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Ecology, 89(1), 2008, pp. 248–258 Ó 2008 by the Ecological Society of America A NEARLY NEUTRAL MODEL OF BIODIVERSITY SHU-RONG ZHOU1,2 AND DA-YONG ZHANG1,3 1 State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China 2 Laboratory of Arid and Grassland Ecology under the Ministry of Education, School of Life Sciences, Lanzhou University, Lanzhou 730000, China Abstract. S. P. Hubbell’s unified neutral theory of biodiversity has stimulated much new thinking about biodiversity. However, empirical support for the neutral theory is limited, and several observations are inconsistent with the predictions of the theory, including positive correlations between traits associated with competitive ability and species abundance and correlations between species diversity and ecosystem functioning. The neutral theory can be extended to explain these observations by allowing species to differ slightly in their competitive ability (fitness). Here, we show that even slight differences in fecundity can greatly reduce the time to extinction of competitors even when the community size is large and dispersal is spatially limited. In this case, species richness is dramatically reduced, and a markedly different species abundance distribution is predicted than under pure neutrality. In the nearly neutral model, species co-occur in the same community not because of, but in spite of, ecological differences. The more competitive species with higher fecundity tend to have higher abundance both in the metacommunity and in local communities. The nearly neutral perspective provides a theoretical framework that unites the sampling model of the neutral theory with theory of biodiversity affecting ecosystem function. Key words: coexistence; competitive asymmetries; dispersal limitation; metacommunity; nearly neutral model; species diversity. INTRODUCTION A perennial challenge in ecology is to explain the maintenance of species diversity within communities (e.g., Hutchinson 1959, May 1975, Pacala and Tilman 1993, Chesson 2000). In this context, Hubbell’s (2001) unified neutral theory of biodiversity provides a simple and counterintuitive explanation of species diversity patterns (see also Bell 2000, 2001, 2003). Based on the hypothesis that all individuals of all species in a trophically delimited community have identical per capita probabilities of birth, death, dispersal, and speciation, Hubbell’s theory predicts that an equilibrium will be established between stochastic extinction of species and appearance of new species through immigration or speciation, depending on the spatial scale considered. Studies stemming from the neutral theory largely fall into two categories. One class of studies focuses on testing the predictions of the neutral models about species diversity patterns (e.g., Bell 2000, 2003, Hubbell 2001, Chave et al. 2002, Condit et al. 2002, Clark and McLachlan 2003, Fargione et al. 2003, McGill 2003, Volkov et al. 2003, McGill et al. 2006). The second line of research is concerned with the fundamental assumptions of the theory (e.g., Zhang and Lin 1997, Yu et al. Manuscript received 30 October 2006; revised 17 May 2007; accepted 21 May 2007. Corresponding Editor: M. Holyoak. 3 Corresponding author. E-mail: [email protected] 248 1998, Enquist et al. 2002, Ricklefs 2003, Chave 2004, Fuentes 2004, Gilbert and Lechowicz 2004, Loreau 2004, Chase 2005, Hubbell 2005, 2006, Leibold and McPeek 2006, Ricklefs 2006). The hypothesis of ecological equivalence is the cornerstone of the neutral theory, albeit rarely tested in empirical studies. In fact, all species in all trophically defined communities violate this assumption to some extent, but Hubbell (2001, 2005, 2006) maintains that neutrality provides a good approximation. Hubbell (2006) also suggests that ecological equivalence may evolve easily and quickly and should be especially commonplace in species-rich communities. Zhang and Lin (1997) challenged the neutral theory on the ground that coexistence among functionally equivalent species is a fragile phenomenon, because even a slight variation from complete equality of species would cause a considerable decline in the time to competitive exclusion. Hubbell (2001) countered by suggesting that dispersal and recruitment limitations, which were not considered in Zhang and Lin’s model, could delay competitive exclusion essentially without any limit by reducing the effect of competitive asymmetries among the species. Hubbell based his argument on two theoretical papers by Tilman (1994) and Hurtt and Pacala (1995), who developed the models in the context of traditional niche theory. As far as we know, the quantitative significance of dispersal limitation has not been fully investigated with reference to neutral or January 2008 A NEARLY NEUTRAL MODEL OF BIODIVERSITY nearly neutral models (but see Chave et al. 2002 for an exception). Our aim here is threefold. First, in response to Hubbell’s criticism, we extend Zhang and Lin’s (1997) work by including in the model dispersal limitation. We show that the dramatic