Recognizing structure in harvested populations dynamic pool models

The simple models of harvesting that have been described so far are known as 'surplus yield' models. They are useful as a means of establishing some basic principles (like MSY), and they are good for investigating the possible consequences of different types of harvesting strategy.

But they ignore population structure, and this is a bad fault for two reasons. The first is that 'recruitment' is, in practice, a complex process incorporating adult survival, adult fecundity, juvenile survival, juvenile growth, and so on, each of which may respond in its own way to changes in density and harvesting strategy. The second reason is that most harvesting practices are primarily interested in only a portion of the harvested population (e.g. mature trees, or fish that are large enough to be saleable). The approach that attempts to take these complications into

'dynamic pool' models recognize population structure

Figure 15.13 The dynamic pool approach to fishery harvesting and management, illustrated as a flow diagram. There are four main 'submodels': the growth rate of individuals and the recruitment rate into the population (which add to the exploitable biomass), and the natural mortality rate and the fishing mortality rate (which deplete the exploitable biomass). Solid lines and arrows refer to changes in biomass under the influence of these submodels. Dashed lines and arrows refer to influences either of one submodel on another, or of the level of biomass on a submodel or of environmental factors on a submodel. Each of the submodels can itself be broken down into more complex and realistic systems. Yield to humans is estimated under various regimes characterized by particular values inserted into the submodels. These values may be derived theoretically (in which case they are 'assumptions') or from field data. (After Pitcher & Hart, 1982.)

account involves the construction of what are called 'dynamic pool' models.

The general structure of a dynamic pool model is illustrated in Figure 15.13. The submodels (recruitment rate, growth rate, natural mortality rate and fishing rate of the exploited stock) combine to determine the exploitable biomass of the stock and the way this translates into a yield to the fishing community. In contrast to the surplus yield models, this biomass yield depends not only on the number of individuals caught but also on their size (past growth); whilst the quantity of exploitable (i.e. catchable) biomass depends not just on 'net recruitment' but on an explicit combination of natural mortality, harvesting mortality, individual growth and recruitment into catchable age classes.

There are many variants on the general theme (e.g. the submodels can be dealt with separately in each of the age classes and submodels can incorporate as much or as little information as is available or desirable). In all cases, though, the basic approach is the same. Available information (both theoretical and empirical) is incorporated into a form that reflects the dynamics of the structured population. This then allows the yield and the response of the population to different harvesting strategies to be estimated.

This in turn should allow a recommendation to the stockmanager to be formulated. The crucial point is that in the case of the dynamic pool approach, a harvesting strategy can include not only a harvesting intensity, but also a decision as to how effort should be partitioned amongst the various age classes.

A classic example of a dynamic pool model in action concerned the Arcto-Norwegian cod fishery, the most northerly of the Atlantic stocks (Garrod & Jones, 1974). The age class structure of the late 1960s was used to predict the medium-term effects on yield of different fishing intensities and different mesh sizes in the trawl. Some of the results are shown in Figure 15.14. The temporary peak after 5 or so years is a result of the very large 1969 year-class working through the population. Overall, however, it is clear that the best longer term prospects were predicted for a low fishing intensity and a large mesh size. Both of these give the fish more opportunity to grow (and reproduce) before they are caught, which is important because yield is measured in biomass, not simply in numbers. Higher fishing intensities and mesh sizes of 130 mm were predicted to lead to overexploitation of the stock.

dynamic pool models can lead to valuable recommendations...

Sadly, Garrod and Jones' recommendations were ignored by those with the power to determine fishing strategies. Mesh sizes were not increased until 1979, and then only from 120 to 125 mm. Fishing intensity never dropped below 45% and catches of 900,000 tonnes were taken in the late 1970s. Not surprisingly perhaps, surveys late in 1980 showed that these and other North Atlantic cod stocks were very seriously depleted as a result of overfishing. North Sea cod reach sexual maturity around the age of 4 years, but the species has been so heavily exploited that some 1 year olds are now harvested and 2 year olds are almost fully exploited, leaving only 4% of 1 year olds to survive to age 4 (Cook et al., 1997).

Rattans (climbing spiny palms whose stems are used for weaving and furniture making in Southeast Asia) are threatened with overexploitation in a similar way, with harvesters cutting stems too young and reducing their ability to resprout (MacKinnon, 1998).

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