On the statistical mechanics of species abundance distributions

A central issue in ecology is that of the factors determining the relative abundance of species within a natural community. The proper application of the principles of statistical physics to species abundance distributions (SADs) shows that simple ecological properties could account for the near universal features observed. These properties are (i) a limit on the number of individuals in an ecological guild and (ii) per capita birth and death rates. They underpin the neutral theory of Hubbell (2001), the master equation approach of  [Volkov et?al., 2003] and [Volkov et?al., 2005] and the idiosyncratic (extreme niche) theory of Pueyo et al. (2007); they result in an underlying log series SAD, regardless of neutral or niche dynamics. The success of statistical mechanics in this application implies that communities are in dynamic equilibrium and hence that niches must be flexible and that temporal fluctuations on all sorts of scales are likely to be important in community structure.     

How selection structures species abundance distributions

How do species divide resources to produce the characteristic species abundance distributions seen in nature? One way to resolve this problem is to examine how the biomass (or capacity) of the spatial guilds that combine to produce an abundance distribution is allocated among species. Here we argue that selection on body size varies across guilds occupying spatially distinct habitats. Using an exceptionally well-characterized estuarine fish community, we show that biomass is concentrated in large bodied species in guilds where habitat structure provides protection from predators, but not in those guilds associated with open habitats and where safety in numbers is a mechanism for reducing predation risk. We further demonstrate that while there is temporal turnover in the abundances and identities of species that comprise these guilds, guild rank order is conserved across our 30-year time series. These results demonstrate that ecological communities are not randomly assembled but can be decomposed into guilds where capacity is predictably allocated among species.     

Taking species abundance distributions beyond individuals

The species abundance distribution (SAD) is one of the few universal patterns in ecology. Research on this fundamental distribution has primarily focused on the study of numerical counts, irrespective of the traits of individuals. Here we show that considering a set of Generalized Species Abundance Distributions (GSADs) encompassing several abundance measures, such as numerical abundance, biomass and resource use, can provide novel insights into the structure of ecological communities and the forces that organize them. We use a taxonomically diverse combination of macroecological data sets to investigate the similarities and differences between GSADs. We then use probability theory to explore, under parsimonious assumptions, theoretical linkages among them. Our study suggests that examining different GSADs simultaneously in natural systems may help with assessing determinants of community structure. Broadening SADs to encompass multiple abundance measures opens novel perspectives in biodiversity research and warrants future empirical and theoretical developments.     

Spatial scaling of species abundance distributions

Species abundance distributions are an essential tool in describing the biodiversity of ecological communities. We now know that their shape changes as a function of the size of area sampled. Here we analyze the scaling properties of species abundance distributions by using the moments of the logarithmically transformed number of individuals. We find that the moments as a function of area size are well fitted by power laws and we use this pattern to estimate the species abundance distribution for areas larger than those sampled. To reconstruct the species abundance distribution from its moments, we use discrete Tchebichef polynomials. We exemplify the method with data on tree and shrub species from a 50 ha plot of tropical rain forest on Barro Colorado Island, Panama. We test the method within the 50 ha plot, and then we extrapolate the species abundance distribution for areas up to 5 km². Our results project that for areas above 50 ha the species abundance distributions have a bimodal shape with a local maximum occurring for the singleton classes and that this maximum increases with sampled area size.     

Models for the logarithmic species abundance distributions

Three models, developed by Karlin, McGregor and Ewens to describe evolving populations of selectively neutral genotypes, are shown to lead to various versions of Fisher's logarithmic series distribution for species abundance. Statistical inference procedures and measures of diversity which have been developed in one of the two contexts are therefore also applicable in the other context, and the paper reviews and extends these links. Some work of Fisher, Good and Rao is shown to be based on a faulty version of the logarithmic distribution, which, nevertheless, is a good approximation to a consistent version.     

Predicting community rank‐abundance distributions under current and future climates

Understanding influences of environmental change on biodiversity requires consideration of more than just species richness. Here we present a novel framework for understanding possible changes in species' abundance structures within communities under climate change. We demonstrate this using comprehensive survey and environmental data from 1748 woody plant communities across southeast Queensland, Australia, to model rank‐abundance distributions (RADs) under current and future climates. Under current conditions, the models predicted RADs consistent with the region's dominant vegetation types. We demonstrate that under a business as usual climate scenario, total abundance and richness may decline in subtropical rainforest and shrubby heath, and increase in dry sclerophyll forests. Despite these opposing trends, we predicted evenness in the distribution of abundances between species to increase in all vegetation types. By assessing the information rich, multidimensional RAD, we show that climate‐driven changes to community abundance structures will likely vary depending on the current composition and environmental context.     