decrease in the time to fixation (extinction of competitors) caused by very small differences in per capita fecundity can overwhelm the effects of dispersal limitation. Second, drawing on an analogy with the nearly neutral theory in population genetics (Ohta and Gillespie 1996, Ohta 2002), we extend Hubbell’s neutral model by introducing slight differences in species’ competitive ability (per capita fecundity). Using the nearly neutral model, we are able to evaluate the importance of competitive asymmetries among species versus ecological drift in shaping community structure. We show that adding even very slight differences in per capita fecundity into Hubbell’s model will dramatically reduce species richness and leads to markedly different species abundance distributions. Finally, a positive correlation between a species’ per capita fecundity and relative abundance arises in the nearly neutral model for the common species at both metacommunity and local community levels. The latter prediction is related to recent empirical findings on grassland communities (Harpole and Tilman 2006). THE NEARLY NEUTRAL MODEL We first examine the effect of interspecific differences in species’ per capita fecundity on the time to competitive exclusion in a spatially explicit simulation of an isolated two-species metacommunity of Jm individuals. We subsume all aspects of offspring production, offspring survivorship, and offspring establishment into per capita fecundity. Initially, the two species are equally abundant and the individuals are randomly distributed on a square lattice of size L 3 L. The total number of cells in the landscape (L2) equals the community size Jm. The landscape is assumed to be a torus, that is, cells on the right edge are neighbors of those on the left and cells on the bottom are neighbors of those on the top. This assumption avoids any spurious edge effects. We assume that the two species are identical in all respects except per capita fecundity. When an individual in a cell dies, a new individual will occupy the cell immediately, according to species’ dispersal kernel and per capita fecundities (see Appendix A for the algorithm). There are no empty cells in the landscape, and the dynamics of the community is a zero-sum game (Hubbell 2001). In the simulations, we let L be 16, 32, 64, or 128, with community size (J m ) of 16 2 , 32 2 , 64 2 , or 128 2 , respectively. Parameter w is the per capita fecundity factor of the focal species relative to the non-focal species and has the values 1.0 (the neutral case, no difference in species’ per capita fecundity), 1.01, 1.05, 1.1, 1.2, 1.3, 1.4, and 1.5. Given the values of Jm and w, the scale of dispersal varies from global dispersal to the 249 opposite extreme of nearest neighbor dispersal through the intermediate cases in which dispersal distance r is over two or four cells, respectively. Dispersal is uniform within the distance r. As in Yu et al. (1998), we use absolute time rather than relative time, with the former referring to the actual time interval and the latter to the number of individual deaths. For example, in a tropical rain forest tree community, the absolute time may be characterized in terms of years. Number of deaths in one time interval (year) is denoted by D, and can be calculated as the turnover rate times the number of individuals in the community. In this paper, we use a moderate turnover rate of 1.7% per year reported for tropical forests (Swaine et al. 1987). For each parameter set, we run 100 independent simulations and found the median of the time to fixation (extinction or complete dominance; MTF) among 100 replicates. The reason for using median rather than arithmetic mean is that the distribution of the time to fixation is generally not normal (cf. Hubbell 2001). The number of times the species with higher fecundity wins the competition trial is also recorded. In the second model, we investigate the influence of unequal fecundities on species richness and relative abundances, with dispersal limitation occurring only from the metacommunity to the local community. We follow the algorithm described in Hubbell (2001) to form a metacommunity consisting of Jm ¼ 1 3 105 individuals, with the fundamental biodiversity number h ¼ 100. In contrast to Hubbell’s model, when a new species enters the metacommunity, we select its per capita fecundity from the normal distribution N(1, r2), where r is standard deviation; other distributions (uniform or exponential) lead to essentially the same conclusion. A species’ per capita fecundity will fall in the range (1 3r, 1 þ 3r) with probability 99.7%. We use values of r ¼ 0, 0.001, 0.002, and 0.003, where r ¼ 0 is the neutral case. We denote by wi the relative per capita fecundity of species i. We first construct the abundance distribution in the metacommunity. When a randomly selected individual in the metacommunity is eliminated, one new individual is recruited. With probability h/(h þ Jm 1), the new recruit will be a new species, otherwise it will be one of the existing species. In the latter case, the probability of birth of species i is wiPi/Rj wjPj, where the sum is taken over all species in the metacommunity and Pj is the abundance of species j in the metacommunity. Note that the recruitment of existing species is biased by their per capita fecundities. Simulation is continued until the metacommunity has reached a stochastic equilibrium, roughly after 10 000 turnovers of the metacommunities. The distribution of species’ relative abundances is obtained by averaging over the abundance of the species with the same rank in different simulations of 100 replicate metacommunities (Jm ¼ 1 3 105 and h ¼ 100). 