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Stability Analyses of the 50/50 Sex Ratio Using Lattice Simulation

The observed sex ratio is nearly one half in many animals including humans. Fisher explained that the 50/50 sex ratio is optimal. However, the 50/50 sex ratio seems highly unstable because a slight deviation from 50/50 changes the optimal ratio to the opposite extremes; zero or unity. Thus sex ratio should be fluctuating wildly around 50/50. In contrast, the observed 50/50 sex ratios in wild populations seem to be very stable. There should be some unknown mechanisms to stabilize the sex ratio 50/50. We build the lattice model of mating populations. Each cell represents a male, a female, or an empty site. We perform lattice simulation by two different methods: local interaction (lattice model) and global interaction. In the case of lattice model, chance of reproduction is determined based on the numbers of males and females adjacent to the vacant site. In the global interaction method, we select four sites randomly instead of the adjacent sites. The highest density is achieved in the 50/50 sex ratio. This density peak stands out sharply in the lattice simulation, but it is rather flat in the global interaction. With a high mortality, the 50/50 sex ratio becomes the sole survivor; all other ratios becomes extinct. The stability and persistence of the 50/50 sex ratio becomes evident especially in a harsh environment. The superiority of the 50/50 sex ratio in the lattice model is due to the decreased chance of mating in a local site, known as the Allee effect. Our approach can extend to show that any value of sex ratio is evolutionary stable.