Hubbell's fundamental biodiversity parameter and the Simpson diversity index

Central to Hubbell's neutral theory of biodiversity is a universal, dimensionless fundamental biodiversity parameter that is the product of community size and speciation rate. One of the most important discoveries of Hubbell's theory is that the species‐abundance distribution and the species–area relationship of the neutral metacommunity is completely determined by this fundamental biodiversity parameter, although the diversity patterns of the local community are collectively determined by the biodiversity parameter and migration. Using the relative abundance of species and following the concept of heterozygosity of population genetics, here we developed an analytical relationship between this biodiversity parameter and the well‐known Simpson diversity index. This relationship helps bridge the evolutionary aspect of biodiversity to the ecological and statistical aspect of the diversity. The relationship between these two parameters suggests that diversity patterns of the metacommunity can also be equally described by the Simpson index. This relationship provides an alternative approach to interpret and estimate the fundamental biodiversity parameter for the metacommunity.     

Community differentiation on landscapes: drift, migration and speciation

Theories of the differentiation of ecological communities on landscapes have typically not considered evolutionary dynamics. Here we analytically study the expected differentiation among local communities in a large metacommunity, undergoing speciation, ecological drift and intercommunity dispersal, in the context of neutral theory. We demonstrate that heterogeneity in species diversity and abundance arises among communities when local communities are small and intercommunity migration is infrequent. We propose a new measure to describe community differentiation, defined as the average correlation or the average probability (C_st) that two randomly sampled individuals of the same species within local communities are from the same ancestor. The effects of driving forces (migration, mutation, and ecological drift) are incorporated into the two-level hierarchical community structure in a finite island model of neutral communities. Community differentiation can increase the effective metacommunity size or the Hubbell's fundamental species diversity in the metacommunity by a factor (1−C_st)⁻¹. Significant community differentiation arises when C_st≠0. Intercommunity migration promotes species diversity in local communities but reduce species diversity in the metacommunity. In either the finite or infinite island case, one can estimate the number of intercommunity migrants by using multiple local community datasets when the speciation is negligible in the neutral local communities, or by using the metacommunity dataset when the speciation is included in the local neutral communities. These results highlight the significance of the evolutionary mechanisms in generating heterogeneous communities in the absence of complicated ecological processes on large landscapes.     

Metacommunity speciation models and their implications for diversification theory

The emergence of new frameworks combining evolutionary and ecological dynamics in communities opens new perspectives on the study of speciation. By acknowledging the relative contribution of local and regional dynamics in shaping the complexity of ecological communities, metacommunity theory sheds a new light on the mechanisms underlying the emergence of species. Three integrative frameworks have been proposed, involving neutral dynamics, niche theory, and life history trade‐offs respectively. Here, we review these frameworks of metacommunity theory to emphasise that: (1) studies on speciation and community ecology have converged towards similar general principles by acknowledging the central role of dispersal in metacommunities dynamics, (2) considering the conditions of emergence and maintenance of new species in communities has given rise to new models of speciation embedded in the metacommunity theory, (3) studies of diversification have shifted from relating phylogenetic patterns to landscapes spatial and ecological characteristics towards integrative approaches that explicitly consider speciation in a mechanistic ecological framework. We highlight several challenges, in particular the need for a better integration of the eco‐evolutionary consequences of dispersal and the need to increase our understanding on the relative rates of evolutionary and ecological changes in communities.     

Asymmetry in species regional dispersal ability and the neutral theory

The neutral assumption that individuals of either the same or different species share exactly the same birth, death, migration, and speciation probabilities is fundamental yet controversial to the neutral theory. Several theoretical studies have demonstrated that a slight difference in species per capita birth or death rates can have a profound consequence on species coexistence and community structure. Whether asymmetry in migration, a vital demographic parameter in the neutral model, plays an important role in community assembly still remains unknown. In this paper, we relaxed the ecological equivalence assumption of the neutral model by introducing differences into species regional dispersal ability. We investigated the effect of asymmetric dispersal on the neutral local community structure. We found that per capita asymmetric dispersal among species could reduce species richness of the local community and result in deviations of species abundance distributions from those predicted by the neutral model. But the effect was moderate compared with that of asymmetries in birth or death rates, unless very large asymmetries in dispersal were assumed. A large difference in species dispersal ability, if there is, can overwhelm the role of random drift and make local community dynamics deterministic. In this case, species with higher regional dispersal abilities tended to dominate in the local community. However, the species abundance distribution of the local community under asymmetric dispersal could be well fitted by the neutral model, but the neutral model generally underestimated the fundamental biodiversity number but overestimated the migration rate in such communities.     

