Harvesting unstable populations:: red grouse Lagopus lagopus scoticus (Lath.) in the United Kingdom

The optimal harvesting strategies for unstable populations are explored using first discrete time models and second a continuous time model specifically applied to the destabilising effects of the caecal nematode Trichostrongylus tenuis on the dynamics of red grouse Lagopus lagopus scoticus. In discrete time models, with overcompensation generating either cyclic or chaotic fluctuations in abundance harvesting can act as both a stabilising and a destabilising process. Maximum yields occur at the harvesting rate that coincides with the point where the harvesting stabilises the overcompensation. Optimal harvesting rates increase with the degree of overcompensation although these are more vulnerable to overharvesting. Harvesting in the continuous time model provides similar results, although observed hunting records do not appear to be stabilised by harvesting. Empirical data on the mortality caused by other natural enemies of red grouse, the hen harrier Circus cyaenus and the louping ill virus, show that these mortalities do stabilise grouse dynamics. One explanation is that both hen harriers and louping ill virus cause significant mortality to chicks before the infective stages of T. tenuis are laid down on the ground, whereas shooting takes place after the infective stages are laid down and thus do not stabilise the populations.