Interactions between harvesting, noise and territoriality in a model of red grouse population cycles

1 Population cycles are mostly thought to arise through extrinsic rather than intrinsic processes. However, in red grouse (Lagopus lagopus scoticus), intrinsic male territoriality has been proposed as a driver of the cycles, possibly in conjunction with an extrinsic interaction with specialist parasitic worms. Here we examine how harvesting and environmental noise may also interact with territoriality to determine how grouse populations cycle. 2 A stochastic model of grouse dynamics based on the territoriality hypothesis is developed, including harvesting and the effects of nonterritorial birds on aggressiveness. Cycles are detected in 97% of populations simulated over realistic parameter ranges, and these exhibit similar statistical properties to those reported in studies of multiple grouse populations. As observed, cycle periods are shorter at higher breeding productivities. 3 The model demonstrates the destabilizing influence of delayed density-dependent territorial aggressiveness. Cycle amplitudes are higher when annual changes in aggression are larger and when nonterritorial males provoke greater aggression. Intriguingly, the model suggests how an interaction between aggressiveness and parasites may operate. It is known that males with high worm burdens show dramatic decreases in aggressiveness in the year following a peak in territoriality. When this is included in the model, via larger crashes in aggression, amplitudes are higher, despite a reduction in overall aggressiveness. 4 Environmental stochasticity interacts with territoriality to determine the form of the cycles, but this is mediated through its 'colour' or temporal autocorrelation. For example, uncorrelated white noise increases amplitudes, while autocorrelated red noise has the opposite effect. However, noise increases cycle periods whatever the colour. 5 Harvesting occurs before territorial competition. This reduces the pool of males competing for territories and so increases recruitment and population densities. However, crashes can then be more extreme so cycle amplitudes are higher. With harvesting at ~150% of current typical levels, which is within observed variation, the dynamics exhibit a sharp transition to a state where cyclicity is reduced, periods are shorter and amplitudes lower. 6 The model suggests that to understand regional variation in red grouse cycles, interactions between territoriality, productivity, harvesting and noise must be considered