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.     

Weak climatic associations among British plant distributions

Aim Species distribution models (SDMs) are used to infer niche responses and predict climate change‐induced range shifts. However, their power to distinguish real and chance associations between spatially autocorrelated distribution and environmental data at continental scales has been questioned. Here this is investigated at a regional (10 km) scale by modelling the distributions of 100 plant species native to the UK. Location UK. Methods SDMs fitted using real climate data were compared with those utilizing simulated climate gradients. The simulated gradients preserve the exact values and spatial structure of the real ones, but have no causal relationships with any species and so represent an appropriate null model. SDMs were fitted as generalized linear models (GLMs) or by the Random Forest machine‐learning algorithm and were either non‐spatial or included spatially explicit trend surfaces or autocovariates as predictors. Results Species distributions were significantly but erroneously related to the simulated gradients in 86% of cases (P < 0.05 in likelihood‐ratio tests of GLMs), with the highest error for strongly autocorrelated species and gradients and when species occupied 50% of sites. Even more false effects were found when curvilinear responses were modelled, and this was not adequately mitigated in the spatially explicit models. Non‐spatial SDMs based on simulated climate data suggested that 70–80% of the apparent explanatory power of the real data could be attributable to its spatial structure. Furthermore, the niche component of spatially explicit SDMs did not significantly contribute to model fit in most species. Main conclusions Spatial structure in the climate, rather than functional relationships with species distributions, may account for much of the apparent fit and predictive power of SDMs. Failure to account for this means that the evidence for climatic limitation of species distributions may have been overstated. As such, predicted regional‐ and national‐scale impacts of climate change based on the analysis of static distribution snapshots will require re‐evaluation.     

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.     

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.     

Spatially explicit neutral models for population genetics and community ecology: Extensions of the Neyman-Scott clustering process

Spatially explicit models relating to plant populations have developed little since Felsenstein (1975) pointed out that if limited seed dispersal causes clustering of individuals, such models cannot reach an equilibrium. This paper aims to resolve this issue by modifying the Neyman-Scott cluster point process. The new point processes are dynamic models with random immigration, and the continuous increase in the clustering of individuals stops at some level. Hence, an equilibrium state is achieved, and new individual-based spatially explicit neutral coalescent models are established. By fitting the spatial structure at equilibrium to individual spatial distribution data, we can indirectly estimate seed dispersal and effective population density. These estimates are improved when genetic data are available, and become even more sophisticated if spatial distribution and genetic data pertaining to the offspring are also available.     

Scaling issues of neutral theory reveal violations of ecological equivalence for dominant Amazonian tree species

Neutral models are often used as null models, testing the relative importance of niche versus neutral processes in shaping diversity. Most versions, however, focus only on regional scale predictions and neglect local level contributions. Recently, a new formulation of spatial neutral theory was published showing an incompatibility between regional and local scale fits where especially the number of rare species was dramatically under‐predicted. Using a forward in time semi‐spatially explicit neutral model and a unique large‐scale Amazonian tree inventory data set, we show that neutral theory not only underestimates the number of rare species but also fails in predicting the excessive dominance of species on both regional and local levels. We show that although there are clear relationships between species composition, spatial and environmental distances, there is also a clear differentiation between species able to attain dominance with and without restriction to specific habitats. We conclude therefore that the apparent dominance of these species is real, and that their excessive abundance can be attributed to fitness differences in different ways, a clear violation of the ecological equivalence assumption of neutral theory.     

Assessment of spatial discordance of primary and effective seed dispersal of European beech (Fagus sylvatica L.) by ecological and genetic methods

Spatial discordance between primary and effective dispersal in plant populations indicates that postdispersal processes erase the seed rain signal in recruitment patterns. Five different models were used to test the spatial concordance of the primary and effective dispersal patterns in a European beech (Fagus sylvatica) population from central Spain. An ecological method was based on classical inverse modelling (SSS), using the number of seed/seedlings as input data. Genetic models were based on direct kernel fitting of mother‐to‐offspring distances estimated by a parentage analysis or were spatially explicit models based on the genotype frequencies of offspring (competing sources model and Moran‐Clark's Model). A fully integrated mixed model was based on inverse modelling, but used the number of genotypes as input data (gene shadow model). The potential sources of error and limitations of each seed dispersal estimation method are discussed. The mean dispersal distances for seeds and saplings estimated with these five methods were higher than those obtained by previous estimations for European beech forests. All the methods show strong discordance between primary and effective dispersal kernel parameters, and for dispersal directionality. While seed rain was released mostly under the canopy, saplings were established far from mother trees. This discordant pattern may be the result of the action of secondary dispersal by animals or density‐dependent effects; that is, the Janzen‐Connell effect.     

