The consequences of constrained sex allocation in diploids and haplodiploids under local mate competition

Unmated females in haplodiploid populations may enjoy reproductive success but with the constraint that all their offspring-developing from unfertilised eggs-are male. The presence of such females, constrained to produce only male offspring, is expected to lead to a corresponding female bias being favoured among the offspring of unconstrained females. Godfray (J Evol Biol 3, 3-17) derived a mathematical expression for the unbeatable sex allocation strategy for unconstrained females in the context of local mate competition in 2-foundress patches, and concluded that there is negligible impact of the presence of constrained females on the unbeatable sex allocation of unconstrained females. However, Godfray's result assumes diploid-rather than haplodiploid-genetics and his derivation contains a mathematical error. We correct Godfray's error and extend his model to incorporate haplodiploid genetics. This results in a more substantial impact of constrained females on the sex allocation behaviour of unconstrained females under local mate competition.