Abstract
Users of stock production models assume that a time series of catch-per- effort data reflects changes in the size of a self-sustaining biological population. This assumption is often violated in analyses of fisheries that have undergone changes in the areal coverage of the fishing fleet because the fraction of the population that is available to fishing also changes. Furthermore, the problem is aggravated when there is biomass transfer (in the form of migration) between the exploited and unexploited segments of the population. We present a general production model that can be used to understand the dynamics of equilibrium population size and yield as functions of fishing mortality and exploitable population fraction. We then develop two simple subsets of this model in which biomass transfer is either nil or high between the unexploited and exploited fractions, and we discuss methods to estimate the models' parameters given data on catch, effort, and area. The application of the models is illustrated with data on the fishery for yellowfin tuna Thunnus albacares in the eastern Pacific.