Stable two-allele polymorphisms maintained by fluctuating fitnesses and seed banks: Protecting the blues in Linanthus parryae

Motivated by data demonstrating fluctuating relative and absolute fitnesses for white- versus blue-flowered morphs of the desert annual Linanthus parr yae, we present conditions under which temporally fluctuating selection and fluctuating contributions to a persistent seed bank will maintain a stable single-locus polymorphism. In L. parryae, blue flower color is determined by a single dominant allele. To disentangle the underlying diversity-mainta ining mechanism from the mathematical complications associated with departu res from Hardy-Weinberg genotype frequencies and dominance, we successively analyze a haploid model, a diploid model with three distinguishable genoty pes, and a diploid model with complete dominance. For each model, we presen t conditions for the maintenance of a stable polymorphism, then use a diffu sion approximation to describe the long-term fluctuations associated with t hese polymorphisms. Our protected polymorphism analyses show that a genotyp e whose arithmetic and geometric mean relative fitnesses are both less than one can persist if its relative fitness exceeds one in years that produce the most offspring. This condition is met by data from a population of L. p arryae whose white morph has higher fitness (seed set) only in years of rel atively heavy rain fall. The data suggest that the observed polymorphism ma y be explained by fluctuating selection. However, the yearly variation in f lower color frequencies cannot be fully explained by our simple models, whi ch ignore age structure and possible selection in the seed bank, We address two additional questions-one mathematical, the other biological-concerning the applicability of diffusion approximations to intense selection and the applicability of long-term predictions to datasets spanning decades for po pulations with long-lived seed banks.