Evolutionary trade–offs at two time–scales: competition versus persistence

Abstract

The evolution of many natural systems is complicated due to dynamics at a mixture of time–scales. This is especially true when there is a trade–off between large reproductive rates and long–term persistence; such behaviour is frequently observed in disease models. In this paper, a simple partial differential equation model is formulated which describes the evolutionary dynamics of two disease strains in a metapopulation: one strain is a better short–term competitor; the other has greater persistence. By considering the behaviour of means and higher–order moments, analytical expressions for the evolutionary behaviour are produced in the case when the two strains are phenotypically close.