it is able to generate many of the observed macroecological patterns like species and individual/ area relations, abundance/range size, or frequency / rank order distributions (Hubbell 2001). Bell (2001) argued that the neutral model approach is also able to generate non-random species spatial distribution patterns. He compared correlations between species co-occurrences of the model with randomized data and found the neutral model to produce more positive correlations (and therefore non-random distributions) than expected. This result would contradict the assembly rules 1 and 5 of Diamond s model. Bell did not explicitly refer to any assembly rule model and his model runs were not intended as an explicit test for nonrandom co-occurrences. However, it seems worthwhile to study the neutral model approach to see whether it is able to generate non-random species spatial distribution patterns. A comparison of the neutral model results with the results of Gotelli and McCabe (2002) would also be a test for the neutral model approach. Methods Modelling species spatial distribution I used the zero-sum multinomial neutral model approach of Hubbell (2001) to generate local assemblages from metacommunities. 100 individuals each of 5, 6, 7,..., 25 model species were placed in a stepwise process (individual after individual) into the cells of a grid of 25 cells (sites). The original version of the null models of Bell (2001) and Hubbell (2001) assumes a homogeneous landscape, where all sites have the same properties. To study whether initial cell heterogeneity influences community structures I performed the whole model approach for metacommunities, whose species were initially randomly distributed over the grid and for metacommunities, whose species had an aggregated distribution. This is essentially the same as to deal with a heterogeneous landscape. Aggregation was introduced by placing 1 to 12 individuals per step (Peres-Neto et al. 2001). In the homogeneous grids the cells contained in nearly all cases all species of the metacommunity and 73 to 116 individuals (25 species: m/100, s/12). In the heterogeneous grids single cells contained between 32 and 195 individuals after placement (25 species: m/100, s/38) and between 24% and 92% of the number of species in the metacommunity (m/54%, s/22%). I measured species spatial distribution patterns with the index of Lloyd (Lloyd 1967). In the homogeneous grids the index of Lloyd had a mean of m/1.16 (s/0.23) indicating a Poisson random distribution. In the heterogeneous grids Lloyd index values ranged between 0.5 and 14 (m/4.31, s/2.29). The stepwise placing process caused that initial species spatial distribution patterns were not more correlated than expected by chance (tested by the variance test with density data of Schluter 1984). Individual numbers per cell remained constant during model run. After placement single local birth and death process were counterbalanced by immigration and emigration processes without dispersal limitation (Hubbell 2001). For each model run such single processes were repeated 500, 1000, 2000, and 4000 times the initial number of individuals in the metapopulation. Metapopulation species numbers were held constant by a point mutation speciation process (Hubbell 2001). For each species number the above simulation was repeated 20 times resulting in a total of 21/20/420 metacommunities for each of the four runtime classes. The whole modelling approach was done with the program NeutralCom (Ulrich 2003, available together with manual at www. uni.torun.pl//ulrichw). Measuring co-occurrences I studied species co-occurrences using three indices: the number of species combinations (Pielou and Pielou 1968), the number of perfect checkerboards (Gotelli 2000), and the checkerboard score (C-score) introduced by Stone and Roberts (1990). Gotelli (2000) and Gotelli and McCabe (2002) describe these measures and their performance in detail. I used EcoSim 7.00 (Gotelli and Entsminger 2002) for computing random matrices and standardized effect sizes. I used fixed sum row and column constraints and the sequential swap algorithm 604 OIKOS 107:3 (2004)

Table 1. Summary results of C-scores, No. of checkerboard scores and species combination scores from 420 assemblages placed into homogeneous grids. Given are numbers of assemblages with higher score values after the neutral model run than directly after placement and the probability that this number is larger than expected from a binomial distribution. Given are also the numbers of assemblages with score values above or below 1.96. 