UW Aquatic & Fishery Sciences Quantitative Seminar

**Mark D. Scheuerell**^{1}, Casey Ruff^{2}

^{1}, Casey Ruff

^{2}

^{1}Fish Ecology Division, Northwest Fisheries Science Center

^{2}Skagit River System Cooperative

**
Using hierarchical Bayesian models for improved estimation of the stock-recruit dynamics for Pacific salmon
**

## Abstract

A variety of models exist to describe population dynamics in discrete time. For fishes such as Pacific salmon, Rickerâ€™s model is perhaps the most commonly used because of its relatively simple form, and the ease with which the parameters are estimated. In practice, however, a number of necessary model assumptions are typically violated because the independent variable is measured with error (e.g., the number of spawners is an expansion from redd- or weir-counts); unaccounted for error exists in the response variable because age-composition data are typically non-exhaustive and therefore imprecise; and the model is treated like an observation model, but it is meant to be a process model. Furthermore, missing data lead to incomplete estimates of recruits and subsequent loss of data and power. Although recognition of these problems is not new (e.g., Hilborn & Walters 1992), implementation of better approaches has been slow to gain traction. Therefore, we show how a hierarchical Bayesian model can be used instead to provide a more complete assessment of data and parameter uncertainty, as well as address missing data. As an example, we apply the model to data for steelhead trout (Oncorhynchus mykiss) from the Skagit River in western Washington. Specifically, we use 33 years (1978-2010) of escapement estimates (1996, 1997 missing) and age composition from a terminal fishery (1984, 2000 missing). For comparison, we also show how estimates of intrinsic productivity from the standard least-squares approach are biased high and overly precise, which poses unique problems for the management of at-risk species at low abundance.