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

Abstract

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.

The role of stressors in altering eco‐evolutionary dynamics

“…Experimental and theoretical evidence has shown that the amount of genetic variation can affect the link of rapid evolution to population dynamics (Becks et al, 2010;Cortez, 2017;Steiner & Masse, 2013), with increasing additive genetic variation leading to a higher probability of altering the population dynamics. Thus, factors or processes that affect standing genetic variation can have a substantial impact on the evolution-to-ecology link.…”

How (co)evolution alters predator responses to increased mortality: extinction thresholds and hydra effects

“…By holding the prey trait or predator trait fixed, the coevolutionary model reduces to a model with a single evolving species. Throughout, we only focus on systems at stable equilibrium and do not consider systems exhibiting eco-evolutionary cycles; the cyclic dynamics of the model when one or both species are evolving have been studied previously by the authors (Cortez and Ellner 2010, Cortez 2015, 2018 We also assume increased predator offense comes at the cost of increased mortality (e.g., resistance to newt toxicity in garter snakes comes at the cost of reduced survival due to reduced speed; Brodie and Brodie 1999).…”

“…Individual prey with higher defense are assumed to be better defended against all predator phenotypes and individual predators with higher offense are assumed to have higher capture rates for all prey phenotypes; this corresponds to a unidirectional axis of vulnerability (Abrams 2000). Throughout, we only focus on systems at stable equilibrium and do not consider systems exhibiting eco-evolutionary cycles; the cyclic dynamics of the model when one or both species are evolving have been studied previously by the authors (Cortez and Ellner 2010, Cortez 2015, 2018…”

Destabilizing evolutionary and eco-evolutionary feedbacks drive empirical eco-evolutionary cycles

“…In general, stability of a whole system is influenced by the effects species’ densities have on the dynamics of population densities (ecological feedbacks), the effects species’ traits have on the dynamics of evolving traits (evolutionary feedbacks), and the effects population densities and evolving traits have on each other’s dynamics (eco-evolutionary feedbacks). Previous theoretical work (7; 15; 16; 17) has explored when these feedbacks have stabilizing versus destabilizing effects, and shown that the strengths of those effects increase or decrease with changes in the relative rates of ecological and evolutionary change. Specifically, stability of the whole system in the slow evolution limit is determined by ecological and eco-evolutionary feedbacks whereas stability of the whole system in the fast evolution limit is determined by evolutionary and eco-evolutionary feedbacks.…”

“…Building on prior theoretical work (7; 15; 16), we develop a method using feedbacks defined in terms of the stability of a subsystem, i.e., the interactions and dynamics of a set of variables when all other variables are held fixed (e.g., the ecological subsystem defines the dynamics of all population densities when all population-level traits are held fixed). Our method identifies how the stabilities of complementary pairs of subsystems (e.g., ecological vs. evolutionary subsystems) at the equilibrium of the whole system and the interactions between them (e.g., the effects the evolutionary subsystem has on the ecological subsystem) influence the stability of the whole system.…”