A search for maximum species abundances in ecological communities under conditional diversity optimization

Replicator equations and the principle of minimal production of information

Many complex systems in mathematical biology and other areas can be described by the replicator equation. We show that solutions of a wide class of replicator equations minimize the KL-divergence of the initial and current distributions under time-dependent constraints, which in their turn, can be computed explicitly at every instant due to the system dynamics. Therefore, the Kullback principle of minimum discrimination information, as well as the maximum entropy principle, for systems governed by the replicator equations can be derived from the system dynamics rather than postulated. Applications to the Malthusian inhomogeneous models, global demography, and the Eigen quasispecies equation are given.

The maximum entropy formalism and the idiosyncratic theory of biodiversity

Why does the neutral theory, which is based on unrealistic assumptions, predict diversity patterns so accurately? Answering questions like this requires a radical change in the way we tackle them. The large number of degrees of freedom of ecosystems pose a fundamental obstacle to mechanistic modelling. However, there are tools of statistical physics, such as the maximum entropy formalism (MaxEnt), that allow transcending particular models to simultaneously work with immense families of models with different rules and parameters, sharing only well-established features. We applied MaxEnt allowing species to be ecologically idiosyncratic, instead of constraining them to be equivalent as the neutral theory does. The answer we found is that neutral models are just a subset of the majority of plausible models that lead to the same patterns. Small variations in these patterns naturally lead to the main classical species abundance distributions, which are thus unified in a single framework.

From plant traits to plant communities: a statistical mechanistic approach to biodiversity

We developed a quantitative method, analogous to those used in statistical mechanics, to predict how biodiversity will vary across environments, which plant species from a species pool will be found in which relative abundances in a given environment, and which plant traits determine community assembly. This provides a scaling from plant traits to ecological communities while bypassing the complications of population dynamics. Our method treats community development as a sorting process involving species that are ecologically equivalent except with respect to particular functional traits, which leads to a constrained random assembly of species; the relative abundance of each species adheres to a general exponential distribution as a function of its traits. Using data for eight functional traits of 30 herbaceous species and community-aggregated values of these traits in 12 sites along a 42-year chronosequence of secondary succession, we predicted 94% of the variance in the relative abundances.