Dispersal and diversity – unifying scale‐dependent relationships within the neutral theory

The response of species diversity to dispersal capability is inherently scale‐dependent: increasing dispersal capability is expected to increase diversity at the local scale, while decreasing diversity at the metacommunity scale. However, these expectations are based on model formulations that neglect dispersal limitation and species segregation at the local scale. We developed a unifying framework of dispersal–diversity relationships and tested the generality of these expectations. For this purpose we used a spatially‐explicit neutral model with various combinations of survey area (local scale) and landscape size (metacommunity scale). Simulations were conducted using landscapes of finite and of conceptually infinite size. We analyzed the scale‐dependence of dispersal‐diversity relationships for exponentially‐bounded versus fat‐tailed dispersal kernels, several levels of speciation rate and contrasting assumptions on recruitment at short dispersal distances. We found that the ratio of survey area to landscape size is a major determinant of dispersal–diversity relationships. With increasing survey‐to‐landscape area ratio the dispersal–diversity relationship switches from monotonically increasing through a U‐shaped pattern (with a local minimum) to a monotonically decreasing pattern. Therefore, we provide a continuous set of dispersal–diversity relationships, which contains the response shapes reported previously as extreme cases. We suggest the mean dispersal distance with the minimum of species diversity (minimizing dispersal distance) for a certain scenario as a key characteristic of dispersal–diversity relationships. We show that not only increasing mean dispersal distances, but also increasing variances of dispersal can enhance diversity at the local scale, given a diverse species pool at the metacommunity scale. In conclusion, the response of diversity to variations of dispersal capability at spatial scales of interest, e.g. conservation areas, can differ more widely than expected previously. Therefore, land use and conservation activities, which manipulate dispersal capability, need to consider the landscape context and potential species pools carefully.     

Sampling Hubbell's neutral theory of biodiversity

In the context of neutral theories of community ecology, a novel genealogy‐based framework has recently furnished an analytic extension of Ewens’ sampling multivariate abundance distribution, which also applies to a random sample from a local community. Here, instead of taking a multivariate approach, we further develop the sampling theory of Hubbell's neutral spatially implicit theory and derive simple abundance distributions for a random sample both from a local community and a metacommunity. Our result is given in terms of the average number of species with a given abundance in any randomly extracted sample. Contrary to what has been widely assumed, a random sample from a metacommunity is not fully described by the Fisher log‐series, but by a new distribution. This new sample distribution matches the log‐series expectation at high biodiversity values (θ > 1) but clearly departs from it for species‐poor metacommunities (θ < 1). Our theoretical framework should be helpful in the better assessment of diversity and testing of the neutral theory by using abundance data.     

Confronting different models of community structure to species-abundance data: a Bayesian model comparison

Species abundances are undoubtedly the most widely available macroecological data, but can we use them to distinguish among several models of community structure? Here we present a Bayesian analysis of species‐abundance data that yields a full joint probability distribution of each model's parameters plus a relatively parameter‐independent criterion, the posterior Bayes factor, to compare these models. We illustrate our approach by comparing three classical distributions: the zero‐sum multinomial (ZSM) distribution, based on Hubbell's neutral model, the multivariate Poisson lognormal distribution (MPLN), based on niche arguments, and the discrete broken stick (DBS) distribution, based on MacArthur's broken stick model. We give explicit formulas for the probability of observing a particular species‐abundance data set in each model, and argue that conditioning on both sample size and species count is needed to allow comparisons between the two distributions. We apply our approach to two neotropical communities (trees, fish). We find that DBS is largely inferior to ZSM and MPLN for both communities. The tree data do not allow discrimination between ZSM and MPLN, but for the fish data ZSM (neutral model) overwhelmingly outperforms MPLN (niche model), suggesting that dispersal plays a previously underestimated role in structuring tropical freshwater fish communities. We advocate this approach for identifying the relative importance of dispersal and niche‐partitioning in determining diversity of different ecological groups of species under different environmental conditions.     

