Partial paternity does not always select for female-biased care.

The theoretical literature predicts that parentage differences between the sexes, due to females mating with multiple males, select males to provide less parental care and females to care more for the offspring. We formulate simple evolutionary games to question the generality of this prediction. We find that the relationship between paternal care and fitness gained from extra-pair matings is important. A trade-off between these two quantities is required for partial paternity and complete maternity to bias the evolutionary stable strategy (ESS) toward more female care. We argue that this trade-off has been implicitly or explicitly assumed in most previous theories. However, if there is no trade-off between paternal care and extra-pair matings, parentage differences do not influence the ESS sex roles. Moreover, it is also possible for these two quantities to have a positive relationship, in which case we predict selection for male care is possible. We support these predictions using agent-based simulations. We also consider the possibility that caring males have greater opportunities to guard their paternity, and find that this mechanism can also select for male-biased care. Hence, we derive the conditions under which male care may be selected despite partial paternity and complete maternity.