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.     

Age structure in neutral theory resolves inconsistencies related to reproductive-size threshold

Aims Neutral theory consists of a suite of models that assume ecological equivalence among individual organisms. They have been most commonly applied to tropical forest tree communities either as null models or as approximations. Neutral models typically only include reproductive adults; therefore, fitting to empirical tree community data requires defining a reproductive-size threshold, which for trees is usually set arbitrarily to a diameter at breast height (DBH) of 100 mm. The inevitable exclusion of some reproductive adults and inclusion of some saplings cause a non-random sampling bias in neutral model fits. Here, we investigate this problem and resolve it by introducing simple age structure into a neutral model.Methods We compared the performance and sensitivity of DBH threshold of three variants of a spatially explicit neutral model: the traditional model, a model incorporating random sampling and a model with two distinct age classes—reproductive adults and saplings. In the age-structured model, saplings are offspring from adults that disperse according to a Gaussian dispersal kernel around the adults. The only extra parameter is the ratio of adults to saplings, which is not a free parameter but directly measurable. We used species–area relationships (SARs) to explore the predicted effect of saplings on the species richness at different scales in our model. We then evaluated the three model variations to find the parameters required to maintain the observed level of species richness in the 50-ha plot on Barro Colorado Island (BCI). We repeated our analysis filtering the data at different minimum tree-size thresholds in order to find the effect this threshold has on our results. Lastly, we used empirical species–individual relationships (SIRs) to test the pre-existing hypothesis that environmental filtering is the primary cause of differences between the assemblage of saplings and that of adults on BCI.Important findings Our age-structured neutral model was characterized by SARs that were insensitive to the presence of saplings at large scales and highly sensitive to them at small scales. Both models without age structure were highly sensitive to the DBH threshold chosen in a way that could not be explained based on random samplings alone. The age-structured neutral model, which allowed for non-random sampling based on life stage, was consistent with species richness observations. Our analysis of empirical SIRs did not support environmental filtering as a dominant force, but it did show evidence for other differences between age classes. Age can now be easily incorporated into future studies of neutral models whenever there is a concern that a sample is not entirely composed of reproductive adult individuals. More generally, we suggest that modeling studies using tree data subject to a minimum size threshold should consider the sensitivity of their results to that threshold.     

A coalescence approach to spatial neutral ecology

Neutral models in ecology have attracted much attention in recent literature. They can provide considerable insight into the roles of non-species-specific factors (e.g. stochasticity, dispersal, speciation) on community dynamics but often require intensive simulations, particularly in spatial settings. Here, we clearly explain existing techniques for modelling spatially explicit neutral processes in ecology using coalescence. Furthermore, we present several novel extensions to these methods including procedures for dealing with system boundaries which enable improved investigation of the effects of dispersal. We also present a semi-analytical algorithm that calculates the expected species richness in a sample, for any speciation rate. By eliminating the effect of stochasticity in the speciation process, we reduce the variance in estimates of species richness. Our benchmarks show that the combination of existing coalescence theory and our extensions produces higher quality results in vastly shorter time scales than previously possible: years of simulation time are reduced to minutes. As an example application, we find parameters for a spatially explicit neutral model to approximate the species richness of a tropical forest dataset.     

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.     

