Analytic solution of Hubbell's model of local community dynamics

Recent theoretical approaches to community structure and dynamics reveal that many large-scale features of community structure (such as species-rank distributions and species-area relations) can be explained by a so-called neutral model. Using this approach, species are taken to be equivalent and trophic relations are not taken into account explicitly. Here we provide a general analytic solution to the local community model of Hubbell's neutral theory of biodiversity by recasting it as an urn model i.e.a Markovian description of states and their transitions. Both stationary and time-dependent distributions are analysed. The stationary distribution -- also called the zero-sum multinomial -- is given in closed form. An approximate form for the time-dependence is obtained by using an expansion of the master equation. The temporal evolution of the approximate distribution is shown to be a good representation for the true temporal evolution for a large range of parameter values.Comment: 10 pages, 2 figure

Body size and the relative abundance of species

Existing models of species abundance distributions (SADs) can be divided into those that are based on concepts of common limited niche space (niche apportionment models, neutral models) and those that invoke standard statistical distributions (e. g. log-series, lognormal). While the first type of models assumes that competitive interactions lead to observed SADs, the models of the second type appear to be mainly statistical descriptors of SADs without deeper biological meaning. None of the models explicitly includes species body size as a factor influencing species abundances. Further, with the exception of recent neutral models they are not embedded into basic ecological and evolutionary models to explain local diversity and ecosystem functioning. Here I present a new random walk model of species abundances that is based on two well known ecological distributions, the abundance - body weight distribution and the species - body weight distribution to define long-term upper abundance boundaries (carrying capacities). I show that a simple random walk of species abundances around the carrying capacities not only generates observed SADs but is also able to explain other patterns of community structure like core - satellite distributions, temporal patterns of species turnover, variance - mean ratios, and biomass distributions