Linking dispersal, immigration and scale in the neutral theory of biodiversity

In the classic spatially implicit formulation of Hubbell's neutral theory of biodiversity a local community receives immigrants from a metacommunity operating on a relatively slow timescale, and dispersal into the local community is governed by an immigration parameter m . A current problem with neutral theory is that m lacks a clear biological interpretation. Here, we derive analytical expressions that relate the immigration parameter m to the geometry of the plot defining the local community and the parameters of a dispersal kernel. Our results facilitate more rigorous and extensive tests of the neutral theory: we conduct a test of neutral theory by comparing estimates of m derived from fits to empirical species abundance distributions to those derived from dispersal kernels and find acceptable correspondence; and we generate a new prediction of neutral theory by investigating how the shapes of species abundance distributions change theoretically as the spatial scale of observation changes. We also discuss how our main analytical results can be used to assess the error in the mean-field approximations associated with spatially implicit formulations of neutral theory.     

Dispersal, edaphic fidelity and speciation in species-rich Western Australian shrublands: evaluating a neutral model of biodiversity

Over evolutionary time, the number of species in a community reflects the balance between the rate of speciation and the rate of extinction. Over shorter time‐scales local species richness is also affected by how often species move into and out of the local community. These processes are at the heart of Hubbell's ‘unified neutral theory of biodiversity’ ( Hubbell 2001 ). Hubbell's spatially implicit, dispersal‐limited neutral model is the most widely used of the many implementations of neutral theory and it provides an estimate of the rate of speciation in a metacommunity (if metacommunity size is known) and the rate at which species migrate into the local community from the wider metacommunity. Recently, this neutral model has been used to compare rates of speciation and migration in the species‐rich fynbos of South Africa and in neotropical forests. Here we use new analytical methods for estimating the neutral model's parameters to infer speciation and dispersal rates for three sites in species‐rich sclerophyll shrublands (equivalent to fynbos) in Western Australia (WA). Our estimates suggest that WA shrublands are intermediate between fynbos and tropical rainforest in terms of speciation and dispersal. Although a weak test, the model predicts species abundance distributions and species accumulation curves similar to those observed at the three sites. The neutral model's predictions also remain plausible when confronted with independent data describing: (1) known edaphic relationships between sites, (2) estimates of metacommunity species richness and (3) rates of speciation among resprouters and nonsprouters. Two of the site pairs, however, show species turnovers significantly different from those predicted by the spatially implicit form of the neutral model that we use. This suggests that non‐neutral processes, in this case probably edaphic specialisation, are important in the WA shrubland metacommunity. The neutral model predicts similar rates of speciation in resprouter and sprouter taxa, a finding supported by recent molecular phylogenies. Finally, when converted into temporally scaled speciation rates and species longevities, the estimates produced by the neutral model seem implausible. The apparent departure from neutrality in the turnover of species between some sites and the implausible temporal dynamics may be due to the particular model chosen and does not reduce the significance of our other results, which confirm that local dispersal limitation, coupled with broader scale edaphic fidelity, combine to structure this biodiverse metacommunity.     

A neutral sampling formula for multiple samples and an 'exact' test of neutrality

As the utility of the neutral theory of biodiversity is increasingly being recognized, there is also an increasing need for proper tools to evaluate the relative importance of neutral processes (dispersal limitation and stochasticity). One of the key features of neutral theory is its close link to data: sampling formulas, giving the probability of a data set conditional on a set of model parameters, have been developed for parameter estimation and model comparison. However, only single local samples can be handled with the currently available sampling formulas, whereas data are often available for many small spatially separated plots. Here, I present a sampling formula for multiple, spatially separated samples from the same metacommunity, which is a generalization of earlier sampling formulas. I also provide an algorithm to generate data sets with the model and I introduce a general test of neutrality that does not require an alternative model; this test compares the probability of the observed data (calculated using the new sampling formula) with the probability of model-generated data sets. I illustrate this with tree abundance data from three large Panamanian neotropical forest plots. When the test is performed with model parameters estimated from the three plots, the model cannot be rejected; however, when parameter estimates previously reported for BCI are used, the model is strongly rejected. This suggests that neutrality cannot explain the structure of the three Panamanian tree communities on the local (BCI) and regional (Panama Canal Zone) scale simultaneously. One should be aware, however, that aspects of the model other than neutrality may be responsible for its failure. I argue that the spatially implicit character of the model is a potential candidate.     

