Estimating migratory game-bird productivity by integrating age ratio and banding data

Context. Reproduction is a critical component of fitness, and understanding factors that influence temporal and spatial dynamics in reproductive output is important for effective management and conservation. Although several indices of reproductive output for wide-ranging species, such as migratory birds, exist, there has been no theoretical justification for their estimators or associated measures of variance. Aims. The aims of our research were to develop statistical justification for an estimator of reproduction and associated variances on the basis of an existing national wing-collection survey and banding data, and to demonstrate the applicability of this estimator to a migratory game bird. Methods. We used a Bayesian hierarchical modelling approach to integrate wing-collection data, which provides information on population age ratios, and band-recovery data, which provides information on recovery probabilities of various age classes, for American woodcock (Scolopax minor) to estimate productivity and associated measures of variance. We present two models of relative vulnerability between age classes: one model assumed that adult recovery probabilities were higher, but that annual fluctuations were synchronous between the two age classes (i.e. an additive effect of age and year). The second model assumed that adults, on average, had higher recovery probabilities than did juveniles and that annual fluctuations were asynchronous through time (i.e. an interaction between age and year). Key results. Fitting our models within a hierarchical Bayesian framework efficiently incorporates the two data types into a single estimator and derives appropriate variances for the productivity estimator. Further, use of Bayesian methods enabled us to derive credible intervals that avoid the reliance on asymptotic assumptions. When applied to American woodcock data, the additive model resulted in biologically realistic and more precise age-ratio estimates each year and is adequate when the relative vulnerability to sampling only slightly varies or does not vary among components of a population (e.g. age, sex class) among years. Therefore, we recommend using woodcock indices from our analysis based on this model. Conclusions. We provide a flexible modelling framework for estimating productivity and associated variances that can incorporate ecological covariates to explore various factors that could drive annual dynamics in productivity. Applying our model to the American woodcock data indicated that assumptions about the variability in relative recovery probabilities could greatly influence the precision of our productivity estimator. Therefore, researchers should carefully consider the assumption of temporally variable relative recovery probabilities (i.e. ratio of juvenile to adults' recovery probability) for different age classes when applying this estimator. Implications. Several national and international management strategies for migratory game birds in North America rely on measures of productivity from harvest survey parts collections, without a justification of the estimator or providing estimates of precision. We derive an estimator of productivity with realistic measures of uncertainty that can be directly incorporated into management plans or ecological studies across large spatial scales.