SIMULTANEOUS-OPTIMIZATION OF EGG DISTRIBUTION AND SEX ALLOCATION IN APATCH-STRUCTURED POPULATION

The reproductive strategy of a female distributing her eggs over many patches comprises decisions on (1) how many eggs to deposit in a given patch, (2) what sex ratio to produce, and (3) how many patches to vis it. In this article simultaneous evolutionarily stable strategy (ESS) solutions are presented for cases in which them is local mate competit ion and these three decisions interact, a situation that has not been studied previously. Y. Yamaguchi developed a model of optimum sex allo cation for foundresses that contribute different numbers of eggs to on e patch. Yamaguchi's model is extended hem to examine the more general case in which females distribute their eggs over several patches. The key element is that females that visit a larger number of patches (re lative to other females) and thus produce smaller clutches in each pat ch should produce a (relatively) smaller proportion of daughters. Thes e females obtain a higher fitness per egg but invest more time in trav eling. A simultaneous ESS is obtaining for three variables, that is, c lutch size, sex ratio, and number of patches visited, and for two diff erent cases, namely, egg-limited females (no travel costs) and time-li mited females (traveling is costly). Analyis shows that sex-allocation strategies can be an important driving force in the distribution of e ggs over patches. The predictions of these models are strongly influen ced by whether or not the females are able to use information about ea ch other's clutch size. To test the validity of the model predictions, the dispersal behavior of plant-inhabiting predatory mites (Acari: Ph ytoseiidae) is considered in detail. The females distribute their eggs over many patches even when there is an ample supply of food. The mod els suggest that dispersal of the predatory mite females is a conseque nce of the sex-allocation games they play.