Beta diversity in spatially implicit neutral models: a new way to assess species migration

The spatially implicit neutral model (SINM) of S. P. Hubbell predicts species' abundance distributions at two levels: local communities where extinction balances immigration, characterized by the immigration number I, and the metacommunity, a source pool of migrants where speciation balances extinction. Previously, a plot's I was estimated from its species abundance distribution. Here, we relate neutral theory to the additive partitioning of species diversity and calculate the immigration rate into different plots from the variation in species composition among them. We revisit the G(ST) statistic of population genetics to introduce a new version, G(ST)(k), conditional on each community sample k. We derive an analytical expectation of G(ST)(k) as a function of the local immigration number, I(k), under a generalized version of the SINM, which allows the pool of migrants to deviate from the large-scale speciation-extinction balance. Simulations and field data suggest that G(ST)(k) provides reasonable estimates of immigration numbers, which were compared with the results from alternative likelihood-based estimations.     

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.     

Estimating and interpreting migration of Amazonian forests using spatially implicit and semi‐explicit neutral models

With many sophisticated methods available for estimating migration, ecologists face the difficult decision of choosing for their specific line of work. Here we test and compare several methods, performing sanity and robustness tests, applying to large‐scale data and discussing the results and interpretation. Five methods were selected to compare for their ability to estimate migration from spatially implicit and semi‐explicit simulations based on three large‐scale field datasets from South America (Guyana, Suriname, French Guiana and Ecuador). Space was incorporated semi‐explicitly by a discrete probability mass function for local recruitment, migration from adjacent plots or from a metacommunity. Most methods were able to accurately estimate migration from spatially implicit simulations. For spatially semi‐explicit simulations, estimation was shown to be the additive effect of migration from adjacent plots and the metacommunity. It was only accurate when migration from the metacommunity outweighed that of adjacent plots, discrimination, however, proved to be impossible. We show that migration should be considered more an approximation of the resemblance between communities and the summed regional species pool. Application of migration estimates to simulate field datasets did show reasonably good fits and indicated consistent differences between sets in comparison with earlier studies. We conclude that estimates of migration using these methods are more an approximation of the homogenization among local communities over time rather than a direct measurement of migration and hence have a direct relationship with beta diversity. As betadiversity is the result of many (non)‐neutral processes, we have to admit that migration as estimated in a spatial explicit world encompasses not only direct migration but is an ecological aggregate of these processes. The parameter m of neutral models then appears more as an emerging property revealed by neutral theory instead of being an effective mechanistic parameter and spatially implicit models should be rejected as an approximation of forest dynamics.     

Universal scaling of species‐abundance distributions across multiple scales

The scale‐dependent species abundance distribution (SAD) is fundamental in ecology, but few spatially explicit models of this pattern have thus far been studied. Here we show spatially explicit neutral model predictions for SADs over a wide range of spatial scales, which appear to match empirical patterns qualitatively. We find that the assumption of a log‐series SAD in the metacommunity made by spatially implicit neutral models can be justified with a spatially explicit model in the large area limit. Furthermore, our model predicts that SADs on multiple scales are characterized by a single, compound parameter that represents the ratio of the survey area to the species’ average biogeographic range (which is in turn set by the speciation rate and the dispersal distance). This intriguing prediction is in line with recent empirical evidence for a universal scaling of the species‐area curve. Hence we hypothesize that empirical SAD patterns will show a similar universal scaling for many different taxa and across multiple spatial scales.     

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.     

What can observational data reveal about metacommunity processes?

A key challenge for community ecology is to understand to what extent observational data can be used to infer the underlying community assembly processes. As different processes can lead to similar or even identical patterns, statistical analyses of non‐manipulative observational data never yield undisputable causal inference on the underlying processes. Still, most empirical studies in community ecology are based on observational data, and hence understanding under which circumstances such data can shed light on assembly processes is a central concern for community ecologists. We simulated a spatial agent‐based model that generates variation in metacommunity dynamics across multiple axes, including the four classic metacommunity paradigms as special cases. We further simulated a virtual ecologist who analysed snapshot data sampled from the simulations using eighteen output metrics derived from beta‐diversity and habitat variation indices, variation partitioning and joint species distribution modelling. Our results indicated two main axes of variation in the output metrics. The first axis of variation described whether the landscape has patchy or continuous variation, and thus was essentially independent of the properties of the species community. The second axis of variation related to the level of predictability of the metacommunity. The most predictable communities were niche‐based metacommunities inhabiting static landscapes with marked environmental heterogeneity, such as metacommunities following the species sorting paradigm or the mass effects paradigm. The most unpredictable communities were neutral‐based metacommunities inhabiting dynamics landscapes with little spatial heterogeneity, such as metacommunities following the neutral or patch sorting paradigms. The output metrics from joint species distribution modelling yielded generally the highest resolution to disentangle among the simulated scenarios. Yet, the different types of statistical approaches utilized in this study carried complementary information, and thus our results suggest that the most comprehensive evaluation of metacommunity structure can be obtained by combining them.     