Integrating environmental and spatial processes in ecological community dynamics

The processes controlling the abundances of species across multiple sites form the cornerstone of modern ecology. In these metacommunities, the relative importance of local environmental and regional spatial processes is currently hotly debated, especially in terms of the validity of neutral model. I collected 158 published data sets with information on community structure, environmental and spatial variables. I showed that approximately 50% of the variation in community composition is explained by both environmental and spatial variables. The majority of the data sets were structured by species-sorting dynamics (SS), followed by a combination of SS and mass-effect dynamics. While neutral processes were the only structuring process in 8% of the collected natural communities, disregarding neutral dispersal processes would result in missing important patterns in 37% of the studied communities. Moreover, metacommunity characteristics such as dispersal type, habitat type and spatial scale predicted part of the detected variation in metacommunity structure.     

Evaluating the performance of neutrality tests of a local community using a niche‐structured simulation model

Understanding the processes that underlie species diversity and abundance in a community is a fundamental issue in community ecology. While the species abundance distributions (SADs) of various natural communities may be well explained by Hubbell's neutral model, it has been repeatedly pointed out that Hubbell's SAD‐fitting approach lacks the ability to detect the effects of non‐neutral factors such as niche differentiation; however, our understanding of its quantitative effect is limited. Herein, we conducted extensive simulations to quantitatively evaluate the performance of the SAD‐fitting method and other recently developed tests. For simulations, we developed a niche model that incorporates the random stochastic demography of individuals and the nonrandom replacements of those individuals, i.e. niche differentiation. It therefore allows us to explore situations with various degrees of niche differentiation. We found that niche differentiation has strong effects on SADs and the number of species in the community under this model. We then examined the performance of these neutrality tests, including Hubbell's SAD‐fitting method, using extensive simulations. It was demonstrated that all these tests have relatively poor performance except for the cases with very strong niche structure, which is in accordance with previous studies. This is likely because two important parameters in Hubbell's model are usually unknown and are commonly estimated from the data to be tested. To demonstrate this point, we showed that the precise estimation of the two parameters substantially improved the performance of these neutrality tests, indicating that poor performance can be owed to overfitting Hubbell's neutral model with unrealistic parameters. Our results therefore emphasize the importance of accurate parameter estimation, which should be obtained from data independent of the local community to be tested.     

群落生态学的中性理论

生物多样性的分布格局和维持机制一直是群落生态学研究的核心问题,其中的关键是物种的共存机制。长期以来,生态位分化的思想在这一研究领域占据着主导地位。然而这一理论在解释热带雨林很高的物种多样性时遇到了困难。而以Hubbell为代表提出的群落中性漂变理论则假定在同一营养级物种构成的群落中不同物种的不同个体在生态学上可看成是完全等同的;物种的多度随机游走,群落中的物种数取决于物种灭绝和物种迁入/新物种形成之间的动态平衡。在这一假定之下,该理论预言了两种统计分布。一种是集合群落在点突变形成新物种的模式下其各个物种相对多度服从对数级数分布,而受扩散限制的局域群落以及按照随机分裂为新物种模式形成的集合群落则服从零和多项式分布。与生态位理论相反,中性理论不以种间生态位差异作为研究群落结构的出发点,而是以物种间在个体水平上的对等性作为前提。该理论第一次从基本生态学过程(出生、死亡、迁移、物种分化)出发,给出了群落物种多度分布的机理性解释,同时其预测的物种多度分布格局在实际群落中也得到了广泛的印证。因此,中性理论自诞生以来便在生态学界引发了极大的反响,也包括一些反对的声音。该文重点综述了关于中性理论的假设、预测和物种形成模式等方面的最新研究进展,包括中性理论本身的发展、关于中性理论的假设和预测的合理性检验以及在集合群落尺度上物种分化模式的讨论;并指出未来发展方向可能是在生态位理论和中性理论之间架起一座桥梁,同时发展包含随机性的群落生态位模型,以及允许种间差异的近中性模型。     