250 SHU-RONG ZHOU AND DA-YONG ZHANG With the metacommunity constructed as described here, we investigated the influence of unequal fecundities on species richness and the distribution of relative abundances in local communities. For each metacommunity, a local community of size J ¼ 2000 was randomly sampled. In the local communities, each species has the same per capita fecundity as in the corresponding metacommunity. To model local community dynamics, we eliminate a randomly selected individual, which is then replaced either by an immigrant from the metacommunity or by an offspring of the existing species in the local community. The rate of dispersal m from the metacommunity is selected to be 0.002, 0.01, 0.05, or 0.25, respectively. Thus with probability m an individual from the metacommunity occupies the vacancy, and the probability that this immigrant is an offspring of existing species is proportional to each species’ relative abundance in the metacommunity weighted by the species’ per capita fecundity. With probability 1 m, the new recruit comes from the local community, and with probability wiNiL/Rj wjNjL the new recruit is an offspring of species i, where the sum is taken over all species in the local community and NjL is the local abundance of species j. The local dynamics are iterated until a stochastic equilibrium is reached after, again, about 10 000 turnovers of the local community. The distribution of species relative abundances is the average of 100 replicate local communities drawn from the same metacommunity and assuming the same dispersal rate m. Additionally, while calculating the distributions of species’ relative abundances in the metacommunity and in the local community, we recorded the relationship between species’ per capita fecundities and their relative abundances. RESULTS The median time to fixation (MTF) decreases by more than an order of magnitude as the interspecific difference in per capita fecundity (w) increases, no matter whether there is any dispersal limitation or not (Fig. 1). The most dramatic decline in coexistence time occurs when there is only a slight fecundity difference, w , 1.1. For example, in a community of 4096 individuals with nearest neighbor dispersal, MTF is about 272 972 time intervals (years) in the neutral model, but 44 726 time intervals in the case of w ¼ 1.01 (a decrease of 84%) and only 11 757 time intervals when w ¼ 1.05 (a decrease of 96%). The decrease in MTF due to a difference in per capita fecundity becomes more pronounced as the community size increases (Fig. 1). For example, in the largest simulated community of 16 384 individuals with nearest neighbor dispersal, MTF is about 1 145 566 time intervals (years) in the neutral model, but only 63 420 time intervals in the case of w ¼ 1.01 (a decrease about 96%) and only 14 136 time intervals when w ¼ 1.05 (a decrease of 99%). The species with a relative fecundity advantage of w ¼ 1.01 wins 70 times among 100 Ecology, Vol. 89, No. 1 simulation trials when the metacommunity is 16 3 16, and always wins when w is 1.05 or larger. For larger metacommunities, i.e., L ¼ 32, 64, and 128 in our simulation, the superior competitor wins invariably. These results suggest that competitive exclusion plays a far more important role than demographic stochasticity, even when species differ only slightly in competitive ability. Hubbell (2001) argued that even with unequal fecundities in the species, there would be a huge increase in the time to extinction of competitors in Zhang and Lin’s model as community size increases to very large values. However, Fig. 2 shows that dramatic increase in MTF with community size only occurs in the neutral case (w ¼ 1.0); even for the small interspecific difference, w ¼ 1.05, there is no longer a significant increase in MTF with increasing community size. Similarly, dispersal limitation does not have as much influence on species coexistence as implied by Hubbell, and even the extreme case of nearest neighbor dispersal only doubled MTF in our simulations. In our simulation, random initial distribution of the species is assumed. But even when the species are initially highly clumped the effect of dispersal limitation is still limited under non-neutral conditions (Appendix B). In brief, when a slight difference in species’ per capita fecundity is introduced into the neutral model, coexistence time will decline dramatically, significantly weakening the effects of within-community dispersal limitation and large community size. Fig. 3 illustrates