Keywords
sex ratio, lattice model, allee effect, evolutionary maintainable strategy
Start Date
1-7-2004 12:00 AM
Abstract
The observed sex ratio is nearly one half in many animals including humans. Fisher explained thatthe 50/50 sex ratio is optimal. However, the 50/50 sex ratio seems highly unstable because a slight deviationfrom 50/50 changes the optimal ratio to the opposite extremes; zero or unity. Thus sex ratio should befluctuating wildly around 50/50. In contrast, the observed 50/50 sex ratios in wild populations seem to bevery stable. There should be some unknown mechanisms to stabilize the sex ratio 50/50. We build the latticemodel of mating populations. Each cell represents a male, a female, or an empty site. We perform latticesimulation by two different methods: local interaction (lattice model) and global interaction. In the case oflattice model, chance of reproduction is determined based on the numbers of males and females adjacent tothe 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 latticesimulation, but it is rather flat in the global interaction. With a high mortality, the 50/50 sex ratio becomes thesole survivor; all other ratios becomes extinct. The stability and persistence of the 50/50 sex ratio becomesevident especially in a harsh environment. The superiority of the 50/50 sex ratio in the lattice model is due tothe decreased chance of mating in a local site, known as the Allee effect. Our approach can extend to showthat any value of sex ratio is evolutionary stable.
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 thatthe 50/50 sex ratio is optimal. However, the 50/50 sex ratio seems highly unstable because a slight deviationfrom 50/50 changes the optimal ratio to the opposite extremes; zero or unity. Thus sex ratio should befluctuating wildly around 50/50. In contrast, the observed 50/50 sex ratios in wild populations seem to bevery stable. There should be some unknown mechanisms to stabilize the sex ratio 50/50. We build the latticemodel of mating populations. Each cell represents a male, a female, or an empty site. We perform latticesimulation by two different methods: local interaction (lattice model) and global interaction. In the case oflattice model, chance of reproduction is determined based on the numbers of males and females adjacent tothe 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 latticesimulation, but it is rather flat in the global interaction. With a high mortality, the 50/50 sex ratio becomes thesole survivor; all other ratios becomes extinct. The stability and persistence of the 50/50 sex ratio becomesevident especially in a harsh environment. The superiority of the 50/50 sex ratio in the lattice model is due tothe decreased chance of mating in a local site, known as the Allee effect. Our approach can extend to showthat any value of sex ratio is evolutionary stable.
