INTEGRATING MARINE PROTECTED AREAS INTO MODELS FOR FISHERY ASSESSMENT AND MANAGEMENT

ABSTRACT. Marine protected areas (MPAs) have been proposed as an insurance policy against fishery management failures and as an integral part of an optimal management system for some fisheries. However, an incorrectly designed MPA can increase the risk of depletion of some species, and can reduce the value of the system of fisheries it impacts. MPAs may alter structural processes that relate fishery outcomes to management variables and thereby compromise the models that are used to guide decisions. New models and data gathering programs are needed to use MPAs effectively. This paper discusses the motivations and methods for incorporating explicitly spatial dynamics of both fish and fishermen into fishery models so that they can be used to assess spatial policies such as MPAs. Some important characteristics and capabilities which these models should have are outlined, and a topical review of some relevant modeling methodologies is provided.     

OPTIMAL-SUSTAINABLE MANAGEMENT OF MULTI-SPECIES FISHERIES: LESSONS FROM A PREDATOR-PREY MODEL

ABSTRACT. In this paper we consider the meaning of sustainable resource management in multi-dimensional resources. Based on the principle of intergenerational fairness, we define fisheries management as sustainable if it does not lead to a decline in the net present value of the fishery. If sustainability, or intergenerational fairness, were held as an obligation by fishery managers, then the traditional present-value maximization objective would be constrained. Using numerical solutions to a simple predator-prey model, we explore how the optimal-sustainable management of this fishery would differ from management that seeks to maximize the present value of the benefits. General lessons regarding the meaning of sustainable fishery management are discussed.     

A STOCHASTIC FEEDBACK MODEL FOR OPTIMAL MANAGEMENT OF RENEWABLE RESOURCES

Analytical expressions for optimal harvest of a renewable resource stock which is subject to a stochastic process are found. These expressions give the optimal harvest as an explicit feedback control law. All relations in the model, including the stochastic process, may be arbitrary functions of the state variable (stock). The objective function, however, is at most a quadratic function in the control variable (yield). A quadratic objective function includes the cases of downward sloping demand and increasing marginal costs which are the most common sources for nonlinearities in the economic part of the model. When it is assumed that there is a moratorium on harvest for stock sizes below a certain level (biological barrier), it is shown that the barrier requirements influence the optimal harvest paths throughout.     

SUSTAINABLE YIELDS IN FISHERIES: UNCERTAINTY,RISK‐AVERSION,AND MEAN‐VARIANCE ANALYSIS

Abstract We consider a model of a fishery in which the dynamics of the unharvested fish population are given by the stochastic logistic growth equation Similar to the classical deterministic analogon, we assume that the fishery harvests the fish population following a constant effort strategy. In the first step, we derive the effort level that leads to maximum expected sustainable yield, which is understood as the expectation of the equilibrium distribution of the stochastic dynamics. This replaces the nonzero fixed point in the classical deterministic setup. In the second step, we assume that the fishery is risk averse and that there is a tradeoff between expected sustainable yield and uncertainty measured in terms of the variance of the equilibrium distribution. We derive the optimal constant effort harvesting strategy for this problem. In the final step, we consider an approach that we call the mean‐variance analysis to sustainable fisheries. Similar as in the now classical mean‐variance analysis in finance, going back to Markowitz [1952] , we study the problem of maximizing expected sustainable yields under variance constraints, and with this, minimizing the variance, e.g., risk, under guaranteed minimum expected sustainable yields. We derive explicit formulas for the optimal fishing effort in all four problems considered and study the effects of uncertainty, risk aversion, and mean reversion speed on fishing efforts.     

COMPARING PROACTIVE AND REACTIVE MANAGEMENT: MANAGING A TRANSBOUNDARY FISH STOCK UNDER CHANGING ENVIRONMENT

Environmental change in general, and climate change in particular, can lead to changes in distribution of fish stocks. When such changes involve transboundary fish stocks, the countries sharing the stock need to reconsider their harvesting policies. We investigate the effects of changing stock distribution on the optimal fishing policies in a two players’ noncooperative game. We compare reactive management, under which the manager ignores future distributional shifts (knowingly or unknowingly), with proactive management where the manager considers such shifts in his decisions. A dynamic programming model is developed to identify closed‐loop Nash strategies. We show that the role of two players is symmetric under reactive management but asymmetric under proactive management where managers anticipate future changes in stock ownership. The player losing the stock tends to harvest more aggressively compared to the player gaining the stock who acts more conservatively. Strategic interactions show tendency for complementary actions that can change abruptly during the ownership transition. The differences between management regimes vary from quantitative to qualitative; differences are minimal for stocks with little or no schooling, whereas highly schooling stocks may avoid collapse only under proactive management.