How Gaussian competition leads to lumpy or uniform species distributions

A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is 'lumped' (or 'clumped'), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either uniform or lumped species distributions. Here we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity. In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model. We analyze the origin of this sensitivity and discuss it in the context of recent applications of the model.Comment: 11 pages, 3 figures, revised versio

The role of sex separation in neutral speciation

Neutral speciation mechanisms based on isolation by distance and sexual selection, termed topopatric, have recently been shown to describe the observed patterns of abundance distributions and species-area relationships. Previous works have considered this type of process only in the context of hermaphrodic populations. In this work we extend a hermaphroditic model of topopatric speciation to populations where individuals are explicitly separated into males and females. We show that for a particular carrying capacity speciation occurs under similar conditions, but the number of species generated decreases as compared to the hermaphroditic case. Evolution results in fewer species having more abundant populations.Comment: 18 pages + 8 figure

Conditions for neutral speciation via isolation by distance

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)The branching of new species from an ancestral population requires the evolution of reproductive isolation between groups of individuals. Geographic separation of sub-populations by natural barriers, if sustained for sufficiently long times, may lead to the accumulation of independent genetic changes in each group and to mating incompatibilities (Mayr, 2001; Fitzpatrick et al., 2009). A similar phenomenon may occur in the absence of barriers via isolation by distance if the population is distributed over large areas (de Aguiar et al., 2009; Etienne and Haegeman, 2011; Gavrilets et al., 2000). The first demonstration of this process was based on computer simulations employing agent-based models. Recently, analytical results were derived combining network theory, to model the spatial structure of the population, and an ansatz that accounts for the effect of forbidding mating between individuals that are too different genetically (de Aguiar and Bar-Yam, 2011). The main result obtained with this approach is an expression that indicates when speciation is possible as a function of the parameters describing the population. The aim of this work is to test this analytical result by comparing it with numerical simulations for a hermaphroditic population (de Aguiar et al., 2009) and for a population whose individuals are explicitly separated into males and females (Baptestini et al., 2013). We show that the analytical formula is indeed a very good overall description of the simulations and that the exponents describing dependence of the critical threshold of speciation with the parameters are in good agreement with the simulations. (C) 2013 Elsevier Ltd. All rights reserved.3355156Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP