Bayesian Catch Curve Analysis

Catch curves have been used to estimate survival and instantaneous mortality for fish and wildlife populations for many years. In order to better analyze catch curve data from the Apostle Islands population lake trout Salvelinus namaycush in Lake Superior, we develop a Bayesian approach to catch curve analysis. First, the proposed Bayesian approach is illustrated for a single catch curve and then extended to multiple years of data. We also relax the model assumption of a stable age distribution to allow random effects across years. The proposed models are compared with the traditional methods using the focused DIC. There are many potential advantages to the Bayesian approach over the traditional methods such as least squares and maximum likelihood, based on large sample theory. Bayesian estimates are valid for finite samples, and efficient numerical methods can be used to obtain estimates of instantaneous mortality. We conclude that many benefits can be obtained from the Bayesian approach to a single catch curve and to multiple years of data, such as closed-form variance estimates and the ability to both model and estimate the process variation of survival rates.