Coevolutionary chase in exploiter-victim systems with polygenic characters

I study the dynamics of a simple quantitative genetic model describing coevolution of two antagonistic species of the victimexploiter type [ In this model \ individuals are di}erent with respect to an additive polygenic character that is under direct stabilizing selection and which also determines the strength of within and between species interactions [ The model assumes that between species interactions are most intense when the victim|s and exploiter|s phenotypes match [ I show that a cyclic coevolutionary chase is possible under a broad range of conditions [ In most cases \ the system cycles if the {{victim| | has a stronger incentive to win and:or a larger genetic variance \ and is under stronger stabilizing selection than the {{exploiter|| [ The results presented here provide counter!examples to recent studies that "0# question the applicability of {{Red Queen| | and {{arms race| | metaphors for continuously varying traits^ "1 # argue for the existence of crucial di}erences between major and minor loci dynamics ^ and "2# attribute a stabilizing role to coevolution[ 7 0886 Academic Press Limited