Discreteness induced extinction

Abstract

Two simple models based on ecological problems are discussed from the point of view of non-equilibrium statistical mechanics. It is shown how discrepant may be the results of the models that include spatial distribution with discrete interactions when compared with the continuous analogous models. In the continuous case we have, under certain circumstances, the population explosion. When we take into account the finiteness of the population, we get the opposite result, extinction. We will analyze how these results depend on the dimension d of the space and describe the phenomenon of the “Discreteness Inducing Extinction” (DIE). The results are interpreted in the context of the “paradox of sex”, an old problem of evolutionary biology.