Using functional diversity patterns to explore metacommunity dynamics: a framework for understanding local and regional influences on community structure

The metacommunity concept, describing how local and regional scale processes interact to structure communities, has been successfully applied to patterns of taxonomic diversity. Functional diversity has proved useful for understanding local scale processes, but has less often been applied to understanding regional scale processes. Here, we explore functional diversity patterns within a metacommunity context to help elucidate how local and regional scale processes influence community assembly. We detail how each of the four metacommunity perspectives (species sorting, mass effects, patch dynamics, neutral) predict different patterns of functional beta‐ and alpha‐diversity and spatial structure along two key gradients: dispersal limitation and environmental conditions. We then apply this conceptual model to a case study from alpine tundra plant communities. We sampled species composition in 17 ‘sky islands’ of alpine tundra in the Colorado Rocky Mountains, USA that differed in geographic isolation and area (key factors related to dispersal limitation) and temperature and elevation (key environmental factors). We quantified functional diversity in each site based on specific leaf area, leaf area, stomatal conductance, plant height and chlorophyll content. We found that colder high elevation sites were functionally more similar to each other (decreased functional beta‐diversity) and had lower functional alpha‐diversity. Geographic isolation and area did not influence functional beta‐ or alpha‐diversity. These results suggest a strong role for environmental conditions structuring alpine plant communities, patterns consistent with the species sorting metacommunity perspective. Incorporating functional diversity into metacommunity theory can help elucidate how local and regional factors structure communities and provide a framework for observationally examining the role of metacommunity dynamics in systems where experimental approaches are less tractable.     

Detecting local diversity‐dependence in diversification

Whether there are ecological limits to species diversification is a hotly debated topic. Molecular phylogenies show slowdowns in lineage accumulation, suggesting that speciation rates decline with increasing diversity. A maximum‐likelihood (ML) method to detect diversity‐dependent (DD) diversification from phylogenetic branching times exists, but it assumes that diversity‐dependence is a global phenomenon and therefore ignores that the underlying species interactions are mostly local, and not all species in the phylogeny co‐occur locally. Here, we explore whether this ML method based on the nonspatial diversity‐dependence model can detect local diversity‐dependence, by applying it to phylogenies, simulated with a spatial stochastic model of local DD speciation, extinction, and dispersal between two local communities. We find that type I errors (falsely detecting diversity‐dependence) are low, and the power to detect diversity‐dependence is high when dispersal rates are not too low. Interestingly, when dispersal is high the power to detect diversity‐dependence is even higher than in the nonspatial model. Moreover, estimates of intrinsic speciation rate, extinction rate, and ecological limit strongly depend on dispersal rate. We conclude that the nonspatial DD approach can be used to detect diversity‐dependence in clades of species that live in not too disconnected areas, but parameter estimates must be interpreted cautiously.     

Species diversity in local neutral communities

We extend the neutral theory of macroecology by deriving biodiversity models (relative species abundance and species-area relationships) in a local community-metacommunity system in which the local community is embedded within the metacommunity. We first demonstrate that the local species diversity patterns converge to that of the metacommunity as the size (scale) of the embedded local community increases. This result shows that in continuous landscapes no sharp boundaries dividing the communities at the two scales exist; they are an artificial distinction made by the current spatially implicit neutral theory. Second, we remove the artificial restriction that speciation cannot occur in a local community, even if the effects of local speciation are small. Third, we introduce stochasticity into the immigration rate, previously treated as constant, and demonstrate that local species diversity is a function not only of the mean but also of the variance in immigration rate. High variance in immigration rates reduces species diversity in local communities. Finally, we show that a simple relationship exists between the fundamental diversity parameter of neutral theory and Simpson's index for local communities. Derivation of this relationship extends recent work on diversity indices and provides a means of evaluating the effect of immigration on estimates of the fundamental diversity parameter derived from relative species abundance data on local communities.     

