A model is constructed to study the effects of local mate competition and multiple mating on the optimum allocation of resources between the male and female reproductive brood in social hymenopteran colonies from the 'points of view' of the queen (parental manipulation theory) as well as the workers (kin selection theory). Competition between pairs of alleles specifying different sex investment ratios is investigated in a game theoretic frame work. All other things being equal, local mate competition shifts the sex allocation ratio in favour of females both under queen and worker control. While multiple mating has no effect on the queen's optimum investment ratio, it leads to a relatively male biased investment ratio under worker control. Under queen control a true Evolutionarily Stable Strategy (ESS)does not exist but the 'best' strategy is merely immune from extinction. A true ESS exists under worker control in colonies with singly mated queens but there is an asymmetry between the dominant and recessive alleles so that for some values of sex ratio a recessive allele goes to fixation but a dominant allele with the same properties fails to do so. Under multiple mating, again,a true ESS does not exist but a frequency dependent region emerges. The best strategy here is one that is guaranteed fixation against any competing allele with a lower relative frequency. Our results emphasize the need to determine levels of local mate competition and multiple mating before drawing any conclusions regarding the outcome of queen-worker conflict in social hymenoptera. Multiple mating followed by sperm mixing, both of which are known to occur in social hymenoptera, lower average g netic relatedness between workers and their reproductive sisters. This not only shifts the optimum sex ratio from the workers 'point of view' in favour of males but also poses problems for the kin selection theory. We show that kin recognition resulting in the ability to invest in full but not in half sisters reverts the sex ratio back to that in the case of single mating and thus completely overcomes the hurdles for the operation of kin selection.
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