Estimating spawning salmon abundance from visual surveys: a hierarchical model of arrival and exit dynamics

Spawner abundance is a fundamental variable for salmon management models, but conventional methods (trapezoidal area under the curve) do not estimate the precision of abundance, and risk being biased by an assumed residence time. Here we present a hierarchical model that predicts visual counts of spawners by modelling the process and timing of spawner arrivals and exits. Our model provides annual estimates of spawner abundance, arrival timing, arrival spread, exit timing, and exit spread. By directly estimating these parameters and integrating uncertainty into abundance estimates, our approach improves the accuracy and reliability of spawner abundance estimates. We first demonstrate how the model accurately recovers parameters from simulated data, and then demonstrate its application by estimating 25 years of spawner abundance of wild sockeye salmon in the Okanagan River (BC, Canada). Our median estimated residence time of 9.1 days is shorter than the constant 11 days previously assumed for this population, and has considerable interannual variation (6.2–16.5 days). Thus, our estimated abundances are 15.7% higher, on average, but annual deviations range from -43 to +51%.