Territorial behaviour and population dynamics in red grouse Lagopus lagopus scoticus. II. Population models

1. Recent experiments on cyclic red grouse populations discovered that aggressiveness, induced by testosterone implants, depressed population density for more than a year after the implants were exhausted. 2. This confirms the observation, also made in previous studies of this territorial species, that aggressiveness can determine population density. Additionally, it hints at a form of social memory that sustains the effect of episodes of high aggressiveness after their cause has ceased to exist. 3. We explore the logical consequences of this observation with a simple model of the interaction between population density and aggressiveness. A flexible function describes how aggressiveness changes from year to year as a function of population density. At low densities animals are tolerant to conspecifics and aggressiveness falls from one year to the next. Conversely, at high densities aggressiveness rises. 4. In the model, current aggressiveness is set by aggressiveness in the previous year, and modified by last year's population density (first version) or by current population density (second version). 5. We assume no particular behavioural mechanism underlying this process but derive conditions under which changes in aggressiveness, effected by density, can generate unstable dynamics. 6. The two versions of the model give fluctuations that differ in period and amplitude but have similar conditions for unstable dynamics. Specifically, the more abrupt the transition from tolerant to intolerant behaviour with increasing density, the more likely are cycles to occur. 7. We show how a previous model of the kinship hypothesis for red grouse cycles can be recast in the current terminology, and how the new models offer a more general way of examining red grouse population dynamics.