A Bayesian model for identifying mixed migration strategies, while accounting for sample selection bias

Background/Question/Methods

An important assumption in most observational studies is that individuals selected for observation are representative of some larger study population. Yet, this assumption is often unrealistic. Studies of mixed migration strategies of northern white-tailed deer (Odocoileus virginianus) exemplify the means by which selection bias can lead to biased estimates of population parameters. Deer are often captured on winter yards where deer migrate in response to changing environmental conditions (e.g., snow depth). Yet, not all deer migrate in all years, and the propensity to migrate increases with the severity of the winter. As such, winter captures during mild years are more likely to target deer that migrate every year (i.e. obligate migrators). Characterizing deer as conditional or obligate migrators is also challenging unless deer are  observed for many years and under a variety of winter conditions.  To overcome these challenges, I develop a Bayesian model that incorporates a vector of partially observed states reflecting each individual’s migration strategy (conditional versus obligate migrator). By allowing these states to depend on a measure of winter severity in the year of capture, it is possible to estimate and adjust for selection bias when estimating population-level migration parameters.  

Results/Conclusions

I fit the model to data from a 15 year study, involving 168 adult (> 1.0 year old) female deer in Northern Minnesota, USA. The estimated probability of migrating for conditional migrators increased non-linearly with an index of winter severity, which varied throughout the course of the study. Estimates of selection bias confirmed a priori hypotheses that the study cohort included more obligate migrators in later years following a series of mild winters. In the study population, 6% (95% Bayesian credibility interval = 2.4%, 12%) of deer were estimated to exhibit an obligate migration strategy. Selection biases are likely to be prevalent in many ecological studies due to the difficulties associated with random selection of observational units. Bayesian methods offer attractive framework for addressing these issues due to their ability to incorporate latent or partially observed states and to model direct and indirect links between state variables.