HARVESTING ECONOMIC MODELS AND CATCH‐TO‐BIOMASS DEPENDENCE: THE CASE OF SMALL PELAGIC FISH

Abstract In the case of small pelagic fish, it seems reasonable to consider harvest functions depending nonlinearly on fishing effort and fish stock. Indeed, empirical evidence about these fish species suggests that marginal catch does not necessarily react in a linear way neither to changes in fishing effort nor in fish stock levels. This is in contradiction with traditional fishery economic models where catch‐to‐input marginal productivities are normally assumed to be constant. While allowing for nonlinearities in both catch‐to‐effort and catch‐to‐stock parameters, this paper extends the traditional single‐stock harvesting economic model by focusing on the dependence of the stationary solutions upon the nonlinear catch‐to‐stock parameter. Thus, we analyze equilibrium responses to changes in this parameter, which in turn may be triggered either by climatic or technological change. Given the focus in this study on the case of small pelagic fish, the analysis considers positive but small values for the catch‐to‐stock parameter.     

AN INDICATOR FOR ECOSYSTEM EXTERNALITIES IN FISHING

Ecosystem externalities arise when one use of an ecosystem affects its other uses through the production functions of the ecosystem. We use simulations with a size‐spectrum ecosystem model to investigate the ecosystem externality created by fishing of multiple species. The model is based upon general ecological principles and is calibrated to the North Sea. Two fleets are considered: a “forage fish” fleet targeting species that mature at small sizes and a “large fish” fleet targeting large piscivorous species. Based on the marginal analysis of the present value of the rent, we develop a benefit indicator that explicitly divides the consequences of fishing into internal and external benefits. This analysis demonstrates that the forage fish fleet has a notable economic impact on the large fish fleet, but the reverse is not true. The impact can be either negative or positive, which entails that for optimal economic exploitation, the forage fishery has to be adjusted according to the large fish fishery. With the present large fish fishery in the North Sea, the two fisheries are well adjusted; however, the present combined exploitation level is too high to achieve optimal economic rents.     

A JUVENILE‐ADULT DISCRETE‐TIME PRODUCTION MODEL OF EXPLOITED FISHERY SYSTEMS

Abstract. Previous mathematical modeling of the population dynamics of Georges Bank Atlantic cod fishery employed discrete‐time models without age‐structure. To make use of a much wider variety of data on fisheries and fish stocks than was possible with an unstructured model, we introduce a juvenile‐adult age‐structured production exploited fishery model with a very general recruitment function. We use the age‐structured model to study the interaction between fish exploitation levels and recruitment dynamics. As case studies, we use our model results and historical fish population data from Georges Bank to investigate the impact of recent harvesting levels on the sustainability of cod fishery. We show that a constant harvesting policy with the same harvesting rate of 2007 would lead to the recovery and sustainability of Georges Bank cod fishery.     

A TWO‐STAGE INFORMATION‐THEORETIC APPROACH TO MODELING LANDSCAPE‐LEVEL ATTRIBUTES AND MAXIMUM RECRUITMENT OF CHINOOK SALMON IN THE COLUMBIA RIVER BASIN

ABSTRACT. Many anadromous salmonid stocks in the Pacific Northwest are at their lowest recorded levels, which has raised questions regarding their long‐term persistence under current conditions. There are a number of factors, such as freshwater spawning and rearing habitat, that could potentially influence their numbers. Therefore, we used the latest advances in information‐theoretic methods in a two‐stage modeling process to investigate relationships between landscape‐level habitat attributes and maximum recruitment of 25 index stocks of chinook salmon (Onocorhynchus tshawy‐tscha) in the Columbia River basin. Our first‐stage model selection results indicated that the Ricker‐type, stock recruitment model with a constant Ricker a, i.e., recruits‐per‐spawner at low numbers of fish) across stocks was the only plausible one given these data, which contrasted with previous unpublished findings. Our second‐stage results revealed that maximum recruitment of chinook salmon had a strongly negative relationship with percentage of surrounding subwatersheds categorized as predominantly containing U.S. Forest Service and private moderate‐high impact managed forest. That is, our model predicted that average maximum recruitment of chinook salmon would decrease by at least 247 fish for every increase of 33% in surrounding subwatersheds categorized as predominantly containing U.S. Forest Service and privately managed forest. Conversely, mean annual air temperature had a positive relationship with salmon maximum recruitment, with an average increase of at least 179 fish for every increase in 2°C mean annual air temperature.     

