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This application refers to the use of a group of models loosely based on the work of Thompson and Bell (1934). The models are essentially mathematical depictions of fisheries, or parts of fisheries. They are predictive, in providing estimates of the likely yields, catch rates, mean individual weights of the fish in the catches, stock biomass, etc., from changes in the fishing effort (or fishing mortality), size at first capture, fishing season and fleet composition. As such they form a direct link between fish stock assessment and fisheries management.

The analyses within the models proceed in the opposite direction to virtual population analysis (VPA) and cohort analysis. The latter seek to determine the number of fish that must have been present in the sea and the effort expended to account for a known sustained catch and catch composition. Output from VPA or cohort analysis can be used as input to Thompson and Bell analysis (Sparre and Venema, 1993). This approach, however, has not been adopted here.

There are three broad categories of Thompson and Bell analysis. In the agebased models the estimation of stock numbers, catches, etc., proceeds successively from the youngest to the oldest age classes. In the lengthbased versions the structuring is according to length classes. This is convenient for fisheries having highly selective gears, such as gillnets. Timebased models are the third category, often used in the case of short lived species, such as shrimp. In these the calculations proceed sequentially from one time period (e.g. month) to the next, which is useful when seeking to investigate the effects of seasonal fishery closures.

Thompson and Bell models are highly suited to spreadsheet application. Microsoft's spreadsheet package Excel in particular has a number of features, which are helpful for this purpose. These include routines for automatically creating tables, solving problems by iteration, and for imbedding charts. The purpose of this paper is to provide an introduction to simple Thompson and Bell analysis, and in the process to demonstrate these Excel features, assisted with reference to examples situations from the literature.

Key Features:
A simple Thompson and Bell Yield Analysis. The model provides estimates for the equilibrium yield (= catch weight), mean individual weight, catch rate, exploited biomass, and fishery profit, etc., from emplying different levels of fishing effort. This was achieved by keying alternate values for the fishing effort into cell G32, and recording the estimates for the output. The outputs are displayed in both table and chart form to the right of column P in Figure. These were created using the species Excel features.

Agebased Thompson and Bell model. The model contains a number of nonstandard features. The natural mortality rate from the time of settlement of the abalone to five months of age is treated separately to the mortalities applying in the remainder of life. This immediate postsettlement mortality is density dependent, and within the model it is given a unique valuefrom the literature. In respect to the latter periods of life the mortality rates decrease with age, according to the relationship given in Caddy (1991).

Lengthbased Thompson and Bell model. The model utilises two sets of values for the von Bertalanffy growth parameters L and K. This is very much a nonstandard feature of this application. The parameter values are based on a small quantity of length atage data, in which the ages were determined by counting what were presumed to be daily rings. The data could not be fitted with a single relationship, and hence it was decided to fit separate on Bertalanffy curves for fish above and below 52 cm in length.

Timebased Thompson and Bell model. In this application, each month has been subdivided into four intervals, with the observed monthly fishing efforts divided equally between them. The recruitment was assumed to occur at the beginning of the second, third and fourth intervals, in order to approximate continuous recruitment. The numbers of recruits in each month, and the number present at December 1, were determined independently from the model. This was done using the monthly catch and effort data and the estimate catchability coefficient, as described in the original paper.

System Requirements:
This application requires an IBM or 100% compatible microcomputer with standard peripherals. This workstation must work under DOS/Window 3.1 or higher and necessitates microsoft EXCEL. Release 5 or higher.

Statistics and Information Branch (FIAS)

Fisheries and Aquaculture Department
Food and Agriculture Organization of the United Nations
Viale delle Terme di Caracalla

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