Maintenance and evolution of phenotypic variance in a prey defence trait examined with a dynamic predator-prey model for clonal populations.

Predator-prey systems often feature periodic population cycles. In an empirical system with a heritable prey defence trait, ecological oscillations were previously shown to cause evolution of prey defence on the timescale of the population cycles. In this paper, we develop a phenotypically structured model comprising partial differential equations to investigate the evolutionary dynamics of prey defence during population cycles for a clonally reproducing prey species. We reveal that ecological population cycles not only induce evolutionary oscillations of the mean prey defence trait but also of trait variance. We show that both eco-evolutionary oscillations and stable dynamics lead to high trait variance for a wide range of parameters. For stable dynamics, we show that this is caused by a mutation-selection balance whose impact is larger than in the absence of predators. For oscillatory dynamics, we show that high trait variance is caused by perpetual changes in the direction of selection. Finally, we highlight that switches between stable and oscillatory dynamics depend on the functional form of the cost and efficiency functions of prey defence.