500, 1000, 2000, 4000 denote the runtimes of the model. Scores after /Scores before p(x/210) Scores/1.96 ScoresB//1.96 Before After Before After C-scores 500 260 0.00000 0 38 0 0 1000 220 0.15275 0 42 0 0 2000 240 0.00144 0 52 0 0 4000 222 0.11123 0 39 0 2 No. checkerboards 500 187 0.98601 0 30 0 0 1000 200 0.82306 0 26 0 0 2000 216 0.26296 0 33 0 0 4000 198 0.86914 0 37 0 0 Species combinations 500 145 0.00000 0 3 0 39 1000 109 0.00000 0 1 0 37 2000 126 0.00000 0 1 0 51 4000 132 0.00000 0 1 0 43 for randomization. Standard deviations of effect sizes were computed from 5000 null matrices. Standardized effect sizes are Z-transformed and should have a mean of 0 and a standard deviation of 1). Diamond s assembly rules instead predict mean standardized checkerboard and C-score values significantly above 0 but standardized species combination values below 0 (Gotelli and McCabe 2002). In the case of the model assemblages studied here the initial placing of the species into the grid / especially in the case of the heterogeneous grid / might influence the statistical distribution of index values apart from a theoretical normal Z-distribution. Therefore species co-occurrence patterns after the neutral model run were compared with the theoretical Z-distribution and species co-occurrences directly after placing. Results The simple placement of individuals into the homogeneous and the heterogeneous grids did not result in non-random species co-occurrence patterns (Table 1). All score values were zero showing that all species were present in each of the cells. In the heterogeneous grids 11 to 21 out of 420 C-scores were above 1.96 and 12 to 20 species combination scores below 1.96. These numbers are slightly higher that expected by chance from a standardized normal distribution (10.5 such values are expected). The mean score values after placing into the heterogeneous grid did in no case deviate significantly from zero. The neutral model approach shifted the co-occurrence scores significantly towards the predictions of Table 2. Summary results of C-scores, No. of checkerboard scores and species combination scores from 420 assemblages placed into heterogeneous grids. Given are numbers of assemblages with higher score values after the neutral model run than directly after placement and the probability that this number is larger than expected from a binomial distribution. Given are also the numbers of assemblages with score values above or below 1.96. 500, 1000, 2000, 4000 denote the runtimes of the model. Scores after /Scores before p(x/210) Scores/1.96 ScoresB//1.96 Before After Before After C-scores 500 263 0.00000 14 30 6 2 1000 365 0.00000 21 32 7 1 2000 244 0.00037 14 36 8 2 4000 232 0.01399 11 34 4 2 No. checkerboards 500 217 0.23213 9 25 5 7 1000 208 0.55818 7 13 1 6 2000 237 0.00360 9 26 1 6 4000 222 0.11123 4 29 1 8 Species combinations 500 156 0.00000 2 2 20 31 1000 171 0.00008 1 3 19 31 2000 142 0.00000 3 2 13 40 4000 155 0.00000 0 4 12 37 OIKOS 107:3 (2004) 605

Table 3. Mean score values before and after the neutral model run in homogeneous and heterogeneous grids. 500, 1000, 2000, 4000 denote the runtimes of the model. ***: pb/0.001 that the mean deviates from zero. Homogeneous grids Heterogeneous grids Before After Before After C-scores 500 0 0.489/1.10*** 0.019/0.99 0.409/1.05*** 1000 0 0.449/1.21*** 0.019/1.05 0.379/1.11*** 2000 0 0.549/1.42*** /0.019/1.02 0.339/1.12*** 4000 0 0.429/1.22*** /0.069/1.03 0.219/1.17*** No. checkerboards 500 0 0.289/1.12*** 0.099/1.52 0.189/1.09 1000 0 0.329/1.04*** 0.009/0.64 0.059/0.95 2000 0 0.339/1.12*** 0.039/0.64 0.289/1.08*** 4000 0 0.349/1.08*** /0.039/0.57 0.249/1.11*** Species combinations 500 0 /0.489/1.14*** /0.049/1.06 /0.379/1.06*** 1000 0 /0.579/1.11*** /0.019/1.07 /0.309/1.04*** 2000 0 /0.559/1.20*** 0.009/0.94 /0.499/1.07*** 4000 0 /0.449/1.12*** 0.009/0.97 /0.369/1.14*** Diamond s assembly rule model (Table 1 /3). In all four runtime approaches significantly more assemblages had C-scores that were higher than before model run (Table 1, 2). Mean scores were shifted towards positive values (Table 3). In the heterogeneous grids at least 55% of all assemblages had higher score values after the neutral model runs than before. Between 30 and 52 assemblages had scores above 1.96 (Table 1, 2). These numbers are significantly higher that expected by chance from a standard normal distribution [P(30 values/1.96) B/0.0001]. Even more pronounced were the results for the species combination scores. Mean scores were in all runtime approaches significantly negative (Table 3). In both grid types at least 59% of all assemblages had lower score values after the neutral model runs than before. Interestingly, the placing of species into the heterogeneous grid caused that already between 12 to 20 assemblages had scores below /1.96, whereas 10.5 were expected if a standardized normal distribution would apply. The numbers of checkerboard scores were least affected by the neutral model runs. Score values of single assemblages did not significantly shift into the directions predicted by Diamond s assembly rule model. Nevertheless the ecological drift process resulted in a skewed distribution with significantly more assemblages (13 to 37) having score values above 1.96 than predicted from a simple normal distribution of scores [p(t)b/0.001] (Table 1, 2). The deviations of score values were neither in the homogeneous nor in the heterogeneous grids significantly (pb/0.05) correlated with the number of species in the assemblages (Fig. 1 /3). Discussion Recently, Gotelli and McCabe (2002) showed convincingly that species co-occurrences in natural metacommunities are not random. Instead, they found that the assembly rule model of Diamond is able to explain at least part of the observed variance in species spatial distribution patterns. Diamond s (1975) original model assumed species interactions, especially competition, to be responsible for observed co-occurrence patterns. Fig. 1. Standardized effect sizes in dependence of species numbers for 420 model communities after placement into a heterogeneous grid (runtime: 4000 times the species number). The three distributions do not differ significantly from normality (chi 2 -test p/0.05) in being skewed towards higher or lower effect sizes. 606 OIKOS 107:3 (2004)

