The eco-evolutionary dynamics of a predator-prey system across an r/K continuum

Abstract

The effects of a single trait on more than one ecological function is called ecological pleiotropy. Traits that exhibit ecological pleiotropy are relevant to eco-evolutionary dynamics because the structure of interaction between the trait and its ecological functions alters how eco-evolutionary feedback loops emerge. Density-dependent selection (DDS) assumes that a single trait affects both density-independent and density-dependent population growth through ecological pleiotropy, and is one of the simplest routes for feedback loops. The r/K theory proposes a mechanism by which DDS occurs, but its predictions were poorly explored in an eco-evolutionary context. Some assumptions of the r/K theory seems to be relevant for the eco-evolution of predator-prey interactions. However, the relationship between these theories were poorly explored. Here, we investigate how does the r/K theory relates to the eco-evolution of predator-prey systems. We seek to answer two questions: (1) What are the system’s parameters that affect the predominance of r- and K-selection? (2) Does system’s qualitative behaviour depends on whether the predominant selection on prey population is an r- or a K-selection? To answer these questions, we built a model of differential equations describing the eco-evolutionary dynamics of a predator-prey system. We assume that prey vulnerability to predation is an adaptive trait that affects preys density-dependent growth rate through ecological pleiotropy. Then, we partitioned the selection gradient in its r- and K-selection components and evaluate how their magnitude relates to systems behaviour. We found that stable predator-prey cycles only occurs when K-selection is predominant. When r-selection is predominant, cycles lead to a runaway dynamics. Furthermore, the way predators parameters affect prey position in the r/K continuum depends on how they affect predation risk. While increasing predation risk increases K-selection, decreasing it increases r-selection. We discuss the relevance of the structure of ecological pleiotropy to our results and the perspectives that unifies the r/K theory and eco-evolutionary dynamics.