Genetic variation determines which feedbacks drive and alter predator-prey eco-evolutionary cycles

Evolution can alter the ecological dynamics of communities, but the effects depend on the magnitudes of standing genetic variation in the evolving species. Using an eco-coevolutionary predator-prey model, I identify how the magnitudes of prey and predator standing genetic variation determine when ecological, evolutionary, and eco-evolutionary feedbacks influence system stability and the phase lags in predator-prey cycles. Here, feedbacks are defined by subsystems, i.e., the dynamics of a subset of the components of the whole system when the other components are held fixed; ecological (evolutionary) feedbacks involve the direct and indirect effects between population densities (species traits) and eco-evolutionary feedbacks involve the direct and indirect effects between population densities and traits. When genetic variation is low in both species, ecological feedbacks and eco-evolutionary feedbacks involving either the predator or the prey trait have the strongest effects on system stability, when genetic variation is high in one species, evolutionary and eco-evolutionary feedbacks involving that species' trait have the strongest effects, and, when genetic variation is high in both species, evolutionary feedbacks involving one or both traits and eco-coevolutionary feedbacks involving both traits have the strongest effects. I present the biological conditions under which each feedback can destabilize the whole system and cause predator-prey cycles. Predator-prey cycles can also arise when all feedbacks are stabilizing. This counterintuitive outcome occurs when feedbacks involving many variables are more stabilizing than feedbacks involving fewer variables or vice versa. I also identify how the indirect effects of prey and predator density on the predator dynamics (mediated by evolutionary responses in one or both species) alter the phase lags in predator-prey cycles. I present conditions under which the trait-mediated indirect effects introduce delays that cause the lag between prey and predator peaks to increase. This work explains and unifies empirical and theoretical studies on how predator-prey coevolution alters the dynamics of predator-prey systems and how those effects depend on the magnitudes of prey and predator standing genetic variation.