A neutral model of edge effects

In this paper a spatially implicit neutral model for explaining the edge effects between habitats is proposed. To analyze this model we use two different approaches: a discrete approach that is based on the Master equation for a one step jump process and a continuous approach based on the approximation of the discrete jump process with the Kolmogorov-Fokker-Planck forward and backward equations. The discrete and continuous approaches are applied to analyze the species abundance distributions and the time to species extinction. Moreover, with the aid of the continuous approach a realistic classification of the behavior of species in local communities is developed. The species abundance dynamics at the edge between two distinct habitats is compared with those located in the homogeneous interior habitats using species abundance distributions and the first time to species extinction. We show that the structure of the links between local community and the metacommunity plays an important role on species persistence. Specifically, species at the edge between two distinct metacommunities have higher extinction rate than those in the interior habitats connected only to one metacommunity. Moreover, the same species might be persistent in the homogeneous interior habitat, but its probability of extinction from the edge local community could be very high.     

Species diversity in neutral metacommunities: a network approach

Biologists seek an understanding of the processes underlying spatial biodiversity patterns. Neutral theory links those patterns to dispersal, speciation and community drift. Here, we advance the spatially explicit neutral model by representing the metacommunity as a network of smaller communities. Analytic theory is presented for a set of equilibrium diversity patterns in networks of communities, facilitating the exploration of parameter space not accessible by simulation. We use this theory to evaluate how the basic properties of a metacommunity – connectivity, size, and speciation rate – determine overall metacommunity γ -diversity, and how that is partitioned into α - and β -components. We find spatial structure can increase γ -diversity relative to a well-mixed model, even when θ is held constant. The magnitude of deviations from the well-mixed model and the partitioning into α - and β -diversity is related to the ratio of migration and speciation rates. γ -diversity scales linearly with metacommunity size even as α - and β -diversity scale nonlinearly with size.     

Interaction strength and extinction risk in a metacommunity

Species interactions and connectivity are both central to explaining the stability of ecological communities and the problem of species extinction. Yet, the role of species interactions for the stability of spatially subdivided communities still eludes ecologists. Ecological models currently address the problem of stability by exploring the role of interaction strength in well mixed habitats, or of connectivity in subdivided communities. Here I propose a unification of interaction strength and connectivity as mechanisms explaining regional community stability. I introduce a metacommunity model based on succession dynamics in coastal ecosystems, incorporating limited dispersal and facilitative interactions. I report a sharp transition in regional stability and extinction probability at intermediate interaction strength, shown to correspond to a phase transition that generates scale-invariant distribution and high regional stability. In contrast with previous studies, stability results from intermediate interaction strength only in subdivided communities, and is associated with large-scale (scale-invariant) synchrony. These results can be generalized to other systems exhibiting phase transitions to show how local interaction strength can be used to resolve the link between regional community stability and pattern formation.     

A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit

The genealogical structure of neutral populations in which reproductive success is highly-skewed has been the subject of many recent studies. Here we derive a coalescent dual process for a related class of continuous-time Moran models with viability selection. In these models, individuals can give birth to multiple offspring whose survival depends on both the parental genotype and the brood size. This extends the dual process construction for a multi-type Moran model with genic selection described in Etheridge and Griffiths (2009). We show that in the limit of infinite population size the non-neutral Moran models converge to a Markov jump process which we call the Λ-Fleming-Viot process with viability selection and we derive a coalescent dual for this process directly from the generator and as a limit from the Moran models. The dual is a branching-coalescing process similar to the Ancestral Selection Graph which follows the typed ancestry of genes backwards in time with real and virtual lineages. As an application, the transition functions of the non-neutral Moran and Λ-coalescent models are expressed as mixtures of the transition functions of the dual process.     

