Models, Concepts, and Data Analyses

It is well understood that the spatial structure inherent in most if not all populations can have important implications to the evolutionary dynamics of a wide range of traits. One of the best developed areas of evolutionary theory focusses on the evolution of parasites and spatially explicit models have illustrated the importance of structure within the host to the selection of the infectious organisms. Here we review this theory and show how approximation techniques may be useful in addressing the problem. We show that transmission can be constrained without trade-offs and there is the possibility of multiple stable states due to interactions with self-generated population structures. Models intermediate between local and the mean-field have demonstrated that these effects are not only the result of extreme local interactions and may therefore be applicable not only to plant populations with rigidly local interactions. Advances in this field have mostly been driven by the use of computer simulation, but moment closure approximations offer an opportunity to develop our analytical understanding of these processes. However, advances in these approximation techniques are required for models with extreme local interactions.