Maintenance of polygenic sex determination in a fluctuating environment: an individual-based model.

R. A. Fisher predicted that individuals should invest equally in offspring of both sexes, and that the proportion of males and females produced (the primary sex ratio) should evolve towards 1:1 when unconstrained. For many species, sex determination is dependent on sex chromosomes, creating a strong tendency for balanced sex ratios, but in other cases, multiple autosomal genes interact to determine sex. In such cases, the maintenance of multiple sex-determining alleles at multiple loci and the consequent among-family variability in sex ratios presents a puzzle, as theory predicts that such systems should be unstable. Theory also predicts that environmental influences on sex can complicate outcomes of genetic sex determination, and that population structure may play a role. Tigriopus californicus, a copepod that lives in splash-pool metapopulations and exhibits polygenic and environment-dependent sex determination, presents a test case for relevant theory. We use this species as a model for parameterizing an individual-based simulation to investigate conditions that could maintain polygenic sex determination. We find that metapopulation structure can delay the degradation of polygenic sex determination and that periods of alternating frequency-dependent selection, imposed by seasonal fluctuations in environmental conditions, can maintain polygenic sex determination indefinitely.