How likely is speciation in neutral ecology?

Patterns of biodiversity predicted by the neutral theory rely on a simple phenomenological model of speciation. To further investigate the effect of speciation on neutral biodiversity, we analyze a spatially explicit neutral model based on population genetics. We define the metacommunity as a system of populations exchanging migrants, and we use this framework to introduce speciation with little or no gene flow (allopatric and parapatric speciation). We find that with realistic mutation rates, our metacommunity model driven by neutral processes cannot support more than a few species. Adding natural selection in the population genetics of speciation increases the number of species in the metacommunity, but the level of diversity found in the Barro Colorado Island is difficult to reach.     

Metacommunity size influences aquatic community composition in a natural mesocosm landscape

Ecosystems are often arranged in naturally patchy landscapes with habitat patches linked by dispersal of species in a metacommunity. The size of a metacommunity, or number of patches, is predicted to influence community dynamics and therefore the structure and function of local communities. However, such predictions have yet to be experimentally tested using full food webs in natural metacommunities. We used the natural mesocosm system of aquatic macroinvertebrates in bromeliad phytotelmata to test the effect of the number of patches in a metacommunity on species richness, abundance, and community composition. We created metacommunities of varying size using fine mesh cages to enclose a gradient from a single bromeliad up to the full forest. We found that species richness, abundance, and biomass increased from enclosed metacommunities to the full forest size and that diversity and evenness also increased in larger enclosures. Community composition was affected by metacommunity size across the full gradient, with a more even detritivore community in larger metacommunities, and taxonomic groups such as mosquitoes going locally extinct in smaller metacommunities. We were able to divide the effects of metacommunity size into aquatic and terrestrial habitat components and found that the importance of each varied by species; those with simple life cycles were only affected by local aquatic habitat whereas insects with complex life cycles were also affected by the amount of terrestrial matrix. This differential survival of obligate and non‐obligate dispersers allowed us to partition the beta‐diversity between metacommunities among functional groups. Our study is one of the first tests of metacommunity size in a natural metacommunity landscape and shows that both diversity and community composition are significantly affected by metacommunity size. Synthesis Natural food webs are sensitive to meta‐community size, i.e. the number of patches connected through dispersal. We provide an empirical test using the aquatic foodweb associated within bromeliads as a model system. When we reduced the number of bromeliad patches connect through dispersal, we found a clear change of the foodweb in terms of population sizes, beta diversity, community composition and predator‐prey ratios. The response of individual taxa was predictable based on species traits including dispersal modes, life cycle, and adult resource requirements. Our study demonstrates that community structure is strongly influenced by the interplay of species traits and landscape properties.     

The influence of dispersal on the realized trajectory of a pond metacommunity

Dispersal rates play a critical role in metacommunity dynamics, yet few studies have attempted to characterize dispersal rates for the majority of species in any natural community. Here we evaluate the relationship between the abundances of 179 plankton taxa in a pond metacommunity and their dispersal rates. We find the expected positive relationship between the regional abundances of phytoplankton, protozoa and metazoan zooplankton, which is suggestive of dispersal being a density‐independent per capita rate for these groups. When we tested to see if the rates of dispersing taxa predicted changes in community composition, we found that dispersers had no measurable impact on the short‐term trajectory of local pond communities or mesocosm communities established experimentally (assembled communities), but became increasingly represented in the overall pond metacommunity during the course of the full growing season. In comparison, the composition of experimental mesocosms that lacked any initial zooplankton community (unassembled communities) were found to be driven by dispersal measured at the local pond community but not by dispersal observed across the overall metacommunity. These results suggest that the role of dispersal may shift from a contributor to local, ecological dynamics to that of metacommunity‐wide, colonization–extinction dynamics as communities assemble.     

