A STATE SPACE BIOECONOMIC MODEL OF PACIFIC HALIBUT

Abstract Evaluation of potential economic consequences of alternative management actions requires an understanding of how the biological stock will be affected by the management action and an understanding of the response of economic systems to changes in the timing, magnitude, and size distribution of harvests and changes in the location and catchability of the biological stock. We use a hybrid structural time series model to represent Pacific halibut (Hippoglossus stenolepis) stock and recruitment dynamics and a system of structural equations to represent supply and demand relationships for Pacific halibut from Alaska and British Columbia. Model simulations explore the economic effects of changes in recruitment success, growth rate, and carrying capacity, and changes in international supplies of halibut.     

Optimal pulse fishing policy in stage-structured models with birth pulses

In this paper, we propose exploited models with stage structure for the dynamics in a fish population for which periodic birth pulse and pulse fishing occur at different fixed time. Using the stroboscopic map, we obtain an exact cycle of system, and obtain the threshold conditions for its stability. Bifurcation diagrams are constructed with the birth rate (or pulse fishing time or harvesting effort) as the bifurcation parameter, and these are observed to display complex dynamic behaviors, including chaotic bands with period windows, period-doubling, multi-period-halving and incomplete period-doubling bifurcation, pitch-fork and tangent bifurcation, non-unique dynamics (meaning that several attractors or attractor and chaos coexist) and attractor crisis. This suggests that birth pulse and pulse fishing provide a natural period or cyclicity that make the dynamical behaviors more complex. Moreover, we show that the pulse fishing has a strong impact on the persistence of the fish population, on the volume of mature fish stock and on the maximum annual-sustainable yield. An interesting result is obtained that, after the birth pulse, the population can sustain much higher harvesting effort if the mature fish is removed as early as possible.     

ENTRY AND EXIT OF LABOR AND CAPITAL IN A FISHERY

ABSTRACT. Exit and entry of fishermen, as well as vessels, is modeled explicitly. If the speed of exit and entry of fishermen is less than instantaneous the wage rate varies with the fortunes of the fishing firms and affects the endogenous labor supply creating a second transmission mechanism from profits to effort. There are realistic cases where this mechanism has important effects on the stability of the dynamic system and on the effects of taxes (subsisdies) on the size of the fish stock. If labor supply depends negatively on the wage rate, the immediate effect of an increase in the tax rate is to increase effort and harvest. This condition makes it also more probable that the dynamic system is unstable. In those cases where the dynamic system is unstable the increase in the tax rate increases overexploitation not only in the short‐term but also in the long‐term.     

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.     

OPTIONS FOR THE REGULATION OF MEDITERRANEAN DEMERSAL FISHERIES

Research and management actions are reviewed with respect to demersal fisheries of the Mediterranean since the Second World War, as reflected in the activities of the General Fisheries Council for the Mediterranean, (GFCM). The scientific background to the priority concern expressed for minimum size limits in the 1960's and 1970's is discussed, and in particular, the mesh selectivity experiments that formed the basis for yield per recruit calculations, with respect to the trawl fishery. More recent considerations, changing our perception of the appropriateness of size at first capture of demersal fish as a management tool in trawl fisheries, are reviewed. It is concluded that for multispecies fisheries where the first priority for fishing effort control is not respected, size limits based on size at maturity, rather than yield per recruit criteria, are more feasible, but that changes in mesh size need to take into account subsequent changes in equity between inshore and offshore fleets, and changes in species composition and areas of distribution during the life history. They also need to consider the high landed value of small fish in many Mediterranean fisheries. Alternative, or supplementary, measures to mesh size regulation that affect capture of small fish are also reviewed, including seasonal closures, closed areas, bans on trawling inshore, and regulations on minimum size at sale. A range of problems to be considered prior to deciding on an increase in mesh size are reviewed, including changes in total effort exerted, changes in increases in fishing power (and especially the impacts on the spawning stock), changes in discard rate, “meshing” of small fish, and indirect mortality during fishing. A strategy for introducing new mesh sizes is suggested, with emphasis, where possible, on the experimental approach, and on supplementary measures to control fishing effort. The paper concludes by considering an alternative paradigm to minimum size regulation for demersal fisheries management; namely, the exploitation of juvenile fish, with provision for escapement of a small proportion of large, mature fish offshore, for which exploitation rate declines and remains low. It is suggested that this strategy may be, de facto, the one prevailing in the small mesh size inshore trawl fishery prior to development of offshore fisheries. The implications of this possibility have to be considered seriously if high effort levels are to be maintained while effective size limits are raised.     

