We present an inclusive fitness model on worker-controlled sex investments in eusocial Hymenoptera which expands the existing theory for random mating populations as formulated by Trivers and Hare (1976) and Benford (1978). We assume that relatedness asymmetry is variable among colonies — owing to multiple mating, worker reproduction and polygyny — and that workers are able to assess the relatedness asymmetry in their own colony. A simple marginal value argument shows that “assessing” workers maximize their inclusive fitness by specializing on the production of the sex to which they are relatively more related than the average worker in the population is related to that sex. The model confirms our earlier verbal argument on this matter (Boomsma and Grafen, 1990) and gives further quantitative predictions of the optimal sex ratio of relatedness-asymmetry classes for both infinite and finite, random mating populations.
It is shown that in large populations all but one of the relatedness-asymmetry classes should specialize on the production of one sex only. The remaining, balancing class is selected to compensate any bias induced by the other class(es) such that the population sex ratio reflects the relatedness asymmetry of that balancing class. In the absence of worker-reproduction, the sex ratio compensation by the balancing-class is generally close to 100%, unless the population is very small.
In the Discussion we address explicitly the likelihood of our relatedness-assessment hypothesis and other assumptions made in the model. The relationship of our model with previous theory on sex allocation in eusocial Hymenoptera is worked out in the Appendix.