Assessment of species diversity from species abundance distributions at different localities

We show how the spatial structure of species diversity can be analyzed using the correlation between the log abundances of the species in the communities, assuming that two communities at different localities can be described by a bivariate lognormal species abundance distribution. A useful property of this approach is that the log abundances of the species at two localities can be considered as samples from a bivariate normal distribution defined by only five parameters. The variances and the correlation can be estimated by maximum likelihood methods even if there is no information about the sampling intensity and the number of unobserved species. This method also enables estimation of over-dispersion in the sampling relative to a Poisson distribution that allows sampling adjustment of the estimate of β-diversity. Furthermore, we also obtain a partitioning of species diversity into additive components of α-, β- and γ-diversity. For instance, if the correlation between the log abundances of the species is close to one, the same species will be common and rare in the two communities and the β-diversity will be low. We illustrate this approach by analysing similarities of communities of rare and endangered species of oak-living beetles in south-eastern Norway. The number of recorded species was estimated to be only 48.1% of the total number of species actually present in these communities. The correlations among communities dropped rather quickly with distance with a scaling of order 200 km. This illustrates large spatial heterogeneity in species composition, which should be accounted for in the design of schemes of such devices for assessing species diversity in these habitat-types.     

Sampling species abundance distributions: resolving the veil-line debate

Preston's classic work on the theory of species abundance distributions (SADs) in ecology has been challenged by Dewdney. Dewdney contends that Preston's veil-line concept, relating to the shape of sample SADs, is flawed. Here, I show that Preston's and Dewdney's theories can be reconciled by considering the differing mathematical properties of the sampling process on logarithmic (Preston) versus linear (Dewdney) abundance scales. I also derive several related results and show, importantly, that one cannot reject the log-normal distribution as a plausible SAD based only on sampling arguments, as Dewdney and others have done.     

The effects of intraspecific density dependence on species richness and species abundance distributions

Species richness and patterns of abundance result from the interplay between niche differences, realized as intraspecific density dependence (IDD), and so-called neutral processes that arise when species fitnesses are similar. This paper presents an extension of neutral models that incorporates delays in IDD that could result from resource-mediated competition or through a pathogen pool. These delays reduce standing species richness and qualitatively change the shape of species abundance distributions and render them consistent with the hollow curve shape even in the presence of strong IDD.     

Empirical phylogenies and species abundance distributions are consistent with preequilibrium dynamics of neutral community models with gene flow

Community characteristics reflect past ecological and evolutionary dynamics. Here, we investigate whether it is possible to obtain realistically shaped modeled communities–that is with phylogenetic trees and species abundance distributions shaped similarly to typical empirical bird and mammal communities–from neutral community models. To test the effect of gene flow, we contrasted two spatially explicit individual‐based neutral models: one with protracted speciation, delayed by gene flow, and one with point mutation speciation, unaffected by gene flow. The former produced more realistic communities (shape of phylogenetic tree and species‐abundance distribution), consistent with gene flow being a key process in macro‐evolutionary dynamics. Earlier models struggled to capture the empirically observed branching tempo in phylogenetic trees, as measured by the gamma statistic. We show that the low gamma values typical of empirical trees can be obtained in models with protracted speciation, in preequilibrium communities developing from an initially abundant and widespread species. This was even more so in communities sampled incompletely, particularly if the unknown species are the youngest. Overall, our results demonstrate that the characteristics of empirical communities that we have studied can, to a large extent, be explained through a purely neutral model under preequilibrium conditions.     

Relating species abundance distributions to species-area curves in two Mediterranean-type shrublands

Abstract. Based on both theoretical and empirical studies there is evidence that different species abundance distributions underlie different species‐area relationships. Here I show that Australian and Californian shrubland communities (at the scale from 1 to 1000 m²) exhibit different species‐area relationships and different species abundance patterns. The species‐area relationship in Australian heathlands best fits an exponential model and species abundance (based on both density and cover) follows a narrow log normal distribution. In contrast, the species‐area relationship in Californian shrublands is best fit with the power model and, although species abundance appears to fit a log normal distribution, the distribution is much broader than in Australian heathlands. I hypothesize that the primary driver of these differences is the abundance of small‐stature annual species in California and the lack of annuals in Australian heathlands. Species‐area is best fit by an exponential model in Australian heathlands because the bulk of the species are common and thus the species‐area curves initially rise rapidly between 1 and 100 m². Annuals in Californian shrublands generate very broad species abundance distributions with many uncommon or rare species. The power function is a better model in these communities because richness increases slowly from 1 to 100 m² but more rapidly between 100 and 1000 m² due to the abundance of rare or uncommon species that are more likely to be encountered at coarser spatial scales. The implications of this study are that both the exponential and power function models are legitimate representations of species‐area relationships in different plant communities. Also, structural differences in community organization, arising from different species abundance distributions, may lead to different species‐area curves, and this may be tied to patterns of life form distribution.     

Analytical theory of species abundance distributions of a random community model

We review the history and recent progress of the analytical theories of a random community models. In particular, we focus on a global stability analysis of replicator equations with random interactions and species abundance distributions based on statistical mechanics.     