The influence of niche and neutral processes on a neotropical anuran metacommunity

One of the most important questions in ecology is the relative importance of local conditions (niche processes) and dispersal ability (neutral processes) in driving metacommunity structure. Although many studies have been conducted in recent years, there is still much debate. We evaluated the processes (niche and neutral) responsible for variation in anuran composition in 28 lentic water bodies in southeastern Brazil. Because anurans depend heavily on environmental conditions, we hypothesized that environmental variables (niche processes) are the most important drivers of community composition. Additionally, as anurans have limited dispersal abilities, and the study region presents harsh conditions (high forest fragmentation, low rainfall and long dry season), we expected a lower, but significant, spatial signature in metacommunity structure, due to neutral dynamics. We used a partial redundancy analysis with variation partitioning to evaluate the relative influence of environmental and spatial variables as drivers of metacommunity structure. Additionally, we used a recently developed spatial autocorrelation analysis to test if neutral dynamics can be attributed to the pure spatial component. This analysis is based on predictions that species abundances are independent but similarly spatially structured, with correlograms similar in shape. Therefore, under neutral dynamics there is no expectation of a correlation between the pairwise distance of spatial correlograms and the pairwise correlation of species abundances predicted by the pure spatial component. We found that the environmental component explained 21.5%, the spatial component 10.2%, and the shared component 6.4% of the metacommunity structure. We found no correlation between correlograms and correlation of abundances predicted by the pure spatial component (Mantel test = ?0.109, P = 0.961). In our study, niche‐based processes are the dominant process that explained community composition. However, neutral processes are important because spatial variation can be attributed to pure neutral dynamics rather than to missing spatially structured environmental factors.     

Neighborhood Dependence in Bayesian Spatial Models

The conditional autoregressive model and the intrinsic autoregressive model are widely used as prior distribution for random spatial effects in Bayesian models. Several authors have pointed out impractical or counterintuitive consequences on the prior covariance matrix or the posterior covariance matrix of the spatial random effects. This article clarifies many of these puzzling results. We show that the neighborhood graph structure, synthesized in eigenvalues and eigenvectors structure of a matrix associated with the adjacency matrix, determines most of the apparently anomalous behavior. We illustrate our conclusions with regular and irregular lattices including lines, grids, and lattices based on real maps.     

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.     

集合群落及其在河流鱼类群聚研究中的应用

集合群落(metacommunity)是指多个潜在相互作用的物种通过它们之间的扩散而连接在一起的一组局域群落,目前已成为斑块生境下生物群落结构、格局和动态的重要理论基础之一。斑块动态、物种排序、群体效应和中性模型等4种理论模型,可用于解释不同情形下集合群落内物种的迁移状况,描述集合群落的动态。可采用群落结构或生态学机制等途径,来阐述所研究的群落是属于哪一种特定的集合群落类型。集合群落可用于研究河流鱼类群聚,解释鱼类的群落结构等问题。另外本文还结合我国水域生态环境及水生生物现状,对今后集合群落的研究作了展望。     

Effect of field sampling design on variation partitioning in a dendritic stream network

Variation partitioning is one of the most frequently used method to infer the importance of environmental (niche based) and spatial (dispersal) processes in metacommunity structuring. However, the reliability of the method in predicting the role of the major structuring forces is less known. We studied the effect of field sampling design on the result of variation partitioning of fish assemblages in a stream network. Along with four different sample sizes, a simple random sampling from a total of 115 stream segments (sampling objects) was applied in 400 iterations, and community variation of each random sample was partitioned into four fractions: pure environmentally (landscape variables) explained, pure spatially (MEM eigenvectors) explained, jointly explained by environment and space, and unexplained variance. Results were highly sensitive to sample size. Even at a given sample size, estimated variance fractions had remarkable random fluctuation, which can lead to inconsistent results on the relative importance of environmental and spatial variables on the structuring of metacommunities. Interestingly, all the four variance fractions correlated better with the number of the selected spatial variables than with any design properties. Sampling interval proved to be a fundamentally influential sampling design property because it affected the number of the selected spatial variables. Our findings suggest that the effect of sampling design on variation partitioning is related to the ability of the eigenvectors to model complex spatial patterns. Hence, properties of the sampling design should be more intensively considered in metacommunity studies.