Dynamics of neutral biodiversity

Hubbell's neutral model has become a major paradigm in ecology. Whereas the steady-state structure is well understood, results about the dynamical aspects of the model are scarce. Here we derive dynamical equations for the Simpson diversity index. Both mean and variance of the diversity are proven to satisfy stable linear system dynamics. We show that in the stationary limit we indeed recover previous results, and we supplement this with numerical simulations to validate the dynamical part of our analytical computations. These findings are especially relevant for experiments in microbial ecology, where the Simpson diversity index can be accurately measured as a function of time.     

A new sampling formula for neutral biodiversity

The neutral model of biodiversity, proposed by Hubbell (The Unified Neutral Theory of Biodiversity and Biogeography, Princeton University Press, Princeton, NJ, 2001) to explain the diversity of functionally equivalent species, has been subject of hot debate in community ecology. Whereas Hubbell studied the model mostly by simulations, recently analytical treatments have yielded expressions of the expected number of species of a particular abundance in a local community with dispersal limitation. Moreover, a formula has been offered for the joint likelihood of observing a given species‐abundance dataset in a local community with dispersal limitation, but this formula is too complicated to allow practical applications. Here, I present a much simplified expression that can be regarded as an enhanced version of the famous Ewens sampling formula. It can be used in maximum likelihood methods for quick estimation of the model parameters, using all information in the data, and for model comparison. I also show how to rapidly generate examples of species‐abundance distributions for a given set of model parameters and how to calculate Simpson's diversity index.     

The zero-sum assumption in neutral biodiversity theory

The neutral theory of biodiversity as put forward by Hubbell in his 2001 monograph has received much criticism for its unrealistic simplifying assumptions. These are the assumptions of functional equivalence among different species (neutrality), the assumption of point mutation speciation, and the assumption that resources are continuously saturated, such that constant resource availability implies constant community size (zero-sum assumption). Here we focus on the zero-sum assumption. We present a general theory for calculating the probability of observing a particular species-abundance distribution (sampling formula) and show that zero-sum and non-zero-sum formulations of neutral theory have exactly the same sampling formula when the community is in equilibrium. Moreover, for the non-zero-sum community the sampling formula has this same form, even out of equilibrium. Therefore, the term "zero-sum multinomial (ZSM)" to describe species abundance patterns, as coined by Hubbell [2001. The Unified Neutral Theory of Biodiversity and Biogeography, Princeton University Press, Princeton, NJ], is not really appropriate, as it also applies to non-zero-sum communities. Instead we propose the term "dispersal-limited multinomial (DLM)", thus making explicit one of the most important contributions of neutral community theory, the emphasis on dispersal limitation as a dominant factor in determining species abundances.     

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.     

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.     

Using a goal programming approach to design and evaluate protected areas for the conservation of multiple dimensions of biodiversity

The decline and loss of biodiversity provoked by human activities have caused ecologists and conservationists to center their attention on the design of conservation priority areas (PAs), focusing mainly on species conservation in terms of richness, rarity and/or vulnerability. However, biodiversity has multiple dimensions, evolutionary processes have recently been labeled the ‘missing component’ of conservation strategies, and increasingly more authors are suggesting that the ecological, evolutionary and historical aspects of biodiversity are key components of conservation planning. In this study we develop a prioritization system to design conservation PAs using the wild terrestrial mammals of the Iberian Peninsula as an example. We aim to contribute to the design of more suitable PAs by integrating ecological components of biodiversity (species richness, vulnerability and rarity), evolutionary aspects (accumulated genetic diversification) and historical information relevant to the study area. After selecting a set of biodiversity indicators, we applied a multi-objective technique (extended goal programming) to construct a combined index, where values in the top 90th percentile were then used to select the PAs. According to our most efficient and satisfactory results, some areas highlighted for their conservation are currently categorized as PAs, however, we found that it would be necessary to reconsider their extent, especially in northern Spain, where the historical aspects of biodiversity (the missing component) are more widely present. The need to determine PAs is unquestionable. However, it should also be a priority to move towards a model of sustainable and fair development.     

A methodological approach to identify cheap and accurate indicators for biodiversity assessment: application to grazing management and two grassland bird species

In response to environmental threats, numerous indicators have been developed to assess the impact of livestock farming systems on the environment. Some of them, notably those based on management practices have been reported to have low accuracy. This paper reports the results of a study aimed at assessing whether accuracy can be increased at a reasonable cost by mixing individual indicators into models. We focused on proxy indicators representing an alternative to the direct impact measurement on two grassland bird species, the lapwing Vanellus vanellus and the redshank Tringa totanus. Models were developed using stepwise selection procedures or Bayesian model averaging (BMA). Sensitivity, specificity, and probability of correctly ranking fields (area under the curve, AUC) were estimated for each individual indicator or model from observational data measured on 252 grazed plots during 2 years. The cost of implementation of each model was computed as a function of the number and types of input variables. Among all management indicators, 50% had an AUC lower than or equal to 0.50 and thus were not better than a random decision. Independently of the statistical procedure, models combining management indicators were always more accurate than individual indicators for lapwings only. In redshanks, models based either on BMA or some selection procedures were non-informative. Higher accuracy could be reached, for both species, with model mixing management and habitat indicators. However, this increase in accuracy was also associated with an increase in model cost. Models derived by BMA were more expensive and slightly less accurate than those derived with selection procedures. Analysing trade-offs between accuracy and cost of indicators opens promising application perspectives as time consuming and expensive indicators are likely to be of low practical utility.     

A Bayesian approach to estimate the age-specific prevalence of Schistosoma mansoni and implications for schistosomiasis control

Models that accurately estimate the age-specific infection prevalence of Schistosoma mansoni can be useful for schistosomiasis control programmes, particularly with regard to whether mass drug administration or selected treatment should be employed. We developed a Bayesian formulation of an immigration-death model that has been previously proposed, which used maximum likelihood inference for estimating the age-specific S. mansoni prevalence in a dataset from Egypt. For comparative purposes, we first applied the Bayesian formulation of the immigration-death model to the dataset from Egypt. We further analysed data obtained from a cross-sectional parasitological survey that determined the infection prevalence of S. mansoni among 447 individuals in a village in C?te d'Ivoire. Three consecutive stool samples were collected from each participant and analysed by the Kato-Katz technique. In the C?te d'Ivoire study, the observed S. mansoni infection prevalence was 41.6% and varied with age. The immigration-death model was able to correctly predict 50% of the observed age group-specific point prevalences. The model presented here can be utilized to estimate S. mansoni community infection prevalences, which in turn helps in the strategic planning of schistosomiasis control.