Models for Eco-Evolutionary Extinction Vortices under Balancing Selection.

AbstractThe smaller a population is, the faster it loses genetic diversity as a result of genetic drift. Loss of genetic diversity can reduce population growth rate, making populations even smaller and more vulnerable to loss of genetic diversity. Ultimately, the population can be driven to extinction by this "eco-evolutionary extinction vortex." While there are already quantitative models for extinction vortices resulting from inbreeding depression and mutation accumulation, to date extinction vortices resulting from loss of genetic diversity at loci under various forms of balancing selection have been mainly described verbally. To understand better when such extinction vortices arise and to develop methods for detecting them, we propose quantitative eco-evolutionary models, both stochastic individual-based simulations and deterministic approximations, linking loss of genetic diversity and population decline. Using mathematical analysis and simulations, we identify parameter combinations that exhibit strong interactions between population size and genetic diversity and match our definition of an eco-evolutionary vortex (i.e., per capita population decline rates and per-locus fixation rates increase with decreasing population size and number of polymorphic loci). We further highlight cues that may be exhibited by such populations but find that classical early-warning signals are of limited use in detecting populations undergoing an eco-evolutionary extinction vortex.