Models for Eco-evolutionary Extinction Vortices and their Detection

Abstract

The smaller a population is, the faster it looses genetic variation due to genetic drift. Loss of genetic variation can reduce population growth rate, making populations even smaller and more vulnerable to loss of genetic variation, and so on. Ultimately, the population can be driven to extinction by this "eco-evolutionary extinction vortex". So far, extinction vortices due to loss of genetic variation have been mainly described verbally. However, quantitative models are needed to better understand when such vortices arise and to develop methods for detecting them. Here we propose quantitative eco-evolutionary models, both individual-based simulations and analytic approximations, that link loss of genetic variation and population decline. Our models assume stochastic population dynamics and multi-locus genetics with different forms of balancing selection. Using mathematical analysis and simulations, we identify parameter combinations that exhibit strong interactions between population size and genetic variation as populations decline to extinction and match our definition of an eco-evolutionary vortex, i.e. the per-capita population decline rates and per-locus fixation rates increase with decreasing population size and number of polymorphic loci. We further highlight cues and early warning signals that may be useful in identifying populations undergoing an eco-evolutionary extinction vortex.