Abstract. Surplus-produc- 



tion models, because of their sim- 

 plicity and relatively undemanding 

 data needs, are attractive tools for 

 many stock assessments. This pa- 

 per reviews the logistic production 

 model, starting with the basic dif- 

 ferential equation and continuing 

 with a description of the model de- 

 velopment without the equilibrium 

 assumption. It then describes sev- 

 eral extensions, including "tuning" 

 the model to a biomass index; par- 

 titioning fishing mortality by gear, 

 time, or area; and making projec- 

 tions. Computation of confidence 

 intervals on quantities of interest 

 (e.g. maximum sustainable yield 

 (MSY), effort at MSY, level of stock 

 biomass relative to the optimum 

 level) can be done through boot- 

 strapping, and the bootstrap can 

 also be used to construct nonpara- 

 metric 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 ex- 

 ample is loosely based on swordfish 

 (Xiphias gladius) in the North At- 

 lantic Ocean, but is not intended 

 to describe the actual status of that 

 stock. 



A suite of extensions to a 

 nonequilibrium surplus-production 

 model* 



Michael H. Prager 



Miami Laboratory. Southeast Fisheries Science Center 



National Marine Fisheries Service. NOAA 



75 Virginia Beach Drive, Miami, Florida 33149 



Cooperative Unit for Fisheries Education and Research 

 Rosenstiel School of Marine and Atmospheric Science 

 University of Miami, 4600 Rickenbacker Causeway, Miami, Florida 33149 



Despite the prevalence of age-struc- 

 tured population models, surplus- 

 production models — which gener- 

 ally do not incorporate age struc- 

 ture — 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 age- 

 structured models cannot be ap- 

 plied. 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 of production models is their 

 simplicity; from a scientific point of 

 view, this makes exploration of their 

 properties easier; from a manage- 

 ment point of view, it makes their 

 results easier to present and under- 

 stand (Barber, 1988). 



In this paper, I show that another 

 benefit of these models' simplicity 

 is that model extensions are easily 

 made. Examples of such extensions 

 include modeling several simulta- 

 neous 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 al., 



1985; the CAL model of Parrack, 

 1986; the ADAPT model of Gavaris, 

 1988), modeling changes in catch- 

 ability or population characteristics 

 (e.g. carrying capacity), and esti- 

 mating missing values of fishing ef- 

 fort. Many of these extensions have 

 not been presented before. 



The comprehensiveness of a pro- 

 duction model can be further in- 

 creased by introducing another ex- 

 tension: computation of nonpara- 

 metric 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 vari- 

 ety of circumstances. 



After reviewing the formulation 

 of the simplest surplus-production 

 model (the logistic model), a num- 

 ber of extensions to the model are 

 described. An example, loosely based 

 on swordfish, Xiphias gladius, in 

 the North Atlantic Ocean, is pre- 

 sented to illustrate typical results 

 from the model and the use of many 

 of the extensions. The example, which 

 is not intended to be an assessment 

 of that stock, should not be used to 

 make inferences about stock status. 



Manuscript accepted 18 October 1993 

 Fishery Bulletin 92:374-389 (1994) 



Contribution MIA-92/93-58 of the Miami Laboratory, Southeast Fisheries Science Center, 

 National Marine Fisheries Service. 



374 



