IS FISHING COMPATIBLE WITH ENVIRONMENTAL CONSERVATION: A STOCHASTIC MODEL WITH AN ELEMENT OF SELF‐PROTECTION

Abstract The purpose of this paper is to introduce the impact of fishing activity on a marine ecosystem. The fishing activity is considered not only through annual harvest but also through a second component, called the degree of protection of the fishery environment. This characterizes the environmental impact of fishing. A stochastic dynamic programming problem is presented in infinite horizon, where a sole owner seeks to maximize a discounted expected profit. The main hypothesis states that the stock–recruitment relationship is stochastic and that both components of the fishing activity have an impact on the probability law of the state of the fishery environment. The optimal fishing policy is obtained and compared with standard models. This optimal policy has the following properties: is not a constant escapement policy and indicates an element of self‐protection by the fishery manager. The paper ends with a discussion on the existence of degrees of protection of the fishery environment that take into account the environmental conservation and preservation of economic activity.     

OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.     

MIXED-STOCK VS. TERMINAL FISHERIES: A BIOECONOMIC MODEL

ABSTRACT. This paper develops a bioeconomic model of a fishery conducted on several stocks, a large stock capable of supporting a commercial fishery, and one or more smaller stocks which could be driven to extinction at harvest rates that the larger stock can sustain. The model permits a shifting of effort from a mixed-stock fishery to single-stock fisheries. Such a shift could save the weaker stocks from extinction, but the model highlights economic incentives to reject this option. This points to a fundamental conflict between the preservation of biodiversity and economic pressures to maximize profits. This fundamental conflict has in turn important consequences in current debates over the restructuring of major fisheries including those directed at Pacific salmon.     

EXOGENOUS SHOCKS AND MARINE RESERVES

Abstract The impact on the value of a fishery from exogenous shocks is investigated. Part of the habitat is protected by a marine reserve, while the remaining fishery is managed by optimal, total allowable catch quotas. Shocks of different, spatial nature and with different probability distributions are investigated. The results suggest that reserves are of minor interest as a management tool when shocks affect the stock uniformly. Reserves may substantially enhance the value of the fishery when shocks are nonuniformly spatially distributed.     

Stabilizing management of fluctuating resources

We consider a resource management problem in which the management objective is to minimize fluctuations in resource stocks. Stabilizing management policies constitute the designing of memoryless state feedback control strategies for a discrete time resource model which contains unknown but bounded fluctuations. We also show that the problem of maximizing sustainable yield in an uncertain fishery can be considered as the problem of stabilizing of the stock level.The paper corresponds to an invited talk at the 14th Symposium on Operations Research, Ulm, September 6–8, 1989.The support by Yrjö Jahnsson Foundation is gratefully acknowledged.This work was supported by NSF and AFOSR under grant ECS 8602524.     

THE FAO PRECAUTIONARY APPROACH AFTER ALMOST 10 YEARS: HAVE WE PROGRESSED TOWARDS IMPLEMENTING SIMULATION‐TESTED FEEDBACK‐CONTROL MANAGEMENT SYSTEMS FOR FISHERIES MANAGEMENT?

ABSTRACT. It is almost ten years since the FAO Technical Consultation on the Precautionary Approach to Capture Fisheries took place in Lysekil, Sweden. One outcome from this Technical Consultation was a set of guidelines on the precautionary approach to capture fisheries and species introductions. These guidelines include the need to incorporate harvest control rules in management plans. Harvest control rules should specify what action is to be taken when specified deviations from the operational targets and constraints are observed. The specification should include minimum data requirements for the types of assessment methods to be used for decision‐making. Combinations of harvest control rules, assessment methods and data collection schemes are referred to as management procedures. It is now well‐recognized that using management procedures is likely to lead to improved conservation of fishery resources, and that they should be evaluated to assess whether they are likely to achieve the goals for fishery management given the types of uncertainties that are likely to frustrate this venture. In general, evaluation of management procedures has been based on simulation modeling. This paper reviews the progress that has been made in various fisheries jurisdictions in terms of implementing management procedures, and why and where it has proved difficult or even impossible to implement management procedures.     

