The role of species abundance in determining breeding origins of migratory birds with stable isotopes

Understanding the breeding origins of migratory birds captured on their wintering grounds has important management and conservation implications for declining populations of songbirds. Stable isotopes have recently been used to infer origins for species where application of conventional markers fails. A natural method of linking wintering birds to breeding populations, and one that has not been previously applied to stable isotopes, is based on likelihood. Using a likelihood assignment rule, birds are associated with the breeding population under which their realized isotope signature is most likely to have been generated. We report the first illustration of using likelihood-based assignment with stable isotope data. Moreover, within a probability-based framework for assignment, we argue that a more natural formulation of the assignment problem should be based on the probability of origin given the observed data, or the posterior probability of origin. The relationship between posterior assignment and that based on simple likelihood is embodied in Bayes Rule, which establishes a clear linkage between the distribution of the breeding population (i.e., relative abundance) and probability of origin. We demonstrate likelihood and posterior assignment using a large data set on Black-throated Blue Warblers (Dendroica caerulescens). Our results suggest that relative abundance is likely to be a more crucial consideration in the presence of less geographically structured isotopes, when the distribution of abundance is highly non-uniform, or when the range of the species is geographically restricted