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.     

THE EFFECT OF INFORMATION ON A STOCHASTIC,SPATIALLY DISTRIBUTED FISHERY

ABSTRACT. Survival rates and carrying capacities in a fishery may be strongly affected by variations in climatic factors. When the stock is under the control of a single manager, information about the stochastic growth parameters leads to improved economic returns. However, when the stock is transboundary, additional information concerning the stochastic parameters can lead to over harvesting and in turn to lower economic returns. When the harvests are taken sequentially by more than one fleet, additional information will benefit the first harvester while harming those who follow.     

COEXISTENCE OR EXCLUSION IN A COMPETITIVE COMMON-POOL FISHERY: A REVISIONIST VIEW

ABSTRACT. One of the earliest applications of game theory to renewable resource modeling was Colin Clark's analysis, in 1980, of the competitive exploitation of a common-pool resource. His model described the dynamics of a single Gordon-Schaeffer fish stock, being harvested non-cooperatively by two or more independently managed fleets. He showed that aggressive harvesting by all fleets (a Nash equilibrium) would lead to stock drawdown to a level which would successively eliminate all of the less efficient harvesters. Furthermore, when the fleets were closely matched, the survivor(s) of this aggressive competition would be forced, by the threat of competitors' reentry, to hold the stock in its severely degraded state, and hence to harvest at only marginal profitability. This outcome has often been compared to the open access “tragedy of the commons.” and to the outcome of the well-known “prisoners' dilemma” game. In this article I will argue that, for closely matched fleets, a more likely outcome is that the fleets will tacitly agree, without overt communication, to focus simultaneously on a specific set of coordinated policies which will permit their continuing coexistence and profitable operation. This policy profile also forms a Nash equilibrium, one which is secured by the mutual ability of the fleets to quickly recognize and credibly punish any unilateral deviations from the anticipated actions. Thus the dynamic harvesting game more nearly resembles the repeated prisoners' dilemma than it does the classical single stage version.     

FEATURES OF BIOECONOMICS MODELS FOR THE OPTIMAL MANAGEMENT OF A FISHERY EXPLOITED BY TWO DIFFERENT FLEETS

ABSTRACT. After the extension of the Exclusive Economic Zone, in 1977, to 200 miles, most fish stocks came under jurisdiction of the adjacent coastal states. This development opened prospects of effective management of the open sea fisheries. Coastal states have the right to plan out the operation of so-called by Clarke and Munro “distant water fishing nations” from their Exclusive Economic Zone. Under some arrangements, a foreign fleet is allowed to harvest the resource in the Exclusive Economic Zone area. Clarke and Munro, in [1987] and [1991], focus on the issue of optimum terms and conditions of access and, in doing so, built a multiobjective model. The main goal of the present work is the development of a more general model including more variables and parameters related to the presence of a domestic fleet as well as a distant water fishing nation. The main difficulty resides in sharing the harvesting between the two fleets. The study responds to the realistic problemof coastal states who own enough resource stocks to allow harvesting by several kinds of fleets. Two optimal scenarios are developed, in each of them a solution is given.     

