Dispersal patterns in a harvested willow ptarmigan population

1. Harvest management requires knowledge of whether the harvest is sustainable as a result of compensatory mechanisms, such as dispersal. The effect of recreational harvesting on dispersal patterns in willow ptarmigan Lagopus lagopus was assessed over four hunting seasons in central Norway. 2. A two-parameter Weibull model was fitted to the observed absolute dispersal distance data using maximum likelihood methods. Estimates of the scale and shape parameters for the dispersal probability distribution were calculated, describing the distribution of observed willow ptarmigan dispersal distances. From the parameter estimates of the dispersal model we estimated the standard deviation of the dispersal displacement relevant for population genetic and spatial population dynamic models. 3. The effect of harvesting on dispersal patterns was examined by testing for differences in the scale and shape parameters of dispersal distance distributions in areas with and without harvest. No effect of harvesting was found, either in adults or juveniles. 4. Breeding dispersal of adult birds was estimated as a dispersal probability distribution with scale parameter a = 402 m and shape parameter b = 2.01, corresponding to a dispersal standard deviation of sigma = 284 m. The dispersal probability distribution of adults was not significantly different from a bivariate normal distribution. 5. Natal dispersal had a dispersal probability distribution with scale parameter a = 4206 m and shape parameter b = 1.16, corresponding to a dispersal standard deviation sigma = 3728 m. The dispersal probability distribution of juveniles was not significantly different from an exponential distribution. 6. Synthesis and applications. Reduction of the population density of willow ptarmigan through harvesting at moderate densities does not seem to affect the dispersal distances. Thus, if there is little or no difference in the dispersal probability distribution in harvested and non-harvested areas there will be only weak or no compensation for the harvest, given that natural mortality and reproduction is the same in both areas. Thus, erroneously assuming compensation of harvest by immigration into a local population can lead to overharvest.