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

Reproductive skew models attempt to predict the fraction ofreproduction contributed by each individual that participatesin a communal brood. One potential limitation of these modelsis that individuals make a single, fixed decision about groupmembership and reproductive allocation at the beginning of thebreeding period. While this is appropriate for animals thatreproduce in a synchronous bout, many cooperative breeders produceoffspring over a prolonged period of time. It is likely thatthese species adjust reproductive allocation and group membershipover time in response to temporal shifts in group productivityand ecological constraints. In this paper we adapt transactionalmodels of reproductive skew to a continuous form, generatingtime-dependent functions of reproductive allocation. We derivea general method for predicting temporal changes in group membershipas well as a general expression for reproductive skew acrossthe regions over which a group is stable. Using a linear approximationfor time-dependent reproduction, we derive new expressions forreproductive skew in cases where the subordinate departs duringthe breeding period. In this case we find that the traditionalmodel always overestimates the subordinate's share of reproductionwhen dominants are in control of both reproductive shares andgroup membership (i.e., concessions models). Conversely, wefind that the traditional model always underestimates the subordinate'sshare of reproduction when subordinates are in control of reproductiveshares (i.e., constraint models). We discuss the implicationsof these new calculations in relation to the traditional skewmodels and more recent empirical tests of reproductive skewin animal societies.