the influence of interspecific differentiation in per capita fecundity on species richness and relative abundances in the metacommunity. As expected, the species abundance distribution in the case of very similar species, r ¼ 0.001, is close to the prediction of the neutral model. However, even when r becomes a little bit larger, with r ¼ 0.002 or 0.003, species richness decreases dramatically and the distribution of relative abundances deviates far from the patterns predicted by the neutral theory. At equilibrium, there is a relative deficiency of species with intermediate abundance and relatively more of very abundant or rare species. With a difference in species’ per capita fecundities included in the model, there is an evident positive correlation between per capita fecundity and the rank of the species in abundance for the common species, whereas the per capita fecundity of intermediate and rare species fluctuates around 1, the mean of the initial distribution of species fecundities, with the rarest species having higher variance (Fig. 4). In other words, those species that have higher per capita fecundity have an advantage in competition. The very abundant species account for only less than 20% of all species in the metacommunity. Most of the remaining species are neutral except those very rare species that are new members of the metacommunity (Fig. 4). Turning to the structure of local communities, the influence of fecundity differences among the species is January 2008 A NEARLY NEUTRAL MODEL OF BIODIVERSITY 251 FIG. 1. The influence of interspecific differences in fecundity (w) and dispersal distance (r) on the median time to fixation (MTF) in a two-species community. MTF decreases greatly when fecundity (w) and community size increase. L is the number of contiguous cells in one lattice axis. Note the log scale on the y-axis. similar to that in the metacommunity, but dispersal limitation from the metacommunity (m) is also important (Fig. 5). Strong dispersal limitation at the regional scale results in much fewer species and steeper rank– abundance distributions in local communities (i.e., greater dominance by competitively superior species). The species abundance distribution will become increasingly similar to that of the corresponding metacommunity as dispersal rate m increases (Fig. 5). For local communities, there is once again a striking positive correlation between relative fecundity and species rank in abundance (Fig. 6). However, this relationship is somewhat different than in the corresponding metacommunity, as now the fecundity of all species within a local community is greater at equilib- rium than the mean. The reason for this difference is that the rare species in the metacommunity have little chance to enter the local community, and only species with high relative fecundity will persist for a long time. In this case, we may conclude that small competitive asymmetries among species play a large role in community structure. We fitted the neutral model to simulated data from the nearly neutral local communities with J ¼ 2000, h ¼ 100, r ¼ 0.001 or 0.002 under different dispersal rates, using the method of Etienne (2005). The results are shown in Appendix C. In the case of low dispersal rates from the metacommunity (m ¼ 0.002 and m ¼ 0.01), the neutral model fits to the nearly neutral local communities reasonably well, though not as good as some real 252 SHU-RONG ZHOU AND DA-YONG ZHANG FIG. 2. The influences of community size, dispersal distance (nearest neighbor vs. global), and interspecific differences in fecundity on median time to fixation (MTF). MTF increases proportionally as the community size increases, but a dramatic increase in MTF with community size occurs only in the neutral drift case. Increase in MTF due to dispersal limitation is moderate. Note that w ¼ 1.0 under the neutral model. Note the log scale on both axes. communities (Volkov et al. 2003, Hubbell 2006). Under such situations the dispersal rate (m) tends to be much overestimated whereas the fundamental biodiversity number (h) tends to be greatly underestimated. Thus the failure to reject the null hypothesis based on a neutral model does not necessarily vindicate the neutral assumption of ecological equivalence: ‘‘neutral pattern’’ does not imply a neutral process (cf. Purves and Pacala 2005, Walker 2007). Ecology, Vol. 89, No. 1 neutral theory as a simple extension of the neutral theory. Relaxing neutrality but without resorting to a more complex concept of niche differentiation, our nearly neutral framework effectively removes many of the inconsistencies between the original neutral model and empirical data. It also enables us to achieve several novel insights into species coexistence and community structure. Neutral theory clearly does not predict which species are rare and which are abundant. In contrast, the nearly neutral theory presented in this paper predicts a positive correlation between traits associated with competitive ability and species abundance: the most abundant species are also the most competitive (see Figs. 4 and 6). We relate