Eco-evolutionary feedbacks between prey densities and linkage disequilibrium in the predator maintain diversity

Diversity occurs at multiple scales. Within a single population, there is diversity in genotypes and phenotypes. At a larger scale, within ecological communities, there is diversity in species. A number of studies have investigated how diversity at these two scales influence each other through what has been termed eco-evolutionary feedbacks. Here we study a three-species ecological module called apparent competition, in which the predator is evolving in a trait that determines its interaction with two prey species. Unlike previous studies on apparent competition, which employed evolutionary frameworks with very simple genetics, we study an eco-evolutionary model in which the predator's trait is determined by two recombining diallelic loci, so that its mean and variance can evolve, as well as associations (linkage disequilibrium) between the loci. We ask how eco-evolutionary feedbacks with these two loci affect the coexistence of the prey species and the maintenance of polymorphisms within the predator species. We uncover a novel eco-evolutionary feedback between the prey densities and the linkage disequilibrium between the predator's loci. Through a stability analysis, we demonstrate how these feedbacks affect polymorphisms at both loci and, among others, may generate stable cycling.