Evolution can alter the stability and dynamics of ecological communities; for example, prey evolution can drive cyclic dynamics in predator-prey systems that are not possible in the absence of evolution. However, it is unclear how the magnitude of additive genetic variation in the evolving species mediates those effects. In this study, I explore how the magnitude of prey additive genetic variation determines what effects prey evolution has on the dynamics and stability of predator-prey systems. I use linear stability analysis to decompose the stability of a general eco-evolutionary predator-prey model into components representing the stabilities of the ecological and evolutionary subsystems as well as the interactions between those subsystems. My results show that with low genetic variation, the cyclic dynamics and stability of the system are determined by the ecological subsystem. With increased genetic variation, disruptive selection always destabilizes stable communities, stabilizing selection can stabilize or destabilize communities, and prey evolution can alter predator-prey phase lags. Stability changes occur approximately when the magnitude of genetic variation balances the (in)stabilities of the ecological and evolutionary subsystems. I discuss the connections between my stability results and prior results from the theory of adaptive dynamics.

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.

We develop a method to identify how ecological, evolutionary, and eco-evolutionary feedbacks influence system stability. We apply our method to nine empirically parametrized eco-evolutionary models of exploiter–victim systems from the literature and identify which particular feedbacks cause some systems to converge to a steady state or to exhibit sustained oscillations. We find that ecological feedbacks involving the interactions between all species and evolutionary and eco-evolutionary feedbacks involving only the interactions between exploiter species (predators or pathogens) are typically stabilizing. In contrast, evolutionary and eco-evolutionary feedbacks involving the interactions between victim species (prey or hosts) are destabilizing more often than not. We also find that while eco-evolutionary feedbacks rarely altered system stability from what would be predicted from just ecological and evolutionary feedbacks, eco-evolutionary feedbacks have the potential to alter system stability at faster or slower speeds of evolution. As the number of empirical studies demonstrating eco-evolutionary feedbacks increases, we can continue to apply these methods to determine whether the patterns we observe are common in other empirical communities.