Analytical evidence for scale-invariance in the shape of species abundance distributions

The distribution of species abundances within an ecological community provides a window into ecological processes and has important applications in conservation biology as an indicator of disturbance. Previous work indicates that species abundance distributions might be independent of the scales at which they are measured which has implications for data interpretation. Here we formulate an analytically tractable model for the species abundance distribution at different scales and discuss the biological relevance of its assumptions. Our model shows that as scale increases, the shape of the species abundance distribution converges to a particular shape given uniquely by the Jaccard index of spatial species turnover and by a parameter for the spatial correlation of abundances. Our model indicates that the shape of the species abundance distribution is taxon specific but does not depend on sample area, provided this area is large. We conclude that the species abundance distribution may indeed serve as an indicator of disturbances affecting species spatial turnover and that the assumption of conservation of energy in ecosystems, which is part of the Maximum Entropy approach, should be re-evaluated.     

Predicting species distributions in poorly-studied landscapes

Conservationists are increasingly relying on distribution models to predict where species are likely to occur, especially in poorly-surveyed but biodiverse areas. Modeling is challenging in these cases because locality data necessary for model formation are often scarce and spatially imprecise. To identify methods best suited to modeling in these conditions, we compared the success of three algorithms (Maxent, Mahalanobis Typicalities and Random Forests) at predicting distributions of eight bird and eight mammal species endemic to the eastern slopes of the central Andes. We selected study species to have a range of locality sample sizes representative of the data available for endemic species of this region and also that vary in their distribution characteristics. We found that for species that are known from moderate numbers (N = 38–94) of localities, the three methods performed similarly for species with restricted distributions but Maxent and Random Forests yielded better results for species with wider distributions. For species with small numbers of sample localities (N = 5–21), Maxent produced the most consistently successful results, followed by Random Forests and then Mahalanobis Typicalities. Because evaluation statistics for models derived from few localities can be suspect due to the poor spatial representation of the evaluation data, we corroborated these results with review by scientists familiar with the species in the field. Overall, Maxent appears to be the most capable method for modeling distributions of Andean bird and mammal species because of the consistency of results in varying conditions, although the other methods have strengths in certain situations. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Moving beyond assumptions to understand abundance distributions across the ranges of species

The assumption that species are most abundant in the center of their range and decline in abundance toward the range edges has a long history in the ecological literature. This assumption has driven basic and applied ecological and evolutionary hypotheses about the causes of species range limits and their responses to climate change. Here, we review recent studies that are taking biogeographical ecology beyond previously held assumptions by observing populations in the field across large parts of the species range. When these studies combine data on abundance, demographics, organismal physiology, genetics and physical factors, they provide a promising approach for teasing out ecological and evolutionary mechanisms of the patterns and processes underlying species ranges.     

Are there species smaller than 1 mm?

The rapid advance in genetic sequencing technologies has provided an unprecedented amount of data on the biodiversity of meiofauna. It was hoped that these data would allow the identification and counting of species, distinguished as tight clusters of similar genomes. Surprisingly, this appears not to be the case. Here, we begin a theoretical discussion of this phenomenon, drawing on an individual-based ecological model to inform our arguments. The determining factor in the emergence (or not) of distinguishable genetic clusters in the model is the product of population size with mutation rate—a measure of the adaptability of the population as a whole. This result suggests that indeed one should not expect to observe clearly distinguishable species groupings in data gathered from ultrasequencing of meiofauna.     

Freshwater species distributions along thermal gradients

The distribution of a species along a thermal gradient is commonly approximated by a unimodal response curve, with a characteristic single optimum near the temperature where a species is most likely to be found, and a decreasing probability of occurrence away from the optimum. We aimed at identifying thermal response curves (TRCs) of European freshwater species and evaluating the potential impact of climate warming across species, taxonomic groups, and latitude. We first applied generalized additive models using catchment‐scale global data on distribution ranges of 577 freshwater species native to Europe and four different temperature variables (the current annual mean air/water temperature and the maximum air/water temperature of the warmest month) to describe species TRCs. We then classified TRCs into one of eight curve types and identified spatial patterns in thermal responses. Finally, we integrated empirical TRCs and the projected geographic distribution of climate warming to evaluate the effect of rising temperatures on species’ distributions. For the different temperature variables, 390–463 of 577 species (67.6%–80.2%) were characterized by a unimodal TRC. The number of species with a unimodal TRC decreased from central toward northern and southern Europe. Warming tolerance (WT = maximum temperature of occurrence—preferred temperature) was higher at higher latitudes. Preferred temperature of many species is already exceeded. Rising temperatures will affect most Mediterranean species. We demonstrated that freshwater species’ occurrence probabilities are most frequently unimodal. The impact of the global climate warming on species distributions is species and latitude dependent. Among the studied taxonomic groups, rising temperatures will be most detrimental to fish. Our findings support the efforts of catchment‐based freshwater management and conservation in the face of global warming.