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).     

OPTIMAL HARVEST FEEDBACK RULE ACCOUNTING FOR THE FISHING‐UP EFFECT AND SIZE‐DEPENDENT PRICING

Abstract Fishing leads to truncation of a population's age and size structure. However, large‐sized fish are usually more valuable per unit weight than small ones. Nevertheless, these size‐related factors have mostly been ignored in bioeconomic modeling. Here, we present a simple extension to the Gordon–Schaefer model that accounts for variations in mean individual catch weight, and derive the feedback rule for optimal harvest in this setting. As the Gordon–Schaefer model has no population structure, size effects have to be accounted for indirectly. Here we assume a simple negative relationship between fishing effort and mean individual weight, and a positive relationship between mean catch weight and price. The aim is to emulate alterations of size structure in fish populations due to fishing and the influence of size on price per weight unit and eventually, net revenues. This demonstrates, on a general level, how such size‐dependent effects change the patterns of optimal harvest paths and sustainable revenue in single fish stocks. The model shows clear shifts toward lower levels of optimal effort and yield compared to classical models without size effects. This suggests that ignoring body size could lead to misleading assumptions and policies, potentially causing rent dissipation and suboptimal utilization of renewable resources.     

THE PROBLEM OF NONMALLEABLE CAPITAL REVISITED; A STUDY OF THE PACIFIC HALIBUT FISHERY

It has been suggested in the literature on commercial fisheries that fishing capital may be nonmalleable, i.e., not easily moved from one fleet to another, and that the socially optimal rate of capitalization of boats may depend on the degree of malleability (irreversibility) of the fishing fleet. To find out how irreversibility affects optimal regulation, two of the many possible regulatory tools, unallocated quotas and catch taxes, are examined. These optimal policies are derived, alternatively assuming malleable and nonmalleable fishing capital. Using a simulation of the Pacific halibut fishery, the results obtainable through catch quotas are shown to be inferior to those obtainable through taxes, but that the degree of malleability of capital has a surprisingly small impact on policy. A sensitivity analysis is performed, rerunning these simulations over a variety of parameter values. The previous results are largely borne out.     

REGULATORY CONTROLS AND MARKET POWER EXERTION: A STUDY OF THE PACIFIC HALIBUT INDUSTRY

Regulatory controls designed to manage Pacific halibut fisheries are shown to have altered firms' competitive behavior. Managing catch through open access derbies allowed processors to exert monopsony market power at the vessel level during short seasons. As a result, a significant portion of regulatory rents associated with reduced seasons were captured by processors. Results also indicate that processors have not exerted significant market power at the wholesale level.     

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.     

HARVESTING AN AGE‐STRUCTURED POPULATION AS BIOMASS: DOES IT WORK?

Abstract The economics of fisheries is based heavily on describing fish populations by the surplus production model. Both economists and ecologists have different opinions on whether this approach provides an adequate biological basis for economic analysis. This study takes an age‐structured population model and shows how, under equilibrium conditions, it determines the surplus production model. The surplus production model is then used to solve an optimal feedback policy for a generic optimal harvesting problem. Next, it is assumed that the fishery manager applies this feedback policy even though the fish population actually evolves according to the age‐structured model. This framework is applied to the widow rockfish, Atlantic menhaden, and Pacific halibut fisheries. Population age‐structure contains information on future harvest possibilities. The surplus production model neglects this information and may lead to major deviations between the expected and actual outcomes especially under multiple steady states and nonlinearities.     

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.     

CREATION OF MARINE RESERVES AND INCENTIVES FOR BIODIVERSITY CONSERVATION

Abstract Despite a number of benefits, marine reserves provide neither incentives for fishermen to protect biodiversity nor compensation for financial loss due to the designation of the reserves. To obtain fishermen's support for marine reserves, some politicians have suggested that managers of new marine reserves should consider subsidizing or compensating those fishermen affected by the new operations. The objective of this paper is to apply principal–agent theory, which is still infrequently applied to fisheries, to define the optimal reserve area, fishing effort, and transfer payments in the context of symmetric and asymmetric information between managers and fishermen. The expected optimal reserve size under asymmetric information is smaller than that under symmetric information. Fishing efforts encouraged with a transfer payment are always less compared to those without payment. This reflects the fact that as the manager induces the fishermen to participate in the conservation program, the fishermen will take into account their effects on fish stock by decreasing their effort. Examples are also supplied to demonstrate these concepts.     

