Michael Kopp and Sergey Gavrilets 2004 "COEVOLUTION IN QUANTITATIVE TRAITS: AN EXPLICIT GENETIC MODEL"

Abstract

We develop and analyze an explicit multilocus genetic model of coevolution. We assume that interactions between two species (mutualists, competitors, or victim and exploiter) are mediated by a pair of additive quantitative traits which are also subject to direct stabilizing selection towards intermediate optima. Using a weak selection approximation, we derive analytical results for a symmetric case with equal allelic effects and no mutation, and we complement these results by numerical studies of more general cases. We show that mutualistic and competitive interactions always result in coevolution towards a stable equilibrium with no more than one polymorphic locus per species. Victim-exploiter interactions can lead to a number of different dynamic regimes including evolution towards stable equilibria, cycles, and chaos. At equilibrium, the victim is often characterized by a very large genetic variance whereas the exploiter is polymorphic in no more than one locus. Compared to related one-locus or quantitative genetic models, the multilocus model exhibits two major new properties: First, the equilibrium structure is considerably more complex. We derive detailed conditions for the existence and stability of various classes of equilibria and demonstrate the possibility of multiple simultaneously stable states. Second, the genetic variances change dynamically, which in turn significantly affects the dynamics of the mean trait values. In particular, the dynamics tend to be destabilized by an increase in the number of loci. Thus, dynamic details depend on genetic details.