Anim. Behav., 1985, 33, 519-533 Models of parent-offspring conflict. V. Effects of the behaviour of the two parents G. A. PARKER Department of Zoology, University of Liverpool, Liverpool, L69 3BX, U.K. Abstract. In the absence of any parent-offspring conflict, the total parental investment per offspring should be less when two parents collaborate in caring for the offspring than when only one parent invests. This does not necessarily mean that offspring fare less well when both parents invest. The 'ideal' amount of parental investment for an offspring to take is always greater than is 'ideal' for the parent to allocate (Trivets 1974). The offspring's optimum is higher if the offspring's action affects the reproductive success of only one parent and lower if both parents are affected (e.g. two-parent investment, or lifelong monogamy). The difference between the parental optimum and the offspring optimum depends on the mating system and on the form of conflict (between successive broods, or within broods), and prescribes a 'conflict range'. The extent of conflict cannot be deduced solely from a knowledge of the average relatedness between siblings. The conflict is likely to be resolved by an ESS in which intermediate (compromise) levels of investment are paid out to offspring, which nevertheless continue to make costly demands for yet more investment. The degree of conflict can be measured by the extent to which offspring subject their parents to aggressive demands for extra investment, and is likely to be greater when two parents collaborate equally over investment than when only one parent invests. When only one parent invests, conflict is higher if sibling-competition is between siblings in the same broods (intra-brood) than when it is between progeny in successive broods (inter-brood). However, the reverse will tend to be the case when both parents invest equally. Previous papers in this series have analysed parent- offspring conflict in sexually reproducing diploids when one parent (the female) cares for the offspring (Parker & Macnair 1978, 1979; Macnair & Parker 1978, 1979). These attempted to find evolutionarily stable strategies (ESS; Maynard Smith 1974, 1982) for conflicts between a parent and its offspring over the amount of parental investment (Trivers 1972) that the offspring is to receive (Trivers 1974). The models make simple assumptions about the gene- tics of the conflict (see also Stamps et al. 1978), and have so far been confined to the one-parent case. Predictions over the outcome of parent-off- spring conflict have been varied. Trivers & Hare (1976) give evidence (disputed by Alexander & Sherman 1977) that offspring may have won in worker-queen conflict in certain social hymenop- tera. In contrast, Alexander (1974) proposed that parents are in general more likely to win (but modified his arguments later; Alexander 1979). Parker & Macnair (1979) suggest that the outcome of the conflict will often be a compromise that is intermediate between the interests of the parent and the offspring. At this compromise, parents will give out more investment that is optimal for them, but less than is optimal for each offspring. Off- spring will be aggressive in their attempts to solicit investment, but parents will respond only grudg- ingly to these demands, often denying the demands made of them. Evidence for such behaviour was documented by Trivers (1974). The present paper has three aims: (1) to summar- ize previous results on parent-offspring conflict ESSs; (2) to outline how parental behaviour in- fluences the level of conflict; and (3) to analyse conflict for cases where both parents care for the offspring. The last aim has not been considered previously. HOW CAN CONFLICT ARISE? ParenWoffspring conflict is about the allocation of a parent's reproductive expenditure (investment) between its progeny (Trivers 1974). Essentially, there are two optima, one for the parent and one for the offspring. In sexually-reproducing species, these optima do not coincide, and offspring will be selected to demand more investment than the parent is selected to supply. 519