FISHING YIELD,CURVATURE AND SPATIAL BEHAVIOR: IMPLICATIONS FOR MODELING MARINE RESERVES

ABSTRACT. Given a paucity of empirical data, policymakers are forced to rely on modeling to assess potential impacts of creating marine reserves to manage fisheries. Many modeling studies of reserves conclude that fishing yield will increase (or decrease only modestly) after creating a reserve in a heavily exploited fishery. However, much of the marine reserves modeling ignores the spatial heterogeneity of fishing behavior. Contrary to empirical findings in fisheries science and economics, most models assume explicitly or implicitly that fishing effort is distributed uniformly over space. This paper demonstrates that by ignoring this heterogeneity, yield‐per‐recruit models systematically overstate the yield gains (or understate the losses) from creating a reserve in a heavily exploited fishery. Conversely, at very low levels of exploitation, models that ignore heterogeneous fishing effort overstate the fishing yield losses from creating a reserve. Starting with a standard yield‐per‐recruit model, the paper derives a yield surface that maps spatially differentiated fishing effort into total long‐run fishing yield. It is the curvature of this surface that accounts for why the spatial distribution of fishing effort so greatly affects predicted changes from forming a reserve. The results apply generally to any model in which the long‐run fishing yield has similar curvature to a two‐patch Beverton‐Holt model. A simulation of marine reserve formation in the California red sea urchin fishery with Beverton‐Holt recruitment, eleven patches, and common larval pool dispersal dynamics reinforces these results.     

变捕捞努力量收获模型控制

利用微分包含给出了努力量可变的收获模型,基于生存理论和求解线性规划给出了将单种群数量控制在某范围的方法.最后对于常用的Logistic模型,证明只要控制努力量就可以将种群数量控制在指定范围内.     

QUANTITATIVE METHODS FOR DECISION SUPPORT IN THE ICELANDIC FISHING INDUSTRY

Abstract Modern fisheries already collect vast amount of data, for example, through ERP systems and electronic log‐books. It is however well known that the data are rarely used for improving operational decision making. By converting this data into useable information, decision making in the fishing industry could be improved. This paper attempts to show that quantitative methods can be of use in many aspects of decision making in the fishing industry. The paper proposes a hierarchically structured decision support process based on two different optimization models for supporting the long‐ and short‐term decision making in fisheries. For long‐term planning the paper proposes a linear optimization model that describes the entire operation of a vertically integrated seafood company. For short‐term decision making the paper proposes a mixed integer linear optimization model to assist in organizing vessel trips and deciding catch location with regard to raw material quality and yield obtained in processing.     

Regulation of a prey-predator fishery by taxation

Bioeconomic exploitation of a prey-predator fishery is discussed by using a reasonable catch-rate function instead of the usual 'catch-per-unit-effort hypothesis'. The model is based on the assumption that only the prey species is harvested. A regulatory agency controls exploitation of the fishery by imposing a tax per unit biomass of the landed fish. The fishing effort is taken as a dynamic variable depending on the capital invested in the fishery. The dynamical system consisting of the growth equations of the species and also the fishing effort is formulated. The existence and stability of steady states are discussed. The optimal tax policy is studied with the help of Pontryagin's maximum principle. Finally, some numerical examples are carried out to illustrate the results of the model.     

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.     

FISHERIES AND MARINE PROTECTED AREAS: A SPATIAL BIOECONOMIC ANALYSIS OF DISTRIBUTIONAL IMPACTS

Abstract Marine protected areas (MPAs), used increasingly as a tool for conservation of ocean and coastal environments, typically interact with fisheries. Indeed, implementation of an MPA in a coastal region will likely affect fishing communities along that coast but to differing degrees depending on their location relative to the MPA. The resulting creation of “winners” and “losers” has implications for the acceptance and long‐term viability of the MPA. This paper develops a spatially explicit bioeconomic simulation model to assess the distributional implications resulting from creation of a no‐take MPA. The key assumption is that this results in certain fishers being displaced from the MPA to new fishing locations, leading to decreased fishing time and increased costs. Is it possible for those being displaced to end up as “winners” in the fishery? Analysis of the model indicates that such an outcome can occur in certain circumstances, notably if the biological effects of the MPA produce (i) improved ecosystem health inside the MPA, such that fish stock carrying capacity increases; or (ii) to some extent, high fish stock migration rates between neighboring areas. The results indicate that in creating MPAs, careful attention to their design is needed in order to deal with corresponding distributional impacts on fishing communities.