Models of Red Grouse Cycles. A Family Affair?

Abstract

The lack of parameterised models showing how intrinsic factors might affect population dynamics has contributed to the belief that they are unlikely to explain population cycles. In this paper we use mathematical models to show how a social process, differential territorial behaviour between kin and non-kin, might drive red grouse (Lagopus lagopus scoticus) population cycles. We develop a simple age-structured population model which has space as a limiting resource and examine two versions of it. The first contains no kin effect and is incapable of cyclic behaviour. The second, containing a modification to reflect the effect of kinship on recruitment, shows oscillatory behaviour over most of the parameter space and produces realistic output (period, amplitude, age structure, recruitment), while its quasi-cyclic behaviour is shown to be robust under random parameter variations. Further parameterisation with field data from two study sites in north-east Scotland yields output which resembles the course of observed population cycles. The model predicts that a young cock present in autumn will have a greater probability of recruitment into the territorial population during the increase than during the decline phase of the cycle. This is consistent with field data. The model further predicts that such fluctuations in the probability of recruitment will be synchronous with fluctuations in the size of kin-clusters.