Evolutionary implications for the determination of gametocyte sex ratios under fecundity variation for the malaria parasite

We investigate sex ratio determination strategies for the Malaria parasite based on putative changes in its male fecundity over the lifetime of an infection, and how such strategies might have evolved. We model fitness using the incomplete fertilization limit developed in Teboh-Ewungkem and Yuster (2010). We divide the infection lifetime of a strain into two periods, assume each human is infected by two different strains, and assume that there are two different strategies present among the many strains in the general malaria parasite population. A unique parameter dependent ESS exists for all parameter values in both of our main models, with many such strategies unbeatable. These strategies produce both male and female biased population sex ratios with female bias predominating over most of the parameter space. The first model (SKM) suggests that strains without the ability to detect characteristics of other strains present could still have evolved strategies to vary sex ratio over their lifetimes, and the second model (DKM) suggests strains with detection abilities might have evolved after that. Our analysis suggests that once the ability to detect the population sizes and fecundities of other strains has developed, detection of their sex ratio choices confers no additional selective advantage in that a DKM ESS is still an ESS among sex ratio detecting strategies. The sex ratio choices for each DKM ESS are given by the equilibrium values of the parameter equivalent sex ratio detecting strategy described in Teboh-Ewungkem and Wang (2012), in the case where two strains employing that strategy encounter each other.