Protecting haploid polymorphisms in temporally variable environments

Analysis of a continuous-time model shows that a protected polymorphism can arise in a haploid population subject to temporal fluctuations in selection. The requirements are that population size is regulated in a density-dependent manner and that an allele's arithmetic mean relative growth rate is greater than one when rare and that its harmonic mean relative growth rate is less than one when common. There is no requirement that relative growth rate be frequency dependent. Comparisons with discrete-time models show that the standard formalism used by population genetics ignores forced changes in generation time as rare advantageous alleles sweep into a population. In temporally variable environments, frequency-dependent changes in generation times tend to counteract these invasions. Such changes can prevent fixation and protect polymorphisms.