IMPACTS OF RECREATIONAL FISHING ON THE COMMERCIAL SECTOR: AN EMPIRICAL ANALYSIS OF ATLANTIC MACKEREL

There are often tensions between recreational and commercial uses of marine fisheries. The Atlantic mackerel along the coast of the United States and Canada is one such fishery. Although recreational catch is only a small percent of total catch, it has been suggested that recreational use be incorporated into a broad management scheme for the fishery. This paper measures the costs domestic commercial fishermen incur from the recreational harvest of Atlantic mackerel. The results indicate that the domestic commercial fishery, which takes only a small portion of total commercial catch, would see no significant gain from limiting recreational fishing. An earlier version of this paper was presented at the AERE Workshop on Sport and Commercial Fisheries. Participants at that conference, anonymous referees, and Peter Berck offered valuable suggestions which improved this paper. Any errors are my own.     

Evolutionary dynamics may eliminate all strategies used in correlated equilibrium

We show on a 4×4 example that many dynamics may eliminate all strategies used in correlated equilibria, and this for an open set of games. This holds for the best-response dynamics, the Brown–von Neumann–Nash dynamics and any monotonic or weakly sign-preserving dynamics satisfying some standard regularity conditions. For the replicator dynamics and the best-response dynamics, elimination of all strategies used in correlated equilibrium is shown to be robust to the addition of mixed strategies as new pure strategies.     

THE EFFECTS OF DIFFERENT STRATEGIC VARIABLES IN NONCOOPERATIVE FISHERIES GAMES

Abstract In this paper, we use stock size, harvest quantity, and fishing effort as strategic variables. We model a two‐agent noncooperative fishery game, where the agents (nations) harvest a common fish stock. The planning horizon is infinite. The model is solved successively using one instrument at a time as the strategic variable in the game. The net present values of fishing and the escapement stock level from the three different models are compared to show how the choice of variables affects the results. The choice of strategic variable is not a trivial one, as the results are shown to be sensitive to the discounting, the stock's rate of growth, and the assumptions about the distribution of the fish in response to harvesting.     

HARVESTING A TWO-PATCH PREDATOR-PREY METAPOPULATION

ABSTRACT. A mathematical model for a two-patch predator-prey metapoplation is developed as a generalization of single-species metapopulation harvesting theory. We find optimal harvesting strategies using dynamic programming and La-grange multipliers. If predator economic efficiency is relatively high, then we should protect a relative source prey subpopulation in two different ways: directly, with a higher escapement of the relative source prey subpopulation, and indirectly, with a lower escapement of the predator living in the same patch as the relative source prey subpopulation. Numerical examples show that if the growth of the predator is relatively low and there is no difference between prey and predator prices, then it may be optimal to harvest the predator to extinction. While, if the predator is more valuable compared to the prey, then it may be optimal to leave the relative exporter prey subpopulation unharvested. We also discuss how a ‘negative’ harvest might be optimal. A negative harvest might be considered a seeding strategy.     

IN-SEASON FISHERY MANAGEMENT: A BAYESIAN MODEL

A Bayesian model is presented for optimizing harvest rates on an uncertain resource stock during the course of a fishing season. Pre-season stock status information, in the form of a “prior” probability distribution, is updated using new data obtained through the operation of the fishery, and harvest rates are chosen to achieve a balance between conservation concerns and fishing interests. A series of fishery scenarios are considered, determined by the stock size distribution and the timing distribution; the uncertainty in the fish stock is seen to have a rather complex influence on optimal harvest rates. The model is applied to a specific example, the Skeena River sockeye salmon fishery.     

THE VALUE OF SHORT‐RUN CLIMATE FORECASTS IN MANAGING THE COASTAL COHO SALMON (ONCORHYNCHUS KISUTCH) FISHERY IN WASHINGTON STATE

ABSTRACT. . In recent years our understanding of the intricate connections between climate variability, marine and freshwater environmental conditions and the responses of fish stocks has improved considerably. With predictable relationships between the environment and stock abundance, fishery managers should be able to forecast variation in stock survival and recruitment. Such forecasts present an opportunity for increasing the economic value of fisheries and for achieving other management objectives, such as stock conservation and maintenance of population diversity. After describing a 4‐step framework for addressing the question ‘What is a forecast worth?’ in a fishery decision‐making context, we introduce the management system for Washington's coastal coho salmon (Oncorhynchus kisutch) fishery. Then we apply the 4‐step framework to estimate the value of improved run size forecasts in the annual harvest management of coho salmon in Washington State. Our principal analytical tool is a stochastic simulation model that incorporates the main characteristics of the fishery. The paper concludes with a discussion of opportunities and constraints to the use of climate‐based forecasts in fishery management on various spatial and temporal scales, and we consider the challenges associated with forecasting variations in fish stock size caused by shifts in climate and related ocean conditions.     