A truce with neutral theory: local deterministic factors, species traits and dispersal limitation together determine patterns of diversity in stream invertebrates

1. Studies seeking to explain local patterns of diversity have typically relied on niche explanations, reflected in correlations with local environmental conditions, or neutral theory, invoking dispersal processes and speciation. 2. We used macroinvertebrate community data from 10 streams that varied independently in local ecological conditions and spatial proximity. Neutral theory predicts that similarity in communities will be negatively associated with distance between sites, while niche theory suggests that community similarity will be positively associated with similarity in local ecological conditions. 3. Similarity in total invertebrate, grazer and predator assemblages showed negative relationships with distance and, for grazers and predators, positive relationships with local ecological conditions. However, the best model predicting community similarity in all three cases included aspects of both local ecological conditions and distance between sites. 4. When assemblages were analysed according to dispersal ability, high-dispersal species were shown to be freely accessing all sites and community similarity was not well predicted by either local ecology or spatial separation. Assemblages of species with low and moderate dispersal ability were best predicted by combined models, including distance between sites and local ecological factors. 5. The results suggest that the perceived dichotomy between neutral and local environmental processes in determining local patterns of diversity may not be useful. Neutral and niche processes structured these communities differentially depending on trophic level and species traits. 6. We emphasize the potential for both dispersal processes and local environmental conditions to explain local patterns of diversity.     

Dispersal stochasticity mediates species richness in source–sink metacommunities

Although it is well‐known that dispersal of organisms within a metacommunity will influence patterns of coexistence and richness, theoretical and experimental studies generally assume that dispersal rates are constant through time. However, dispersal is often a highly variable process that can vary seasonally and/or when stochastic events (e.g. wind storms, droughts, floods) occur. Using a well‐known source–sink metacommunity model, we present novel predictions for local and regional species richness when stochasticity in dispersal is expressly considered. We demonstrate that dispersal stochasticity alters some of the predictions obtained with constant dispersal; the peak of the predicted hump‐shaped relationship between dispersal and local species richness is diminished and shifted towards higher values of dispersal. Dispersal stochasticity increases extinction probabilities of inferior competitor species particularly in metacommunities subjected to severe isolation events (i.e. decreases of dispersal) or homogenization events (i.e. sudden increases of dispersal). Our results emphasize how incorporating dispersal stochasticity into theoretical predictions will broaden our understanding of metacommunities dynamics and their responses to natural and human‐related disturbances.     

Predicting food‐web structure with metacommunity models

Synthesis Metacommunity theory aims to elucidate the relative influence of local and regional‐scale processes in generating diversity patterns across the landscape. Metacommunity research has focused largely on assemblages of competing organisms within a single trophic level. Here, we test the ability of metacommunity models to predict the network structure of the aquatic food web found in the leaves of the northern pitcher plant Sarracenia purpurea. The species‐sorting and patch‐dynamics models most accurately reproduced nine food web properties, suggesting that local‐scale interactions play an important role in structuring Sarracenia food webs. Our approach can be applied to any well‐resolved food web for which data are available from multiple locations. The metacommunity framework explores the relative influence of local and regional‐scale processes in generating diversity patterns across the landscape. Metacommunity models and empirical studies have focused mostly on assemblages of competing organisms within a single trophic level. Studies of multi‐trophic metacommunities are predominantly restricted to simplified trophic motifs and rarely consider entire food webs. We tested the ability of the patch‐dynamics, species‐sorting, mass‐effects, and neutral metacommunity models, as well as three hybrid models, to reproduce empirical patterns of food web structure and composition in the complex aquatic food web found in the northern pitcher plant Sarracenia purpurea. We used empirical data to determine regional species pools and estimate dispersal probabilities, simulated local food‐web dynamics, dispersed species from regional pools into local food webs at rates based on the assumptions of each metacommunity model, and tested their relative fits to empirical data on food‐web structure. The species‐sorting and patch‐dynamics models most accurately reproduced nine food web properties, suggesting that local‐scale interactions were important in structuring Sarracenia food webs. However, differences in dispersal abilities were also important in models that accurately reproduced empirical food web properties. Although the models were tested using pitcher‐plant food webs, the approach we have developed can be applied to any well‐resolved food web for which data are available from multiple locations.