Evolutionary trade-offs at two time-scales: competition versus persistence.

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.