The coevolutionary dynamics of antagonistic interactions mediated by quantitative traits with evolving variances

Quantitative traits frequently mediate coevolutionary interactions between predator and prey or parasite and host. Previous efforts to understand and predict the coevolutionary dynamics of these interactions have generally assumed that standing genetic variation is fixed or absent altogether. We develop a genetically explicit model of coevolution that bridges the gap between these approaches by allowing genetic variation itself to evolve. Analysis of this model shows that the evolution of genetic variance has important consequences for the dynamics and outcome of coevolution. Of particular importance is our demonstration that coevolutionary cycles can emerge in the absence of stabilizing selection, an outcome not possible in previous models of coevolution mediated by quantitative traits. Whether coevolutionary cycles evolve depends upon the strength of selection, the number of loci, and the rate of mutation in each of the interacting species. Our results also generate novel predictions for the expected sign and magnitude of linkage disequilibria in each species.