Dynamics of a fishery system in a patchy environment with nonlinear harvesting

In this paper, a stock‐effort dynamical model with two fishing zones is discussed. The nonlinear harvesting function is assumed depending upon stock size as well as fishing effort. The migration of fish is considered between two zones. The harvesting vessels also move between zones to increase their revenue. The movements of fish and fishing vessels between zones are assumed to take place at a faster time scale as compared with processes involving growth and harvesting occurring at a slow time scale. The aggregated model is obtained for total fish stock and fishing effort. This aggregated (reduced) model is analyzed analytically as well as numerically. Biological and bionomic equilibria of the system are obtained, and criteria for local stability or instability of the system are derived. The impact of levels of taxation T on the fish population and on the revenue earned by the fishery is investigated. An optimal harvesting policy is also discussed using the Pontryagin's maximum principle. The aggregated model also exhibits Hopf and transcritical bifurcation with respect to the bifurcation parameter tax T. Numerical simulations are presented to illustrate the results.     

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).     

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.     

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.     

Optimal harvesting of a Gompertz population model with a marine protected area and interval‐value biological parameters

To protect fishery populations on the verge of extinction and sustain the biodiversity of the marine ecosystem, marine protected areas (MPA) are established to provide a refuge for fishery resource. However, the influence of current harvesting policies on the MPA is still unclear, and precise information of the biological parameters has yet to be conducted. In this paper, we consider a bioeconomic Gompertz population model with interval‐value biological parameters in a 2‐patch environment: a free fishing zone (open‐access) and a protected zone (MPA) where fishing is strictly prohibited. First, the existence of the equilibrium is proved, and by virtue of Bendixson‐dulac Theorem, the global stability of the nontrivial steady state is obtained. Then, the optimal harvesting policy is established by using Pontryagin's maximum principle. Finally, the results are illustrated with the help of some numerical examples. Our results show that the current harvesting policy is advantageous to the protection efficiency of an MPA on local fish populations.     

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.     

MODELING A RIGHTS‐BASED APPROACH FOR MANAGING HABITAT IMPACTS OF FISHERIES

ABSTRACT. Limiting adverse consequences of fishing on essential fish habitat has emerged as a key fishery management objective. The conventional approach to providing habitat protection is to create MPAs or marine reserves that prohibit all or certain types of fishing in specific areas. However, there may be more cost‐effective and flexible ways to provide habitat protection. We propose an individual habitat quota (IHQ) system for habitat conservation that would utilize economic incentives to achieve habitat conservation goals cost‐effectively. Individual quotas of habitat impact units (HIU) would be distributed to fishers with an aggregate quota set to maintain a target habitat “stock.” HIU use would be based on a proxy for marginal habitat damage. We use a dynamic, explicitly spatial fishery and habitat simulation model to explore how such a system might work. We examine how outcomes are affected by spatial heterogeneity in the fishery and the scale of habitat regulation. We find that the IHQ system is a highly cost‐effective means of ensuring a given level of habitat protection, but that spatial heterogeneity and the scale of regulation can have significant effects on the distribution of habitat protection.     

DEA-based predictors for estimating fleet size changes when modelling the introduction of rights-based management

The introduction of individual transferable quotas (ITQs) into a fishery is going to change not only the amount of catch a fleet can take, but often also changes the fleet structure, particularly if total allowable catches are decreased. This can have an impact on the economic, social and environmental outcomes of fisheries management. Management Strategy Evaluation (MSE) modelling approaches are recognised as the most appropriate method for assessing impacts of management, but these require information as to how fleets may change under different management systems. In this study, we test the applicability of data envelopment analysis (DEA) based performance measures as predictors of how a fishing fleet might change under the introduction of ITQs and also at different levels of quota. In particular, we test the assumption that technical efficiency and capacity utilisation are suitable predictors of which boats are likely to exit the fishery. We also consider scale efficiency as an alternative predictor. We apply the analysis to the Torres Strait tropical rock lobster fishery that is transitioning to an ITQ-based management system for one sector of the fishery. The results indicate that capacity utilisation, technical efficiency and scale efficiency are reasonable indicators of who may remain in the fishery post ITQs. We find that the use of these measures to estimate the impacts of lower quota levels provides consistent fleet size estimates at the aggregate level, but which individual vessels are predicted to exit is dependent on the measure used.     

