Predicting the temporal dynamics of reproductive skew and group membership in communal breeders

Reproductive skew models attempt to predict the fraction of reproduction contributed by each individual that participates in a communal brood. One potential limitation of these models is that individuals make a single, fixed decision about group membership and reproductive allocation at the beginning of the breeding period. While this is appropriate for animals that reproduce in a synchronous bout, many cooperative breeders produce offspring over a prolonged period of time. It is likely that these species adjust reproductive allocation and group membership over time in response to temporal shifts in group productivity and ecological constraints. In this paper we adapt transactional models of reproductive skew to a continuous form, generating time-dependent functions of reproductive allocation. We derive a general method for predicting temporal changes in group membership as well as a general expression for reproductive skew across the regions over which a group is stable. Using a linear approximation for time-dependent reproduction, we derive new expressions for reproductive skew in cases where the subordinate departs during the breeding period. In this case we find that the traditional model always overestimates the subordinate's share of reproduction when dominants are in control of both reproductive shares and group membership (i.e., concessions models). Conversely, we find that the traditional model always underestimates the subordinate's share of reproduction when subordinates are in control of reproductive shares (i.e., constraint models). We discuss the implications of these new calculations in relation to the traditional skew models and more recent empirical tests of reproductive skew in animal societies.