A Catch-at-Length Analysis that Incorporates a Stochastic Model of Growth

Abstract

A length-structured population model, which incorporates von Bertalanffy growth, is used to describe changes in population abundance over time. The model is incorporated into a catch-at-length algorithm that uses a nonlinear least squares approach to estimate relative abundance, fishing mortality, selectivity, and the von Bertalanffy growth parameters L∞ and k. The algorithm is applied to a simulated data set for Pacific cod (Gadus macrocephalus) and to catch data on Pseudotolithus typus and Decapterus russellii. The parameter estimates of Pacific cod obtained from this algorithm were comparable with the values that were originally used to simulate the data. Although the catch data of P. typus did not exhibit the full range of sizes present in the population due to differential vulnerability of the population to the fishery, the estimates of L∞ and k reflect the growth over the entire size range of the population. Other population estimates for P. typus were in agreement with observed biological information. The estimated growth parameters L∞ and k of D. russellii showed some discrepancy with the information available on mature individuals present in this fishery but appeared to adequately represent year 1 growth. The estimated population and exploitation parameters fit the observed catch-at-length. Estimates made with the catch-at-length approach can be improved by using auxiliary information that may be available on abundance, fishing effort, recruitment, and growth.