this prediction to the recent work of Harpole and Tilman (2006), who studied grassland communities at Cedar Creek, Minnesota, USA, where competition for nitrogen is a key factor structuring communities. They measured in monoculture the species trait R*, minimum level of N in the soil for sustainable growth of the species, and showed that across a variety of gradients in nitrogen availability (experimental manipulation, successional, and large scale natural), species abundance was well predicted by R*, even though the observed abundance distribution was qualitatively consistent with the neutral theory. Harpole and Tilman concluded that the pattern they detected supports some niche mechanism, but we note that their results are also consistent with the nearly neutral model. Our examples in Appendix C demonstrate that local communities of nearly neutral species can often be fitted by a neutral model, especially when dispersal is highly limited at the regional scale from the metacommunity to local communities. According to the nearly neutral theory, the response of species to environmental change DISCUSSION Since the publication of Hubbell’s book in 2001, there has been much discussion of the neutral theory in ecology, both pro and con (Whitfield 2002, Norris 2003, Chave 2004, Gaston and Chown 2005, Alonso et al. 2006, Gewin 2006, Holt 2006, Holyoak et al. 2006, Hu et al. 2006, Adler et al. 2007). Most ecologists regard the neutral assumption of all species being equivalent as highly unrealistic, but Hubbell (2001, 2005, 2006) contends that differences among the species are small enough and their dynamics are sufficiently stochastic to allow the neutral models to capture the essence of the structuring of ecological communities. Apart from the strong psychological bias against neutrality felt by most ecologists, close analyses of several systems have revealed clearly non-neutral patterns (Adler 2004, Chave 2004, Wootton 2005, Gilbert et al. 2006, Harpole and Tilman 2006, McGill et al. 2006). Niche differentiation has been widely considered as the main alternative to neutrality, but this may not be necessary. As in molecular evolution (Ohta and Gillespie 1996, Ohta 2002), we can put forward in ecology, too, the nearly FIG. 3. Metacommunity equilibrium rank–abundance curves for models with and without differences among the species in fecundity. Parameter values: metacommunity size, Jm ¼ 1 3 105; fundamental biodiversity number, h ¼ 100; r is the standard deviation of the normal distribution of the per capita factor for new species. Note the y-axis log scale. January 2008 A NEARLY NEUTRAL MODEL OF BIODIVERSITY 253 FIG. 4. The relationship between species’ per capita fecundity and species rank in abundance within the metacommunity. For definitions of Jm, h, and r, see Fig. 3. would also be non-neutral, again likely correlated with species traits. The generally positive correlation between traits associated with competitive ability and species abundance supports a strong role for competition in community assembly. But plant species richness at Cedar Creek is high despite intense competition for the limiting soil nutrient. This raises the question of how can so many species coexist. Interestingly, Harpole and Tilman (2006) found no evidence for a competition– colonization tradeoff because seed production of particular species in monocultures was independent of their R* values. In the light of the nearly neutral community assembly, superior competitor will not necessarily exclude all other species, provided that there is a steady stream of immigrants from the source metacommunity on the local scale (see also Loreau and Mouquet 1999, Holt 2004, Zillio and Condit 2007) or through speciation at the metacommunity scale (Hubbell 2001). In such circumstances, coexistence occurs in spite of, not because of, species differences. Here we hasten to emphasize that the coexistence of nearly neutral species is not stable (sensu Chesson 2000): most species are in the process of being driven extinct by interactions with dominant species. As in the neutral model, diversity is maintained as a dynamic equilibrium between the extinction of resident species and the appearance of new species through immigration or speciation (Loreau and Mouquet 1999, Fuentes 2004, Zillio and Condit 2007). Leigh et al. (2004) suggested that tropical tree species rarely originate by splitting of large populations, but instead begin with few individuals, essentially in conformity with the point mutation mode of speciation (sensu Hubbell 2001). If so, Leigh et al. argued, species that are now common (likely represented by more than 10 million mature trees) must have spread more quickly than chance allows; otherwise the species appeared well before the origin of angiosperms 140 million years ago, according to the neutral theory. Consequently, Leigh et al. (2004) concluded that tropical tree species can become common and widespread only through an advantage over their competitors. In our nearly neutral model, such competitive advantages are indeed enjoyed by the most abundant species within