Hierarchical Bayesian estimation of unobserved salmon passage through weirs

Abstract

We developed a hierarchical Bayesian model (HBM) to estimate missing counts of Chinook salmon (Oncorhynchus tshawytscha (Walbaum in Artedi, 1792)) at a weir on the Kogrukluk River, Alaska, between 1976 and 2015. The model assumed that fish passage during a breach of the weir was typical of passage during normal operations. Counts of fish passing the weir were missing for some days during the runs, or only partial counts for a given 24-hour period were available. The HBM approach provided more defensible estimates of missing data and total escapement than ad hoc or year-by-year model estimates, because estimates of passage for a given year were informed not only by counts for the current year, but also by counts for all previous years. The results of the HBM yielded less variable estimates of escapement than did ad hoc or year-by-year model estimates. The HBM represents a standardized approach to estimate missing counts and total escapement and eliminates the need for ad hoc estimates of missing counts. The model also provides managers with a measure of uncertainty around estimates of escapement and around estimates of hyper-parameters to define run curves in subsequent years with incomplete fish counts.