Modeling minimum viable population size with multiple genetic problems of small populations

An important goal for conservation is to define minimum viable population (MVP) sizes for long-term persistence. Although many MVP size estimates focus on ecological processes, with increasing evidence for the role of genetic problems in population extinction, conservation practitioners have also increasingly started to incorporate inbreeding depression (ID). However, small populations also face other genetic problems such as mutation accumulation (MA) and loss of genetic diversity through genetic drift that are usually factored into population viability assessments only via verbal arguments. Comprehensive quantitative theory on interacting genetic problems is missing. Here we develop eco-evolutionary quantitative models that track both population size and levels of genetic diversity. Our models assume a biallelic multilocus genome whose loci can be under either a single or interacting genetic forces. In addition to mutation-selection-drift balance (for loci facing ID and MA), we include three forms of balancing selection (for loci where variation is lost through genetic drift). We define MVP size as the lowest population size that avoids an eco-evolutionary extinction vortex after a time sufficient for an equilibrium allele frequency distribution to establish. Our results show that MVP size decreases rapidly with increasing mutation rates for populations whose genomes are only under balancing selection, while for genomes under mutation-selection-drift balance, the MVP size increases rapidly. MVP sizes also increase rapidly with increasing number of loci under the same or different selection mechanisms until a point is reached at which even arbitrarily large populations cannot survive anymore. In the case of fixed number of loci under selection, interaction of genetic problems did not necessarily increase MVP sizes. To further enhance our understanding about interaction of genetic problems, there is need for more empirical studies to reveal how different genetic processes interact in the genome.