Theory and Practical Exercises of System Dynamics      See the book

4.4. THE FISHERY OF SHRIMP A simulation model with Vensim The fishery of shrimp in Mexico is the third more important after mojarra and ostion in the coast of the Gulf of Mexico. In the Pacific coast it is only surpassed by the tuna and the sardine. The economic value of the captures of shrimp makes it the most important of the country since it contributes 40% of the income. The boats of shrimp fishers are 66% of the present fishing fleet, and in 1970 they represented 82% In Sonda de Campeche, at the south of the Gulf of Mexico, the most important specie is the pink shrimp. In seventies they were captured more than 20,000 tons per year. But the captures diminished constantly and at the moment are captured 4,000 tons per year. The fishermen accuse PEMEX, the state oil company, to cause to the collapse when occupying their areas of fishing and to contaminate, although the fishing becomes more to the north and the sea currents concentrate the contamination to the south. Although the estimations point clearly at the overexploitation, between the investigators has arisen an interesting controversy. One of the best investigators of the country suggested that if the number of boats had diminished, mortality by fishing also must be reduced, and, if the captures has not increased, the population is hidden somewhere. If the population has diminished it must be by another cause. He supported its argument with the model of Schaeffer (the same of Verhulst-Pearl but applying biomass instead of the number of individuals and including the fishing) assuming fishery in balance (the capture equals the population growth). In this model if the capture activity is reduced, measured in number of boats, the population of shrimp increases. Nevertheless, it is possible to be argued that the boats of now are more powerful than in the middle of the seventy, the networks are greatest, and the trips are longest (60 days now against 15 days then). The population of shrimp is concentrated now in few places and is more vulnerable to the fleet. Now exits only a fourth part of the historical maximum number of boats. In spite of that the model of Schaeffer is used commonly. More than the model itself, the problem could be their use in this case. It is difficult to work with this model, based in the balance, when observed data shown strong changes, using this model is equivalent to assume that the observed capture has been equal to the population growth. That assumption became in the days in which, without computers, taking it can simplify process to consider the parameters, allowing to make a regression. At the moment, many authors recommend to leave that assumption, and use methods not based in a balance (that simply accept that the captures can be different from the population growth). The second problem is that that this model does not say anything to us of how reacts the fleet to the changes in the fishing (tones). Hilborn and the Walters (1992) proposed a modification that includes the modification of the effort in agreement with the rent (net gain): When the total income is positive new boats enter in the fishery, if it is negative the boats leave this fishery, both at a speed determined by k. When the number of boats diminishes the population of shrimp increases and vice versa. This could cause oscillations in the population of shrimp, in the fishery, and in the effort.

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