Conventional sex roles imply caring females and competitive males. The evolution of sex role divergence is widely attributed to anisogamy initiating a self-reinforcing process. The initial asymmetry in pre-mating parental investment (eggs vs. sperm) is assumed to promote even greater divergence in post-mating parental investment (parental care). But do we really understand the process? Trivers [Sexual Selection and the Descent of Man 1871-1971 (1972), Aldine Press, Chicago] introduced two arguments with a female and male perspective on whether to care for offspring that try to link pre-mating and post-mating investment. Here we review their merits and subsequent theoretical developments. The first argument is that females are more committed than males to providing care because they stand to lose a greater initial investment. This, however, commits the 'Concorde Fallacy' as optimal decisions should depend on future pay-offs not past costs. Although the argument can be rephrased in terms of residual reproductive value when past investment affects future pay-offs, it remains weak. The factors likely to change future pay-offs seem to work against females providing more care than males. The second argument takes the reasonable premise that anisogamy produces a male-biased operational sex ratio (OSR) leading to males competing for mates. Male care is then predicted to be less likely to evolve as it consumes resources that could otherwise be used to increase competitiveness. However, given each offspring has precisely two genetic parents (the Fisher condition), a biased OSR generates frequency-dependent selection, analogous to Fisherian sex ratio selection, that favours increased parental investment by whichever sex faces more intense competition. Sex role divergence is therefore still an evolutionary conundrum. Here we review some possible solutions. Factors that promote conventional sex roles are sexual selection on males (but non-random variance in male mating success must be high to override the Fisher condition), loss of paternity because of female multiple mating or group spawning and patterns of mortality that generate female-biased adult sex ratios (ASR). We present an integrative model that shows how these factors interact to generate sex roles. We emphasize the need to distinguish between the ASR and the operational sex ratio (OSR). If mortality is higher when caring than competing this diminishes the likelihood of sex role divergence because this strongly limits the mating success of the earlier deserting sex. We illustrate this in a model where a change in relative mortality rates while caring and competing generates a shift from a mammalian type breeding system (female-only care, male-biased OSR and female-biased ASR) to an avian type system (biparental care and a male-biased OSR and ASR).
