Local Mate Competition in a Stochastic Environment

The optimal sex ratio under local mate competition requires examination of stochastic factors. Numbers of male and female progeny were considered binomially distributed with the following parameters: the total number of progeny (T) and production rate of males (r, strategic parameter). The total number of progeny may be limited, and the progeny numbers may be differ among females by a stochastic factor. It was assumed that the total number of progeny (T) for all females follows an identical probability mass function. When the total number of progeny (T) is limited, the optimum production rate of males (r) is higher than that predicted by Hamilton′s classical LMC model, which answers no stochasticity in the sex ratio. As the total number of progeny becomes large, the discrepancy between the stochastic model and Hamilton′s model decays. Another stochastic factor also affects the optimum production rate of males (r). A female that colonizes in a group cannot always have precise information on the number of co-foundresses in her group. When the number of co-foundresses in the group is obscure, the optimal production rate of males (r) is lower than that for the exact information.