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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.

1. Dispersal is a fundamental ecological process, so spatial models require realistic dispersal kernels. We compare five different forms for the dispersal kernel of the tansy beetle Chrysolina graminis moving between patches of its host-plant (tansy Tanacetum vulgare) in a riparian landscape. 2. Multi-patch mark-recapture data were collected every 2 weeks over 2 years within a large network of patches and from 2226 beetles. Dispersal was common (28.4% of 880 recaptures after a fortnight) and was more likely over longer intervals, out of small patches, for females and during flooding. Interpatch movement rates did not differ between years and exhibited no density dependence. Dispersal distances were similar for males and females, in both years and over all intervals, with a median dispersal distance of just 9.8 m, although a maximum of 856 m was recorded. 3. A model of dispersal, where patches competed for dispersers based on their size and distance from the beetle's source patch (scaled by the dispersal kernel) was fitted to the field data with a maximum likelihood procedure and each of five alternative kernels. The best fitting had relatively extended tails of long-distance dispersal, while Gaussian and negative exponential kernels performed worst. 4. The model suggests that females disperse more commonly than males and that both are strongly attracted to large patches but do not differ between years, which are consistent with the empirical results. Model-predicted emigration and immigration rates and dispersal phenologies match those observed, suggesting that the model captured the major drivers of tansy beetle dispersal. 5. Although negative exponential and Gaussian kernels are widely used for their simplicity, we suggest that these should not be the models of automatic choice, and that fat-tailed kernels with relatively higher proportions of long-distance dispersal may be more realistic.