A suite of extensions to a nonequilibrium surplus-production model

Cooperative Unit for Fisheries Education and Research Rosenstiel School of Marine and Atmospheric Science University of Miami. 4600 Rickenbacker Causeway. Miami. Florida 33149 Abstract. -Surplus-production models, because of their simplicity and relatively undemanding data needs, are attractive tools for many stock assessments. This paper reviews the logistic production model, starting with the basic differential equation and continuing with a description ofthe model development without the equilibrium assumption. It then describes several extensions, including "tuning" the model to a biomass index; partitioning fishing mortality by gear, time, or area; and making projections. Computation of confidence intervals on quantities of interest (e.g. maximum sustainable yield (MSY), effort at MSY, level ofstock biomass relative to the optimum level) can be done through bootstrapping, and the bootstrap can also be used to construct nonparametric tests of hypotheses about changes in catchability. To fit the model, an algorithm that uses a forward solution of the population equations can be implemented on a small computer. An example of the utility of surplus-production models (illustrating several of these extensions) is given. The example is loosely based on swordfish <Xiphias gladius) in the North Atlantic Ocean, but is not intended to describe the actual status ofthat stock. Despite the prevalence ofage-structured population models, surplusproduction models-which generally do not incorporate age structure-remain useful for analysis of fish population dynamics. These models are of particular value when the catch cannot be aged, or cannot be aged precisely, and therefore agestructured models cannot be applied. Surplus-production models are also useful as a complement to age-structured models, providing another view of the data and the fisheries. An especially appealing aspect ofproduction models is their simplicity; from a scientific point of view, this makes exploration oftheir properties easier; from a management point of view, it makes their results easier to present and understand (Barber, 1988). In this paper, I show that another benefit of these models' simplicity is that model extensions are easily made. Examples ofsuch extensions include modeling several simultaneous or sequential fisheries on the same stock, "tuning" the model to a biomass index (as is often done in age-structured models; e.g. the CAGEAN model of Deriso et aI., 1985; the CAL model of Parrack, 1986; the ADAPT model ofGavaris, 1988), modeling changes in catchability or population characteristics (e.g. carrying capacity), and estimating missing values of fishing effort. Many of these extensions have not been presented before. The comprehensiveness of a production model can be further increased by introducing another extension: computation of nonparametric estimates of variability in the results. These can be obtained by bootstrapping, and can be used both to describe the results more completely and to learn more about the model's behavior under a variety of circumstances. After reviewing the formulation of the simplest surplus-production model (the logistic model), a number of extensions to the model are described. An example, loosely based on swordfish, Xiphias gladius, in the North Atlantic Ocean, is presented to illustrate typical results from the model and the use ofmany ofthe extensions. The example, which is not intended to be an assessment of that stock, should not be used to make inferences about stock status.