NM+: software implementing parentage-based models for estimating gene dispersal and mating patterns in plants

NM+ is computer software designed for making inferences on plant gene dispersal and mating patterns by modelling parentage probabilities of offspring based on the spatially explicit neighbourhood model. NM+ requires a sample of mapped and genotyped candidate parents and offspring; however, offspring may optionally be assigned to single maternal parents (forming so-called half-sib progeny arrays). Using maximum likelihood, NM+ estimates a number of parameters, including proportions of offspring due to self-fertilization, pollen immigration from outside of a defined study site, parameters of pollen (and/or seed) dispersal kernels (exponential-power, Weibull, geometric or 2Dt) and selection gradients relating covariates (phenotypic traits) with male (and/or female) reproductive success. NM+ allows for missing data both in parents and in offspring. It accounts for null alleles and their frequencies can optionally be considered as estimable parameters. Data files are formatted in a table-like structure so they can be easily prepared in a spreadsheet software. By default NM+ is for studying plant populations, however, it can be used for any organism as long as data requirements and model assumptions are met. NM+ runs under Windows, but it can be launched under Linux using WINE emulator. NM+ can be downloaded free of charge from http://www.genetyka.ukw.edu.pl/index_pliki/software.htm.     

A reassessment of equivalence in yield from marine reserves and traditional fisheries managament

Lively debate continues over whether marine reserves can lead to increased fishery yields when compared to conventional, quota‐based management, apparently driven by differences in the complexity and biological richness of the models being used. In an influential article, Hastings and Botsford used an analytically tractable, spatially implicit, non‐age‐structured model to assert that reserves are typically incapable of increasing yields relative to conventional management, regardless of the type (pre‐ or post‐dispersal, involving adults and/or larvae) or functional form (Ricker or Beverton‐Holt) of density dependence present. A recent numerical (simulation) model by Gaylord et al. concludes that reserves can enhance yield compared to conventional management, a result the authors attribute to their spatially‐explicit evaluation of stage‐structured adult growth, survivability and fecundity; and intercohort (adult‐on‐larvae) post‐dispersal density dependent population dynamics. Here we demonstrate that the increased model complexity is not responsible for the different conclusions. We analyze a spatially‐implicit model without stage structure that incorporates intercohort post‐dispersal density dependence. In this simple model we still find annual extirpation of adult populations outside reserves due to fishing to enhance larval recruitment there, allowing for increased yields compared to those achieved when harvest is evenly spread across the entire domain under conventional management. Consideration of neither spatially‐explicit dispersal dynamics nor stage‐structure in adult demographics is required for reserves to substantially improve yield beyond that attainable under conventional management. In contrast, consideration of within cohort post‐dispersal density dependence among larva during settlement in an otherwise identical model generates equivalence in yield between the two management strategies. These results recast a common message characterizing the relative benefit of reserve versus non‐reserve management from “equivalence at best” to “potentially improved”.     

kernelpop,a spatially explicit population genetic simulation engine

Individual‐based, spatially explicit models provide a mechanism to understand distributions of individuals on the landscape; however, few models have been coupled with population genetics. The primary benefits of such a combination is to assess performance of population‐genetic estimators in realistic situations. kernelpop represents a flexible framework to implement almost any arbitrary population‐genetic and demographic model in a spatially explicit context using a variety of dispersal kernels. Estimates of type I error associated with genome scans in metapopulations are provided as an illustration of this software's utility.     

Accounting for spatial autocorrelation in null models of tree species association

A commonly used null model for species association among forest trees is a well‐mixed community (WMC). A WMC represents a non‐spatial, or spatially implicit, model, in which species form nearest‐neighbor pairs at a rate equal to the product of their community proportions. WMC models assume that the outcome of random dispersal and demographic processes is complete spatial randomness (CSR) in the species’ spatial distributions. Yet, stochastic dispersal processes often lead to spatial autocorrelation (SAC) in tree species densities, giving rise to clustering, segregation, and other nonrandom patterns. Although methods exist to account for SAC in spatially‐explicit models, its impact on non‐spatial models often remains unaccounted for. To investigate the potential for SAC to bias tests based upon non‐spatial models, we developed a spatially‐heterogeneous (SH) modelling approach that incorporates measured levels of SAC. Using the mapped locations of individuals in a tropical tree community, we tested the hypothesis that the identity of nearest‐neighbors represents a random draw from neighborhood species pools. Correlograms of Moran's I confirmed that, for 50 of 51 dominant species, stem density was significantly autocorrelated over distances ranging from 50 to 200 m. The observed patterns of SAC were consistent with dispersal limitation, with most species occurring in distinct patches. For nearly all of the 106 species in the community, the frequency of pairwise association was statistically indistinguishable from that projected by the null models. However, model comparisons revealed that non‐spatial models more strongly underestimated observed species‐pair frequencies, particularly for conspecific pairs. Overall, the CSR models projected more significant facilitative interactions than did SH models, yielding a more liberal test of niche differences. Our results underscore the importance of accounting for stochastic spatial processes in tests of association, regardless of whether spatial or non‐spatial models are employed.     

