Adult Sex Ratio dynamics

We assume a discrete time process t = [0, 1, … ] where the fraction of available males to females may change throughout a male’s lifetime. It will change if there are MG males in the population, otherwise it will remain the same as initially determined in each time period. Thus without a significant number of Mate Guarding males (q ≈ 0) then M_t = M₀ and F_t = F₀, and the fitness of the strategies specified above simplifies greatly. If there are MG males in the population then M_t and F_t will change through time as females encountering MG males leave the mating pool. Once MG males are fully gone, then the sex ratio of available females to males is constant. Importantly, the effects MG males have on the operational sex ratio (i.e., those available to mate; OSR) varies both with the ASR and their frequency. In a male-biased ASR, when mate guarding males are common, they reduce the numbers of available females to near 0. However, the effect MG males have on the OSR is much different at female-biased ASRs. These males, by removing themselves from the population, increase the relative numbers of females available to, for example, MM males (see SI).

If there are F_t females and q_tM_t MG males in the population and M_t > F_t, then the probability of a female becoming newly guarded by a male is q_t, making the average number of females being newly guarded by a male is q_tF_t. With M_t and F_t being the number of males and females in the mating pool at time t, and q_t the frequency of non-paired MG males, then

In Figs 2 and ​and33 we investigate contrasting initial sex ratios that are female-biased (M₀ = 100, F₀ = 150) and male-biased (M₀ = 150, F₀ = 100). In Fig. 4 we vary the ASR along a continuous scale.