Fig. 2. Standardized effect sizes in dependence of species numbers for 420 model communities in homogeneous grids after running the neutral model (runtime: 4000 times the species number). The three distributions differ significantly from normality (chi 2 -test pb/0.01) in being skewed towards higher (A and B) or lower (C) effect sizes. Although other models like the habitat checkerboard (Schoener and Adler 1991, Gotelli et al. 1997, Gotelli and McCabe 2002) and the historical checkerboard hypotheses (Cracraft 1988) have been proposed to account for them, the competition model has gained by far most interest and provoked a still ongoing debate (Weiher and Keddy 1999, Gotelli 2000, Gotelli and McCabe 2002). The results of Gotelli and McCabe (2002) seemed to settle this debate in favor of the assembly rule model and in favor of factors others than purely stochastic as the main structuring force. However, the above presented results reopen the discussion again. That natural assemblages have nonrandom co-occurrence patterns does not mean that random processes can t generate them. That stochastic processes can generate highly ordered systems has long been known in chemistry and molecular biology (Anishchenko et al. 2002). In ecology the neutral model approaches of Hubbell (2001) and Bell (2001) have stirred much interest because both authors were able to produce many of the observed macroecological patterns from extremely simple stochastic processes that operate on initially homogeneous communities with identical species properties. The present paper shows that this class of models leads to species co-occurrence patterns that are in many cases non-random and that these patterns are in line with the predictions of Diamond (1975) and the empirical results of Gotelli and McCabe (2002). The question about non-random species cooccurrence patterns should therefore change towards the question whether stochastic processes or species interactions cause them. The fact that non-random co-occurrence patterns appeared in heterogeneous and in the homogeneous grids makes it likely that the neutral model approach shifts non-random species spatial distributions towards fewer species combinations and more pronounced checkerboard patterns irrespective of habitat structure. Because the methods used here are the same than those of Gotelli and McCabe (2002) the results can be compared directly. The standardized effect sizes for species combinations (m/ /0.63) and numbers of checkerboards (m/1.25) Gotelli and McCabe found are higher than the ones reported here for model communities (Table 3). Instead, Gotelli and McCabe found the most pronounced deviation from randomness for C-score values (mean standardized effect size 2.67), whereas the model used here resulted in values of 0.4 to 0.5. Gotelli (2000) already showed that these three indices are only weakly correlated. Although, they all measure species co-occurrences, they identify different aspects of this. The C-score is based on average Fig. 3. Standardized effect sizes in dependence of species numbers for 420 model communities in heterogeneous grids after running the neutral model (runtime: 4000 times the species number). The three distributions differ significantly from normality (chi 2 -test pb/0.01) in being skewed towards higher (A and B) or lower (C) effect sizes. OIKOS 107:3 (2004) 607

co-occurrences (Gotelli 2000). It remains unclear whether the different results point to structural differences between real and model assemblages or whether they simply reflect some hidden statistical properties of the index. The present results are also a test for the neutral model approach. For being of value it should also make realistic predictions about species co-occurrence patterns. There are still few critical tests of the neutral model approach (Whitfield 2002, Hubbell 2003, Ricklefs 2003, Ulrich 2004). These tests focused mainly on species rank order distributions (McGill 2003, Volkov et al. 2003) and evolutionary lineages (Clark and McLachlan 2003). The present results show that ecological drift is also able to generate non-random species co-occurrence patterns similar to the ones found in natural assemblages. Bell (2001) instead predicted that neutral models produce species spatial distributions with more species associations than expected by chance. 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