Positive feedback between demographic and selective fluctuations can greatly amplify the random fluctuation of population size

Abstract

Population sizes fluctuate over time probably due to random variability in the external environment. However, the severity of such fluctuations should depend on the characteristics of a species shaped in its evolutionary history. Previous studies have suggested that species are likely to evolve to minimize demographic fluctuations because an allele causing a smaller variance in offspring number is advantageous. However, this study finds that evolution in the opposite direction, favoring a mutation causing larger fitness fluctuation, occurs in a simple eco-evolutionary model under a randomly changing environment. This requires that (1) the mutant allele is under fluctuating selection within a subset, the field, of the population but neutral in another subset, the refuge, and (2) the field-to-refuge ratio of the carrying capacity is positively correlated to the fitness of the mutant allele. A general condition for the fixation of such a mutation was derived to depend on the relative strengths of demographic and fitness fluctuations and the mutational effect on the carrying capacity. Multi-locus simulations revealed that positive feedback between demography and selection accelerates the sequential fixations of fluctuation-amplifying mutations, leading to a drastic size fluctuation. This study therefore offers an unconventional explanation for large demographic fluctuations.