Resource allocation in the North Sea demersal fisheries: A goal programming approach

The management of a fishery is a complex task generally involving multiple, often conflicting, objectives. These objectives typically include economic, biological and social goals such as improving the income of fishers, reducing the catch of depleted species and maintaining employment.Multicriteria decision making (MCDM) techniques appear wellsuited to such a management problem, allowing compromises between conflicting objectives to be analysed in a structured framework. In comparison to other fields, such as water resource planning, forestry and agriculture, there have been few applications of MCDM to fisheries.In this paper, a goal programming model of the North Sea demersal fishery is presented. The model is used to demonstrate the potential applicability of this type of approach to the analysis and development of fisheries management plans with multiple objectives. Alternative scenarios are considered for the problem, and tradeoffs between given objectives are also highlighted and discussed.     

Determination of a harmonic function with minimal gradient deviation

We find a function u(x, y) harmonic in the upper half-plane y>0 satisfying the conditions grad u(x₀,y₀) b|₂ min, . The solution of the problem is expressed in terms of the Poisson integral for the upper half-plane.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 32, 1990, pp. 55–57.     

Estimates of the visit time in the halfline for a stochastic process

We give lower and upper bounds for the visit probability of a stochastic process in the halfline.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 556–560, April, 1992.     

STEADY STATE AND INTERTEMPORAL MANAGEMENT MODELS FOR MARINE FISHERIES

Abstract Steady state and dynamic management models are developed for analyzing the Malaysian marine fisheries. These models originate from the theoretical concepts of the natural resource economics namely the open access, limited entry and the intertemporal fishery models. Such management models are deemed necessary because of the need to sustain the depleting resource and degrading environment. Marine fisheries had been managed under open access for a long time before government intervention took effect sometime during the 1960s. Open access and government intervention during the earlier phase of economic development contributed to the immediate pressure on fisheries. Community development programs geared to alleviate poverty among the fishermen apparently contradicted the effort of sustaining fisheries. Even today this fundamental management objective of sustainable development of fishery resource is not fully adhered to. This study suggests that ability to sustain fishery requires government intervention that can direct resource use to steady state or intertemporal optimal levels.     

A MODEL OF TROPICAL MARINE RESERVE‐FISHERY LINKAGES

ABSTRACT. The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. In this paper we examine the contribution of fully protected tropical marine reserves to fishery enhancement by modeling marine reserve‐fishery linkages. The consequences of reserve establishment on the long‐run equilibrium fish biomass and fishery catch levels are evaluated. In contrast to earlier models this study highlights the roles of both adult (and juvenile) fish migration and larval dispersal between the reserve and fishing grounds by employing a spawner‐recruit model. Uniform larval dispersal, uniform larval retention and complete larval retention combined with zero, moderate and high fish migration scenarios are analyzed in turn. The numerical simulations are based on Mombasa Marine National Park, Kenya, a fully protected coral reef marine reserve comprising approximately 30% of former fishing grounds. Simulation results suggest that the establishment of a fully protected marine reserve will always lead to an increase in total fish biomass. If the fishery is moderately to heavily exploited, total fishery catch will be greater with the reserve in all scenarios of fish and larval movement. If the fishery faces low levels of exploitation, catches can be optimized without a reserve but with controlled fishing effort. With high fish migration from the reserve, catches are optimized with the reserve. The optimal area of the marine reserve depends on the exploitation rate in the neighboring fishing grounds. For example, if exploitation is maintained at 40%, the ‘optimal’ reserve size would be 10%. If the rate increases to 50%, then the reserve needs to be 30% of the management area in order to maximize catches. However, even in lower exploitation fisheries (below 40%), a small reserve (up to 20%) provides significantly higher gains in fish biomass than losses in catch. Marine reserves are a valuable fisheries management tool. To achieve maximum fishery benefits they should be complemented by fishing effort controls.     

