A flexible Bayesian hierarchical approach for analyzing spatial and temporal variation in the fecal corticosterone levels in birds when there is imperfect knowledge of individual identity

Population cycles have long interested biologists. The ruffed grouse, Bonasa umbellus, is one such species whose populations cycle over most of their range. Thus, much effort has been expended to understand the mechanisms that might control cycles in this and other species. Corticosterone metabolites are widely used in studies of animals to measure physiological stress. We evaluated corticosterone metabolites in feces of territorial male grouse as a potential tool to study mechanisms governing grouse cycles. However, like most studies of corticosterone in wild animals, we did not know the identity of all individuals for which we had fecal samples. This presented an analytical problem that resulted in either pseudoreplication or confounding. Therefore, we derived an analytical approach that accommodated for uncertainty in individual identification. Because we had relatively low success capturing birds, we estimated turnover probabilities of birds on territorial display sites based on capture histories of a limited number of birds we captured. Hence, we developed a study design and modeling approach to quantify variation in corticosterone levels among individuals and through time that would be applicable to any field study of corticosterone in wild animals. Specifically, we wanted a sampling design and model that was flexible enough to partition variation among individuals, spatial units, and years, while incorporating environmental covariates that would represent potential mechanisms. We conducted our study during the decline phase of the grouse cycle and found high variation among corticosterone samples (11.33-443.92. ng/g [. x-=. 113.99. ng/g, SD. =. 69.08, median. =. 99.03. ng/g]). However, there were relatively small differences in corticosterone levels among years, but levels declined throughout each breeding season, which was opposite our predictions for stress hormones correlating with a declining population. We partitioned the residual variation into site, bird, and repetition (i.e., multiple samples collected from the same bird on the same day). After accounting for years and three general periods within breeding seasons, 42% of the residual variation among observations was attributable to differences among individual birds. Thus, we attribute little influence of site on stress level of birds in our study, but disentangling individual from site effects is difficult because site and bird are confounded. Our model structures provided analytical approaches for studying species having different ecologies. Our approach also demonstrates that even incomplete information on individual identity of birds within samples is useful for analyzing these types of data.