Dynamics of a migratory fish population with applications to the management of sablefish in the Northeast Pacific Ocean

Abstract

Quantitative models are developed to describe the dynamics of an age-structured migratory fish population subject to exploitation. Migration rates are quantified, alternative ways of apportioning harvest among areas are examined, and the dynamics of a migratory population is described within the general theoretical framework of a projection matrix model. Application of these modeling efforts is within the context of the sablefish (Anoplopoma fimbria) fishery in the North Pacific Ocean. A Markov model that includes natural and fishing mortality, tag reporting and shedding rates, and migration is used to quantify migration rates of tagged sablefish among fishery regulatory areas. Estimates of annual migration rates out of an area are in the range 19-69% for small (<57 cm fork length (FL)), 25-72% for medium (57-66 cm FL), and 27-71% for large (>66 cm FL) sablefish. The predominant direction of migration along the continental slope is eastward for large sablefish and westward for small sablefish. Most estimates of migration are precise, unconfounded, and robust to perturbations of input constants. An age-structured model that includes migration is constructed to examine harvest policies for sablefish. Areal estimates of yield-per-recruit depends on the geographic distribution of recruitment. In general, when evaluated under the current annual exploitation rate of 10%, apportioning harvest among areas based on areal estimates of biomass and apportionment based on the steady-state distribution of biomass give similar results. A policy of apportionment based on a weighted moving average of areal estimates of available biomass is preferred to others. This policy adapts to current information about geographic distribution of biomass, reduces the effects of measurement error, and does not require estimates of migration probabilities for implementation. The reproduction, mortality and migration of an age-structured fish population are incorporated into a projection matrix model. The model is parameterized to include areal specificity in the stock-recruitment relationship and events such as larval dispersion that is decoupled from local reproduction. For the sablefish fishery where direction of movement is age dependent, fishing at a common rate among areas may be detrimental to the population in a given area. Area-specific fishing strategies can be devised to meet management objectives such as maintenance of areal spawning potential.