the community (Fig. 6). Conversely, Ricklefs (2003, 2006; see also Nee 2005) criticized the neutral theory for its prediction of an unrealistic long life span of abundant species. This quandary seems even more serious for the nearly neutral species, because once some highly fecund species arrived and became abundant they will be expected to persist for an even longer time. However, more competitive species may keep emerging (assuming inheritance in species traits), and tend to displace the current dominant species. For some plant communities, there is evidence suggesting that species diversity promotes productivity and/or stability (Kinzig et al. 2002, Loreau et al. 2002, Cardinale et al. 2006), though not everybody agrees with the interpretation of the data (Hubbell 2006). Complementary resource use via niche differentiation is commonly invoked to explain these relationships (Kin- 254 SHU-RONG ZHOU AND DA-YONG ZHANG Ecology, Vol. 89, No. 1 FIG. 5. Local community equilibrium rank–abundance curves of models with and without differences in species’ per capita fecundities, for different dispersal rates, where m is the rate of immigration from the metacommunity to the local community. Other parameter values: J ¼ 2000, h ¼ 100. For each panel, the line types from top to bottom in the key correspond to the curves from right to left. zig et al. 2002, Loreau et al. 2002). According to the niche differentiation mechanism, species use resources in different ways and consequently more of the available resources are utilized with increasing diversity. Alternatively, a positive diversity effect could represent a sampling effect, in which diverse communities perform better due to higher likelihood that they would contain high yielding species under the particular conditions (e.g., Huston 1997, Cardinale et al. 2006). While the neutral theory is incapable of explaining such biodiversity effects, the nearly neutral model does predict a role for particular species in ecosystem functioning via sampling processes. The sampling effect has been suggested to operate merely as a transient phenomenon (Kinzig et al. 2002, Loreau et al. 2002), but in the nearly neutral perspective it can exert a lasting impact, as evidenced by a recent meta-analysis (Cardinale et al. 2006). Most interestingly, Cardinale et al. (2006) find that, contrary to niche differentiation, the standing stock of, and resource depletion by, the most speciesrich assemblage tends to be no different from that of the single most productive species used in an experiment. We note that this observation can be readily explained by the nearly neutral theory, provided that there is further evidence for exclusion of all but the best competitor. The fact that multiple species continue to exist in these experiments does not necessarily negate this interpretation, because experiments may have been performed at shorter temporal scales or extinction of inferior competitors may be delayed or even prevented due to recurrent external immigration (Loreau and Mouquet 1999, Holt 2004). January 2008 A NEARLY NEUTRAL MODEL OF BIODIVERSITY 255 FIG. 6. The relationship between species’ per capita fecundity and their rank in abundance in local communities with different dispersal rates. Other parameter values: J ¼ 2000, h ¼ 100. So far we have emphasized the similarity and common ground between the neutral and nearly neutral theories in general, and between our work and Hubbell’s in particular. Below we highlight the key differences between the two models. Hubbell (2001, 2005, 2006) proposed that dispersal and recruitment limitation would act as the most important factors to delay competitive exclusion, which in turn would facilitate evolution and long-term coexistence of functionally equivalent or nearequivalent species. Hubbell cited the work of Tilman (1994) and Hurtt and Pacala (1995) as the support to his view. In particular, Hurtt and Pacala (1995) demonstrated that recruitment limitation could overwhelm the effects of strong competitive differences between species on structuring of communities, especially in highly diverse communities where dispersal and recruitment limitation is likely to be most pronounced. However, Hurtt and Pacala modeled only a community of nichedifferentiated species partitioning an environmental axis, and did not consider the neutral or nearly neutral cases. We have shown that when the neutral model is modified to include even slight differences in per capita fecundity, a significant decrease in coexistence time will follow even under the strongest dispersal limitation, the nearest neighbor dispersal. Dispersal limitation can only enhance coexistence to a moderate extent (Fig. 1). Contrary to Hubbell’s (2001) proposition, we suggest that longterm coexistence of nearly neutral competitors lies more with large community size than dispersal limitation. As first noted by Hubbell (2001) himself, relatively small differences among species in per capita mortality or fecundity can nevertheless produce large differences in steady-state relative species abundance, presumably due to hastened competitive exclusion (Fig. 1). In this sense, our previous conclusion (Zhang and Lin 1997) holds: the neutral model of biodiversity is very sensitive to violations of its fundamental assumption of functional equivalence of species (see also Fuentes 2004). 