Hierarchical Bayesian Model for Estimating Migratory Bird Harvest in Canada

The Canadian Wildlife Service (CWS) requires reliable estimates of the harvest of migratory game birds, including waterfowl and murres, to effectively manage populations of these hunted species. The National Harvest Survey is an annual survey of hunters who purchase Canada9s mandatory migratory game bird hunting permit. We use these survey data to estimate the number of birds harvested for each species, as well as hunting activity metrics such as the number of active hunters and days spent hunting. The analytical methods used to generate these estimates have not changed since the survey was first designed in the early 1970s. Here we describe a new hierarchical Bayesian model, which replaces the series of ratio estimators that comprised the old model. We are now using this new model to generate estimates for migratory bird harvests as of the 2019-2020 hunting season, and to generate updated estimates for all earlier years. The hierarchical Bayesian model uses over-dispersed Poisson distributions to model mean hunter activity and harvest (zero inflated Poisson and zero truncated Poisson, respectively). It also includes multinomial distributions to model some key components including, variation in total harvest across periods of the hunting season, the species composition of the harvest within each of those periods, and the age and sex composition in the harvests of a given species. We estimated the parameters of the main Poisson and the multinomial distributions for each year as random effects using first-difference time-series. This time-series component allows the model to share information across years and reduces the sensitivity of the estimates to annual sampling noise. The new model estimates are generally very similar to those from the old model, particularly for the species that occur most commonly in the harvest, and so the results do not suggest any major changes to harvest management decisions and regulations. However, estimates for all species from the new model are more precise and less susceptible to annual sampling error, particularly for species that occur less commonly in the harvest (e.g., sea ducks and other species of conservation concern). This new model, with its hierarchical Bayesian framework, will also facilitate future improvements and elaborations, allowing the incorporation of prior information from the rich literature and knowledge in game bird management and biology.