A MODEL FOR THE BIOECONOMIC EVALUATION OF MARINE PROTECTED AREA SIZE AND PLACEMENT IN THE NORTH SEA

ABSTRACT. The use of marine protected areas (MPAs) as a basic management tool to limit exploitation rates in marine fisheries has been widely suggested. Models are important in predicting the consequences of management decisions and the design of monitoring programs in terms of policy goals. However, few tools are available that consider both multiple fleets and ecosystem scale dynamics. We use a new applied game theory tool, Ecoseed, that operates within a temporally and spatially explicit biomass dynamics model, Ecopath with Ecosim, to evaluate the efficacy of marine protected areas in the North Sea in both ecological and economic terms. The Ecoseed model builds MPAs based on the change in values of predicted economic rents of fisheries and the existence value of biomass pools in the ecosystem. We consider the market values of four fisheries operating in the North Sea: a trawl fishery, a gill net fishery, a seine fishery, and an industrial (reduction) fishery. We apply existence values, scaled such that their aggregate is similar to the total fishery value, to six biomass pools of concern: juvenile cod, haddock, whiting, saithe, seals, and the collective pool ‘Other predators’ that include marine mammals. Four policy options were considered: to maximize the rent only; to maximize the existence values only; to maximize the sum of the rent and existence values; and, finally, to maximize the sum of the rent and the existence values, but excluding only the trawl fleet from the MPA. The Ecoseed model suggests that policy goals that do not include ecological considerations can negatively impact the rents obtained by the different fishing sectors. The existence values will also be negatively impacted unless the MPA is very large. The Ecoseed model also suggests that policy goals based solely on existence values will negatively impact most fisheries. Under policy options that included ecological considerations, maximum benefits were derived from an MPA that covered 25–40% of the North Sea, placed along the southern and eastern coasts. Finally, the Ecoseed model suggests that an exclusion of the trawl fishery only from the MPA can provide small‐to‐substantial positive impacts to most species and fleets; this relative impact depends on level of interaction between the trawl fleet and the other fleets target species (e.g., through bycatch).     

OPTIMAL RECOVERY OF A SHARED RESOURCE STOCK: A DIFFERENTIAL GAME MODEL WITH EFFICIENT MEMORY EQUILIBRIA

We consider an optimal two-country management of depleted transboundary renewable resources. The management problem is modelled as a differential game, in which memory strategies are used. The countries negotiate an agreement among Pareto efficient harvesting programs. They monitor the evolution of the agreement, and they memorize deviations from the agreement in the past. If the agreement is observed by the countries, they continue cooperation. If one of the countries breaches the contract, then both countries continue in a noncooperative management mode for the rest of the game. This noncooperative option is called a threat policy. The credibility of the threats is guaranteed by their equilibrium property. Transfer or side payments are studied as a particular cooperative management program. Transfer payments allow one country to buy out the other from the fishery for the purpose of eliminating the inefficiency caused by the joint access to the resources. It is shown that efficient equilibria can be reached in a class of resource management games, which allow the use of memory strategies. In particular, continuous time transfer payments (e.g., a share of the harvest) should be used instead of a once-and-for-all transfer payment.     

DO ACCURATE STOCK ESTIMATES INCREASE HARVEST AND REDUCE VARIABILITY IN FISHERIES YIELDS?

Abstract Fisheries managers normally make decisions based on stock abundance estimates subject to process, observation, and model uncertainties. Considerable effort is invested in gathering information about stock size to decrease these uncertainties. However, few studies have evaluated benefits from collecting such information in terms of yield and stability of annual harvest. Here, we develop a strategic age‐structured population model for a long‐lived fish with stochastic recruitment, resembling the Norwegian spring‐spawning herring (NSSH, Clupea harengus L.). We evaluate how uncertainties in population estimates influence annual yield, spawning stock biomass (SSB), and variation in annual harvest, using both the proportional threshold harvesting (PTH) and the current harvest control rule for NSSH as harvest strategies. Results show that the consequences of a biased estimate are sensitive to the harvest strategy employed. If the harvest strategy is suitably chosen, the benefits of accurate information are low, and less information about the stock is necessary to maintain high average yield. Reduced harvest intensity effectively removes the need for accurate stock estimates. PTH (a variant of the constant escapement strategy) with low harvest ratio and the current NSSH harvest control rule both provide remarkable stability in yield and SSB. However, decreased uncertainty will often decrease year‐to‐year variation in harvest and the frequency of fishing moratoria.