Unrelated helpers will not fully compensate for costs imposed on breeders when they pay to stay

Unrelated subordinates may invest in costly help to avoid being evicted from groups (the `pay-to-stay' hypothesis). However, the effectiveness of eviction to enforce help should depend on its being applied accurately and on the costs it imposes on both dominants and subordinates. The relative cost of being evicted is a function of the population frequency of eviction when population growth is limited by density-dependent factors. We describe a stage-structured pay-to-stay model incorporating density-dependent population growth, costly eviction and occasional errors. Breeders demand some amount of help and evict subordinates that do not provide it. Helpers decide on the amount of help they will provide. The threat of eviction alone is sufficient to enforce helping. However, helping will not be favoured if helpers do not impose costs on breeders. The amount of help provided is less than the cost that subordinates impose upon breeders, when any help is provided. Thus, the net fitness effect of a helper under pay-to-stay alone is negative, even if it is investing in cooperative behaviour. Constraints on dispersal have no effect on the amount of help, although they may influence the tolerance threshold of breeders and group stability, depending on the mechanism of density dependence.