The simplest theories often have much merit and many limitations, and, in this vein, the
value of neutral theory (NT) of biodiversity has been the subject of much debate over the …

This review provides a pedagogic and self-contained introduction to master equations and
to their representation by path integrals. Since the 1930s, master equations have served as …

In order to better understand the interplay of partnership and competition in population
dynamics, we study a family of generalized May-Leonard models with N species. These …

The relationship between the Moran model and stochastic Lotka-Volterra competition
(SLVC) model is explored via time scale separation arguments. For neutral systems the two …

Ecosystems display a complex spatial organization. Ecologists have long tried to
characterize them by looking at how different measures of biodiversity change across spatial …

Evolutionary game dynamics with two 2-strategy games in a finite population has been
investigated in this study. Traditionally, frequency-dependent evolutionary dynamics are …

In order to model real ecological systems one has to consider many species that interact in
complex ways. However, most of the recent theoretical studies have been restricted to few …

We study a stochastic community model able to interpolate from a neutral regime to a niche
partitioned regime upon varying a single parameter tuning the intensity of niche stabilization …

When four species compete stochastically in a cyclic way, the formation of two teams of
mutually neutral partners is observed. In this paper we study through numerical simulations …

The relationship between the M-species stochastic Lotka-Volterra competition (SLVC) model
and the M-allele Moran model of population genetics is explored via timescale separation …