Estimating nest abundance while accounting for time‐to‐event processes and imperfect detection

Birds and their population dynamics are often used to understand and document anthropogenic effects on biodiversity. Nest success is a critical component of the breeding output of birds in different environments; but to obtain the complete picture of how bird populations respond to perturbations, we also need an estimate of nest abundance or density. The problem is that raw counts generally underestimate actual nest numbers because detection is imperfect and because some nests may fail or fledge before being subjected to detection efforts. Here we develop a state‐space superpopulation capture–recapture approach in which inference about detection probability is based on the age at first detection, as opposed to the sequence of re‐detections in standard capture–recapture models. We apply the method to ducks in which (1) the age of the nests and their initiation dates can be determined upon detection and (2) the duration of the different stages of the breeding cycle is a priori known. We fit three model variants with or without assumptions about the phenology of nest initiation dates, and use simulations to evaluate the performance of the approach in challenging situations. In an application to Blue‐winged Teal Anas discors breeding at study sites in North and South Dakota, USA, nesting stage (egg‐laying or incubation) markedly influenced nest survival and detection probabilities. Two individual covariates, one binary covariate (presence of grazing cattle at the nest site), and one continuous covariate (Robel index of vegetation), had only weak effects. We estimated that 5–10% of the total number of nests were available for detection but were missed by field crews. An additional 6–15% were never available for detection. These percentages are expected to be larger in less intense, more typical sampling designs. User‐friendly software nestAbund is provided to assist users in implementing the method.