256 SHU-RONG ZHOU AND DA-YONG ZHANG An obvious feature of species abundance curves generated by the nearly neutral model is the reduced evenness of communities, with excessive dominance of the common species. In nature, many communities show this pattern of species abundances, including an old growth forest in Peru, cited in Hubbell (2001). More recently, Walker and Cyr (2007) showed that all the phytoplankton communities they examined did not fit the neutral model by at least one of three measures used. Phytoplankton communities deviated from the neutral toward the nearly neutral model by showing consistent over-dominance of one or a few most abundant species. Hubbell (2001) proposed that only a small fraction of the species in a community tend to show overdominance under nearly neutral conditions, with the remaining species being essentially neutral. Our results in Fig. 5 largely confirm this conjecture: less than 20% species are very abundant and have a discernible advantage in competitive ability. Most species in the metacommunity are rare and essentially equal, except some very rare species that are new members of the metacommunity. Non-neutral patterns are often regarded as prima facie evidence for the operation of niche mechanisms, as if the niche concept were the only alternative to neutrality. Indeed, it has been customary to invoke niche differentiation whenever neutrality can be rejected. To many ecologists, unifying niche and neutral approaches would be an obvious step forward (Chave et al. 2002, Tilman 2004, Volkov et al. 2005, Gewin 2006, Gravel et al. 2006, Holt 2006, Liebold and McPeek 2006, Adler et al. 2007, Walker 2007). We do not disagree with this view, but we also urge ecologists to consider the merits of the nearly neutral models. It is lack of stabilizing mechanisms that distinguishes neutral or nearly neutral models from niche models. We advocate that competitive asymmetries in the sense analyzed in this study may be sufficient to provide a parsimonious general explanation of community structure and biodiversity. Finally, we wish to acknowledge the limits of our model in the hope of stimulating further works in this exciting field. First and foremost, we assume a stationary, normal, distribution of per capita fecundity of newly arrived species. This is also the assumption made in Ohta’s nearly neutral model of molecular evolution for the fitness effects of new mutant alleles (Ohta and Gillespie 1996, Ohta 2002). A stationary per capita fecundity of new species means lack of inheritance in species traits and no selection toward the species with highest fitness, which is clearly unrealistic. However, in the presence of inheritance, one may expect that most of the new species will have traits similar to the abundant species. Thus even with the introduction of fitness inequality, most of the species will tend to be closely similar, making our approach (stationary distribution of per capita fecundity, but with very small variance) perhaps a good operational first approximation. Second, our nearly neutral model also assumes, as neutral Ecology, Vol. 89, No. 1 models do, that metacommunities and local communities are in dynamic equilibrium. However, it is possible that the time to equilibrium in the nearly neutral model is so long that the equilibrium distribution will rarely be observed in real ecological communities. Third, our model is still unable to relate species identity to the environment and to address species turnover along environmental gradients, which have been regarded as the major flaws of the neutral theory so far (e.g., Gilbert and Lechowicz 2004). Spatial turnover in species composition is a major determinant of species diversity at the regional scale. Thus, any attempt to understand the structure of ecological communities must take into account the role of species turnover and the factors that influence it. We still have a long way to go toward a full understanding of the role of stochastic processes in community assembly. ACKNOWLEDGMENTS We are grateful to I. Hanski and F. He for constructive criticisms, careful editing, and linguistic help with the manuscript and to M. Holyoak and two anonymous reviewers for very useful comments. We also thank K. Lin for his help with computer simulations. This work was supported by the State Key Basic Research and Development Plan (2007CB106800), the National Natural Science Foundation of China (30670314 and 30628005), and Beijing Normal University. LITERATURE CITED Adler, P. B. 2004. Neutral models fail to reproduce observed species–area and species–time relationships in Kansas grasslands. 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APPENDIX C Maximum-likelihood estimates of h and m, with J ¼ 2000, h ¼ 100, r ¼ 0.001 or 0.002, and various dispersal rates from the metacommunity (Ecological Archives E089-014-A3).