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The views and opinions expressed or implied in this article are those of the author (or authors) and do not necessarily reflect the position of the National Marine Fisheries Service, NOAA. Abstract—Mark-recapture studies using data collected at rotary screw traps (RSTs) are used to estimate abundances of migrating juvenile salmonids exiting natal rearing habitats. Frequently, environmental conditions and mechanical failures decrease RST efficiencies, or completely halt operations, leading to sparse and missing data. In this study, we show how a time-stratified hierarchical Bayesian model framework can incorporate prior information to increase the accuracy and precision of estimates made with sparse and missing data. To do this, we incorporated annually recurring salmonid emigration characteristics into the model using multiple years of data. We compared abundance estimates of the hierarchical multiyear model with 3 single-year Bayesian models, using simulated and real RST data. The hierarchical multiyear model was as accurate and precise as the best model when data were complete and abundant, but outperformed other models when data were sparse and missing for multiweek blocks. For species with low abundances or low detection efficiencies, the hierarchical multiyear model used data from all years and recurring emigration characteristics to increase the accuracy and precision of estimates. This model is a valuable tool for fish and wildlife biologists who repeat mark-recapture studies annually and encounter sparse and missing data. To effectively manage free-ranging animals, information on survival rate, population growth rate, and recruitment are needed to understand factors influencing populations (Fryxell et al., 2014). It is often necessary to know abundances during various life stages to calculate this information but obtaining censuses of natural populations is difficult (Seber, 2002). Studies structured around sighting, capturing, or counting individuals and expanding these counts based on detection or sampling efficiencies are regularly implemented to estimate abundances when a census is not feasible (Nichols, 1992; Mill, 2007). These types of mark-recapture studies have broad application and have been used to estimate abundances of blue whales (Balaenoptera musculus) and humpback whales (Megaptera novaeangliae) (Calambokidis and Barlow, 2004), grizzly bears (Ursus arctos) (Mowat and Strobeck, 2000), herbivorous insects (Kareiva, 1983), and numerous other species so that marked individuals in the population can be detected during later sampling periods. The Lincoln-Petersen model is foundational for estimating abundances using mark-recapture data where unmarked abundance, U, is estimated using the number of marked individuals in the population, n, the number of unmarked individuals counted or captured at a sampling event, u, and the number of marked individuals counted or captured at a sampling event, m:

A multiyear hierarchical Bayesian mark-recapture model incorporating data on recurring salmonid behavior to account for sparse or missing data