THE EFFECTS OF ITQ IMPLEMENTATION: A DYNAMIC APPROACH

ABSTRACT. This paper investigates the intertemporal effects of introducing Individual Transferable Quota, ITQ, fishery management programs on stock size, fleet size and composition, and returns to quota holders and to vessel operators. Theoretical analysis is conducted using a specific version of a general dynamic model of a regulated fishery. It is demonstrated that the effects will differ depending upon the prevailing regulation program, current stock size, and existing fleet size, composition and mobility and upon how the stock and fleet change over time after the switch to ITQs. The paper expands upon previous works by modeling the dynamics of change in fleet and stock size and by allowing for changes in the TAC as stock size changes, by comparing ITQs to different regulations, and by allowing the status quo before ITQ implementation to be something other than a bioeconomic equilibrium. Specific cases are analyzed using a simulation model. The analysis shows that the annual return per unit harvest to quota owners can increase or decrease over the transition period due to counteracting effects of changes in stock and fleet size. With ITQs denominated as a percentage of the TAC, the current annual value of a quota share depends upon the annual return per unit of harvest and the annual amount of harvest rights. Because the per unit value can increase or decrease over time, it is also possible that the total value can do the same. Distribution effects are also studied and it is shown that while the gains from quota share received are the present value of a potentially infinite stream of returns, potential losses are the present value of a finite stream, the length of which depends upon the remaining life of the vessel and the expected time it will continue to operate.     

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.     

Stable and unstable equilibrium states in a fishery–aquaculture model

We study interactions between fishery and aquaculture using a 3D generalized Lotka–Volterra model, where we assume that the aquaculture production may affect the growth rate in the fish stock and the productivity in harvesting. In addition, input demands from both marine industries may result in effort competition. We identify conditions for the coexistence of a unique equilibrium state inside the first octant of the phase space and equilibrium states on its boundary. Conditions for stability and instability of these states are also given, thus showing the possibility of having bistability. The equilibrium point inside the first octant is stable if the growth impact on fishery from sea farming is below the potential productivity in harvesting. In the complementary case, we have an unstable interior equilibrium, and we may then end up in stable equilibrium states on the boundary, where either the fishery or the aquaculture is wiped out. Recommendations for Resource Managers

• More empirical and theoretical research is needed to reveal types of interrelations between fisheries and aquaculture, and their importance for long run stability between the sectors.

• When designing policies for the aquaculture industries, managers should in particular be aware of possible long‐term harmful effects from aquaculture to fisheries.

• Increased areas for sea farming reduce the relative profitability of the fishery, and if the area increases above a certain level, this could wipe out the fishery.

     

A DELURY DEPLETION ESTIMATOR FOR WALLEYE POLLOCK (THERAGRA CHALCO‐GRAMMA) IN THE EASTERN BERING SEA

ABSTRACT. Concerns about local depletion of fish populations are intensifying, as interest becomes focused on finer spatial and temporal scales. We used the DeLury model to investigate local depletion of the eastern Bering Sea walleye pollock population by its fishery by using spatial and temporal scales thought to meet assumptions about closure and applicability. Local depletion is estimated as the slope of logarithmic catch‐per‐unit‐effort (CPUE) from the fishery versus cumulative effort, with data from 1995 1999 stratified by small areas, short seasons and years. Of 237 depletion estimators, 172 had negative slopes, 94 of which were significant, a greater number than would be expected by chance alone. Of the 65 positive slopes, 19 were significantly positive, which is also more than would be expected. Cumulative depletion over a season was inversely related to estimated initial biomass, total catch, and total effort, indicating that depletion is detected more easily in areas of low abundance and consequently lower catch and effort. Our fine‐scale estimates of depletion are much smaller than the overall depletion from annual stock assessments, showing that commercial data alone can be at best a relative index of depletion. This hyperstable relationship may result from the lack of search time in the measure of effort, fish finding technology and schooling behavior of pollock. Evidence also suggests that measures that were taken starting in 1999 to disperse the exploitation pressure in space and time may decrease local depletion, and that pollock may repopulate an exploited area in a relatively short time period (weeks).