THE IMPORTANCE OF TESTING MODELS

13.8 THE IMPORTANCE OF TESTING MODELS

Fishery science has a long tradition of modelling the dynamics of exploited stocks. It was probably one of the first areas of ecology where mathemati- cal models were used extensively, and Volterra was stimulated by market data from the Adriatic fisheries to produce his famous equations relating predator and prey abundances (Kingsland 1985,

287 and see Chapter 10, this volume, equation 10.2). model describes the true process. This means that

Choosing the Best Model for Assessment

The work of Beverton and Holt (1957) was a stun- the scientist is not clear about the process that is ning creation but the models produced were only bringing about the observed events. This could partly confronted by data. Some of the key models, lead to recommendations which would attempt to such as the logistic model of population growth manipulate the wrong variable. For example, in a and the yield-per-recruit model of Beverton and typical tropical country one may observe hundreds Holt (1957), have not been through a proper cycle of stocks of commercial importance, and the con- of prediction and testing against the data.

cept of fish stock assessment becomes cloudy. It is Some fishery biologists, such as Walters (1986), impossible to collect data for, say, 200 stocks in a have proposed ways in which management meas- developing country. At times, fisheries biologists ures could be designed so as to gain information can be tempted to question the usefulness of fish about the predictive capacities of models. So- stock-assessment methodology in general as a tool called adaptive management recognizes that it is for fisheries management in tropical countries often not possible to decide which is the correct (Mahon 1997). model of an exploited population. Walters (1986)

When choosing a model that relies on the con- proposed that managers should be prepared to use cept of individual stocks with an age structure, it is the fishery to obtain information that would allow obviously important to consider the number of differentiation between models. After an initial stocks as well as the problems involved in the assessment, a number of models would be pro- definition of the stocks. Definition of a stock can posed, each of which would make different predic-

be problematic (Begg et al. 1999), and one can ques- tions about how the fishery would influence the tion the usefulness of methods such as VPA when stock. The area of the fishery should then be split faced with a fisheries system with a large number up and different management regimes imposed in of badly defined stocks. Even in temperate and each. This differential exploitation pattern could polar waters, with relatively few stocks, we face se-

be used to test predictions deriving from the differ- vere problems in defining the stocks. ent models. Eventually all but one model would be thrown out as being inadequate. A problem with the approach is that managers are reluctant to

13.9 CONCLUSIONS

manipulate fisheries in a way that could lose fish- ers money. This discussion points up the fact that This chapter outlines the basic structure of models advising on which model to use has to be done that have been applied to fisheries and discusses with extreme caution. A model needs to be chosen the ways in which models can be selected and because it accounts for the data available, not applied. A key theme is that each situation will because it is well known and mathematically require the fisheries scientist to have a deep tractable. This means that a fishery scientist needs knowledge of the biology of the species or eco- to be intimately knowledgeable about the fishery system in question and have the ability to tailor

he or she is working with, know its biology and models to suite the particular conditions. Our create new elements of a model to deal with the discussion of the objectives of models has been particular circumstances observed (Mangel and general but in most cases the output from a model Clark 1988).

is in the form of some type of reference point that In general we do not advocate the use of only can be used to design management measures. The one model, but recommend that different models simplest to grasp might be Maximum Sustainable are tested on the same data set (see also Walters Yield, a concept that has been through several 1986; Hilborn and Mangel 1997). A problem often deaths and reincarnations during its existence encountered is that several models can give the (Larkin 1977; Mace 2001; Punt and Smith 2001). same answer (Schnute and Richards 2001) and Reference points are discussed further in Smith there is insufficient data to determine which et al. (1993), Caddy and Mahon (1995), Quinn and

Chapter 13

Deriso (1999) and Gislason (1999). A particular problem with fishery models is that they are not often tested properly. Models of population growth, such as the logistic, which underlies the surplus production model of Schaefer, are rarely tested to determine if they describe properly the way in which biomass changes over time. It is ob- vious from what is known about the population dynamics of animal populations that the logistic equation is not a good model, mainly because it is deterministic and does not account for time lags inherent in the life histories of most animal species. Yet despite this, logistic models are still used in fisheries. Future work must focus on pro- ducing tested models of population dynamics and fishery scientists must wean themselves away from the so-called traditional models. We need to escape from the legacy of the past.

In this chapter we also try to provide some guid- ance for choosing a model. The first step is to check whether the minimum requirement of the objec- tive is met by the available data. Then check if there is sufficient funding and manpower as well as time available for the collection of additional data specific to the model. If the objectives are not met or are unachievable then the objectives should be changed. The maximum amount of information should be extracted from the data and the model used must be appropriate for the type and quality of data used. It is always important to make the model as simple as possible with the minimum number of parameters and equations, and one should not invent new equations unless they are really needed. Parameters should be estimated by standard methods, preferably using easy-to-obtain commercial software. When a key parameter can- not be estimated, try to make a plausible guess at it rather than ignoring it. All interacting com- ponents of the system should be included. For example, include in the model spatial and tem- poral factors when these are important for the output. Make the model multispecies and/or multi-fleet whenever these components are important for the output, as they usually are. Wherever possible use bioeconomics to model the behaviour of fishers, such as their discard practice. Try to make a deterministic as well as a stochastic

version of the model. The deterministic version is mainly used to understand and check the stochas- tic version. In general terms, match the model to the needs of the user.