Dynamics of Age and Size Composition in a Population Subject to Size-Selective Mortality: Effects of Phenotypic Variability in Growth

Abstract

A stochastic model for the dynamics of age and size distributions in a population subject to size-selective mortality is derived. Growth variability results from both environmental disturbances and intrinsic differences in the expected asymptotic length of the individuals. The selective harvest of larger fish results in a selective removal of intrinsically faster-growing individuals. Estimation trials indicate that sources of growth variability are difficult to identify from standard catch information. The implications of this uncertainty in a yield per recruit analysis are explored, using parameter estimates of Pacific halibut (Hippoglossus stenolepis). At moderate fishing levels yield per recruit increased with the amount of intrinsic variability, but the trend reversed at higher fishing rates. Fishing mortality for maximum expected yield per recruit decreased when the contribution of intrinsic differences to growth variability was larger. Mean spawning biomass was relatively insensitive to the level of phenotypic variability when the population was under moderate-to-heavy exploitation. A standard assumption of yield per recruit analysis, namely, that age-specific selectivities and catch weights are constant, independent of the fishing mortality rate, may result in biassed estimates of mean spawning biomass per recruit, and serious overestimation of optimal fishing levels.