# Frank, S. A. 1985. Are mating and mate competition by the fig wasp Pegoscapus assuetus (Agaonidae) random within a fig? Biotropica 17:170-172

Female-biased sex ratios are often observed in parasitic Hymenoptera that mate within small, isolated groups before dispersing to colonize new hosts (Hamilton 1967, Charnov 1982). In these groups there is both mating between sibs and competition among brothers for mates. Much theoretical attention has been devoted to predicting the sex ratio within the groups for the population structure that occurs in these parasitic wasps (reviewed by Charnov 1982, Frank 1983a). Recent theoretical studies indicate that the proportion of males is negatively correlated with the relatedness among males competing for mates and with the relatedness between mates (Borgia 1982, CoIwell 1982). The predicted sex ratio (males:females) for diploid organisms is 1 - a : 1 + b, where a is the proportion of competitive interactions between brothers, and b is the proportion of matings between sibs (Frank, unpub. ins.). An untested assumption of previous quantitative models (e.g., Hamilton 1967, Taylor and Bulmer 1980, CoIwell 1981) is that mate competition among males and mating occur randomly within a local group. Random mate competition and mating within a group means that if the proportion of sibs in the group is p, then sib mating is expected with probability p, and p of the interactions among males will be between brothers. If a group is founded by n egg-laying females, each producing the same number of eggs, then p = 1/n, and the predicted sex ratio is 1 - 1/n : 1 + 1/n, or, given as males/total, (n - 1)/2n. This is Hamilton's (1967) widely cited result for diploid organisms. The predicted sex ratio for haplodiploid organisms such as fig wasps is slightly more female-biased than for diploids (Hamilton 1979, Taylor and Bulmer 1980, Frank 1983a).

Two empirical studies have been published that report female-biased sex ratios in fig wasps correlated with mate competition and inbreeding (Hamilton 1979, Frank 1983b). Neither study concerned itself with the assumptions of random mate competition and mating in local groups. In this note I report the results of an experiment that yielded correlative evidence inconsistent with these two assumptions.