The effect of differential survivorship on the stability of reproductive queueing

Queues, in which individuals inherit resources in a predictable, temporally stable order, are widespread in animal social groups. We develop an analytic model to explore the effect of differential survivorship on the stability of a reproductive queue. We show that unless fighting for dominance is potentially fatal, future direct benefits are not alone sufficient to stabilize a queue of non-relatives under constant (age-independent) mortality rates, regardless of whether a dominant becomes an isolate or remains a dominant on the death of the first subordinate. In the absence of fatal fighting, stabilization of such a queue by future direct benefits alone requires either the dominant or the subordinate to have age-dependent mortality rates. Even when the queue is stabilized by present direct reproduction, however, the shape of the lifespan distribution can make a significant difference to the size of the required incentive. In contrast to non-relatives, queues of relatives can be stable without age-dependent mortality, so long as relatedness exceeds a critical value; however, age-dependent mortality can lower this critical value.