Quantifying the Growth of Female Pacific Hake (Merluccius productus): An Example of Measuring Uncertainty and Bias in Non-linear Parameter Estimation

Abstract

Estimates of size-at-age are commonly reported in fisheries studies, but statistical uncertainty and intrinsic variability in the growth parameters are less frequently examined. We examine these questions using recently-developed statistical methods for quantifying uncertainty and bias in parameter estimates for nonlinear models with independent and additive Gaussian errors. We also describe diagnostic methods to determine when the usual method for examining parameter uncertainty, linearization, is unacceptable. Both our review and our approach to uncertainty are generally applicable to nonlinear estimation, and not solely restricted to growth models. We illustrate our approach with length-at-age data for female Pacific hake (Merluccius productus) from Georgia Strait, British Columbia. Between-year variation in somatic growth seems to be restricted to the two von Bertalanffy growth parameters K and L∞. Mean asymptotic length declined by about 10% since the late 1970's while the parameter K nearly tripled in value. Closer examination showed that the decline in somatic growth was restricted to the maximum size attained. We argue that the changes are most consistent with selective removal of the largest individuals from the population by the fishery, rather than a response of growth rates to either environmental or density-dependent factors.