Estimating the annual number of breeding attempts from breeding dates using mixture models

Well-established statistical methods exist to estimate variation in a number of key demographic rates from field data, including life-history transition probabilities and reproductive success per attempt. However, our understanding of the processes underlying population change remains incomplete without knowing the number of reproductive attempts individuals make annually; this is a key demographic rate for which we have no satisfactory method of estimating. Using census data to estimate this parameter from requires disaggregating the overlying temporal distributions of first and subsequent breeding attempts. We describe a Bayesian mixture method to estimate the annual number of reproductive attempts from field data to provide a new tool for demographic inference. We validate our method using comprehensive data on individually-marked song sparrows Melospiza melodia, and then apply it to more typical nest record data collected over 45 years on yellowhammers Emberiza citrinella. We illustrate the utility of our method by testing, and rejecting, the hypothesis that declines in UK yellowhammer populations have occurred concurrently with declines in annual breeding frequency.