Sex ratio, body size and seasonality in a solitary bee, Osmia lignaria propinqua Cresson (Hymenoptera: Megachilidae).

Although sex ratio and investment theory have been recently refined and made more mathematically rigorous (Hamilton, 1967; Leigh, 1970; Trivers, 1972; Trivers and Hare, 1976; Charnov, 1978; MacNair, 1978), Fisher's (1930) original arguments remain essentially unchanged. In a panmictic population we expect equal amounts of time and energy to be allocated to the production of each sex. A disproportionate investment in the offspring of one sex will be corrected in subsequent generations by selection for parents that produce the sex in short supply. Because investment must be divided equally between the sexes, the optimal sex ratio is expected to be unity only when the parental effort expended on an average individual of each sex is also equal. If production of a female requires twice the effort as production of a male, the sex ratio should be 2 d :1 9 rather than unity. This study is, in part, an empirical test of sex ratio theory using a solitary bee, Osmia lignaria propinqua Cresson. It was prompted by the paucity of field data currently available to test the accuracy of theoretical formulations. Additionally, observations by Torchio (unpubl.) suggest that the sex ratio of offspring of 0. lignaria varies seasonally. Indeed, seasonal variation in the sex ratio is not uncommon in bees (Michener, 1974), although the reasons for such variability require clarification. Here we document seasonal variability and offer an explanation for it. Until recently (Trivers and Hare, 1976), the interrelationship between the ratio of investment in an average male and female and the sex ratio was not clearly perceived. It is now apparent that sex ratio is related to investment ratio and any study of sex ratio naturally extends to questions of optimal allocation of investment within each sex. Investment expended upon an average individual of each sex in many species is unequal, although total investment in each sex must be equal. Such differences are most clearly manifest in those species that exhibit sexual dimorphism in size. In Osmia lignaria females are distinctly larger than males. Of the explanations proposed for sexual dimorphism, two are frequently cited. Trivers (1972), in elaborating on Darwin (1871), hypothesized that members of the sex that invest most in offspring are subjects of intrasexual competition between members of the other sex. As a result of intrasexual selection (probably sexual selection also), members of the competing sex are expected to be larger and fewer because of the usual positive relation between size and mating success. This explanation is not applicable to 0. lignaria because females are responsible for all but sperm investment in offspring. The second hypothesis (Amadon, 1959; Selander, 1972) argues that sexual dimorphism is frequently due to intersexual competition for resources; a divergence in size reduces overlap in resource use, thereby increasing the overall efficiency of each sex. This hypothesis is not appropriate to 0. lignaria because the sexes do not differ in distribution across the limited number of flower species used for nectar (P. F. T., pers. observ.). We will demonstrate that the asymmetry in investment between individual males and females is probably due to a complicated process involving seasonal changes in resource availability.