Optimum control of a bioeconomic system. The yellowfin tuna (Thunnus albacares) fishery in the eastern Pacific ocean

The present value objective function of the fishery is maximized with the use of optimum control theory and information from 40,000 fishing sets of the Mexican tuna fishing fleet dating from 1980 to 1990. These data were used to obtain standard fishing days (SFD) as a measure of effort of the international fleet in the eastern Pacific Ocean. The Schnute model (1977) was modified and population growth rate, environmental carrying capacity and catchability coefficient were estimated. Operative costs, severa1 prices for the tuna caught and discount rates were used to obtain optimum biomass level (state variable) and effort (control variable). A constant catchability coefficient and a variable one, as an inverse function of biomass level, were considered. In any case, the effort being applied recently is almost double with rcspect to the economic optimum calculated in this work

Analysis of the fishing strategies of the yellowfin tuna (Thunnus Albacares) Eastern Pacific Fishery Based on Monte Carlo simulations of a density-dependent matrix model

 The effect of the fishing effort on the age structure has not been considered in many models. To consider both uncertainty and age structure, a density-dependent matrix model based on a discrete time-form of the logistic equation using the Leslie matrix was employed, with Monte Carlo simulations. A total of 66 different fishing scenarios were structured for the yellowfin tuna (Thunnus albacares) in the eastern Pacific. The experimental design consisted of 400 ten-year runs for each of the 66 fishing scenarios, considering each age-class. The uncertainty was considered for natural mortality, environmental carrying capacity, total number of sets, catch per set of each type (on dolphins, schools and logs), and recruitment. The age structure had the greatest relative importance in the model, according to sensitivity analysis. One way of controlling the age structure is directing the fishing effort towards the three types of fishing sets. The fishing strategies that presented the highest success probability values (percentage of iterations above arbitrary levels) were those with dominance of dolphin-sets, a small amount of school-sets and almost no log-sets. The best fishing strategies obtain high success probabilities for the especially susceptible age-classes and total biomass. These fishing strategies assure higher total catches, minimum juvenile tuna discards and lower incidental catches. The model predicts a 32% difference in the catches between non-dolphin-sets and dolphin-sets

Numeric simulation of fishing effort and strategies (stochastic and cartesian) using cellular automata

A cellular automaton (CA) model is developed to analyze the behavior of fishermen in terms of belonging to a group that exchanges information on fishing and the personal aspect of decision making, defining the fishermen as cartesian or stochastic. This model aims to be the generic structure for a subsequent specific model suitable for a real fishery, and shows how the previously described behavior can be represented in a CA. The results show that, in a simulated world, positive effects are observed in terms of capture or rate of capture, the grouping, and the stochastic behavior in the event of resource scarcity. Also shown is how the behavior of including an explorer has the potential of generating benefits, as well as being risky. If the fishing is good, an independent boat benefits more than the group explorer when sharing this information with the other members of the group (cooperation-competition effect); however, in an adverse situation, the group explorer is not as affected as the independent boat.