Abstract
Sex ratio evolution has been one of the most successful areas of evolutionary theory. Pioneered by Düsing and Fisher under panmixia, and later extended by Hamilton to cover local mate competition (LMC), these models often assume, either implicitly or explicitly, that all females are fertilized. Here, we examine the effects of relaxing this assumption, under both panmictic and LMC models with diploid genetics. We revisit the question of the mathematical relationship between sex ratio and probability of fertilization, and use these results to model sex ratio evolution under risk of incomplete fertilization. We find that (i) under panmixia, mate limitation has no effect on the evolutionarily stable strategy (ESS) sex allocation; (ii) under LMC, mate limitation can make sex allocation less female-biased than under complete fertilization; (iii) contrary to what is occasionally stated, a significant fraction of daughters can remain unfertilized at the ESS in LMC with mate limitation; (iv) with a commonly used mating function, the fraction of unfertilized daughters can be quite large, and (v) with more realistic fertilization functions, the deviation becomes smaller. The models are presented in three equivalent forms: individual selection, kin selection and group selection. This serves as an example of the equivalence of the methods, while each approach has their own advantages. We discuss possible extensions of the model to haplodiploidy.
Highlights
The theory of sex allocation has often been called one of the most successful areas of modern evolutionary theory
Substituting R = 0 into equation (2.5) or (2.7) yields (1 − 2x∗)f (x∗)/x∗ = 0, with the well-known Fisherian ‘equal allocation’ result x* = 1/2. This implies that mate limitation has no effect on the stable sex ratio under panmixia, regardless of the shape of the function f, even in populations that are so sparse that the vast majority of both sexes never find a mate (i.e. f (1/2) is close to 0)
We have examined the effect of mate limitation on sex ratio evolution in Fisherian and Hamiltonian (LMC) models
Summary
The theory of sex allocation has often been called one of the most successful areas of modern evolutionary theory. The model is analysed from individual selection, kin selection and group selection viewpoints, where the last two allow an analysis of the panmictic ‘Fisherian’ scenario as a special case These different interpretations are all equivalent in terms of the evolutionary outcome, but it is useful to present all three: the importance of, e.g. group selection in sex ratio evolution has been much debated [11,12], and researchers with different methodological preferences may choose to focus on a different version of the model, which can be thought of as different causal interpretations of the evolutionary process [13]. The three interpretations of the model serve as an illustration of the mathematical equivalence of the individual, kin and group selection methods
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