Spatial capture–recapture models allowing Markovian transience or dispersal

Spatial capture–recapture (SCR) models are a relatively recent development in quantitative ecology, and they are becoming widely used to model density in studies of animal populations using camera traps, DNA sampling and other methods which produce spatially explicit individual encounter information. One of the core assumptions of SCR models is that individuals possess home ranges that are spatially stationary during the sampling period. For many species, this assumption is unlikely to be met and, even for species that are typically territorial, individuals may disperse or exhibit transience at some life stages. In this paper we first conduct a simulation study to evaluate the robustness of estimators of density under ordinary SCR models when dispersal or transience is present in the population. Then, using both simulated and real data, we demonstrate that such models can easily be described in the BUGS language providing a practical framework for their analysis, which allows us to evaluate movement dynamics of species using capture–recapture data. We find that while estimators of density are extremely robust, even to pathological levels of movement (e.g., complete transience), the estimator of the spatial scale parameter of the encounter probability model is confounded with the dispersal/transience scale parameter. Thus, use of ordinary SCR models to make inferences about density is feasible, but interpretation of SCR model parameters in relation to movement should be avoided. Instead, when movement dynamics are of interest, such dynamics should be parameterized explicitly in the model.     

When do localized natural enemies increase species richness?

The Janzen–Connell hypothesis states that local species‐specific density dependence, mediated through specialist enemies of offspring such as fungal pathogens and insect seed predators, can facilitate coexistence of species by preventing recruitment near conspecific adults. We use spatially explicit simulation models and analytical approximations to evaluate how spatial scales of offspring and enemy dispersal affect species richness. In comparison with model communities in which both offspring and enemies disperse long distances, species richness is substantially decreased when offspring disperse long distances and enemies disperse short distances. In contrast, when both offspring and enemies disperse short distances species richness more than doubles and adults of each species are highly spatially clumped. For the range of conditions typical of tropical forests, locally dispersing specialist enemies may decrease species richness relative to enemies that disperse long distances. In communities where dispersal distances of both offspring and enemies are short, local effects may enhance species richness.     

Immigration,Local Dispersal Limitation,and the Repeatability of Community Composition under Neutral and Niche Dynamics

Repeatability of community composition has been a critical aspect for community structure, which is closely associated with community stability, predictability, conservation biology and ecological restoration. It has been shown that both immigration and local dispersal limitation can affect the community composition in both neutral and niche model. Hence, we use a spatially explicit individual-based model to investigate the potential influence of immigration rate and strength of local dispersal limitation on repeatability in both neutral and niche models. Similarity measures are used to quantify repeatability. We examine the repeatability of community composition among replicate communities (which means the same community repeats many times), and between niche and neutral replicate communities. We find the correlation between repeatability and immigration rate is positive in the neutral model and an inverted unimodal in the niche model. The correlation between repeatability and local dispersal distance is positive in the niche model and negative in the neutral model. High repeatability between niche communities and neutral communities is observed with high immigration rates or when high local dispersal distance appears in the niche model or low local dispersal distance in the neutral model. Our results show that repeatability of community composition is not only dependent on the types of community models (niche vs. neutrality) but also strongly determined by immigration rates and local dispersal limitation.     

Modeling Distribution of Dispersal Distances in Male White-Tailed Deer

Abstract: Dispersal distances and their distribution pattern are important to understanding such phenomena as disease spread and gene flow, but oftentimes dispersal characteristics are modeled as a fixed trait for a given species. We found that dispersal distributions differ for spring and autumn dispersals of yearling male white-tailed deer (Odocoileus virginianus) but that combined data can be adequately modeled based on a log-normal distribution. We modeled distribution of dispersal distances from 3 distinct populations in Pennsylvania and Maryland, USA, based on the relationship between percent forest cover and mean dispersal distance and the relationship between mean and variance of dispersal distances. Our results suggest distributions of distances for dispersing yearling male white-tailed deer can be modeled by simply measuring a readily obtained landscape metric, percent forest cover, which could be used to create generalized spatially explicit disease or gene flow models.