Catch‐to‐stock dependence: The case of small pelagic fishery with bounded harvesting effort

Biologic characteristics of schooling fish species explain why the rates of harvesting in pelagic fisheries are not proportional to the existent stock size and may exhibit no variation between the periods of fish abundance and scarcity. Therefore, the stock‐dependent nonlinearities in catchability must be reflected in the design of flexible fishing policies, which target the sustainable exploitation of this important natural resource. In this study, such nonlinearities are expressed through eventual variability of the “catch‐to‐stock” parameter that measures the sensitivity of an additional catch yield to marginal changes in the fish‐stock level. Using the optimal control modeling framework, we establish that each value of the “catch‐to‐stock” parameter generates a unique steady‐state size of the fish stock and the latter engenders an optimal fishing policy that can be sustained as long as the “catch‐to‐stock” parameter remains unchanged. We also prove the continuous dependence of the steady‐state stock and underlying fishing policy upon the mentioned “catch‐to‐stock” parameter and then focus on the analysis of the equilibrium responses to changes in this parameter induced by external perturbations. Recommendations for Resource Managers

• Marginal catches of pelagic fish stocks do not react in a linear way to changes in existing stock level, and the latter is captured in our model by the “catch‐to‐stock” parameter . Each observable value of engenders a unique steady‐state stock size that defines an optimal fishing policy, which can be sustained as long as remains unchanged.
• The ability of fishery managers to detect variations in the levels of hyperstability expressed by the “catch‐to‐stock” parameter may help them to anticipate new equilibrium responses in stock evolution and to make timely adjustments in the fishing policy.
• Plausible estimations of the “catch‐to‐stock” parameter , as well as detection of its possible alterations, can be carried out within the framework of Management Strategy Evaluation (MSE) approach where different data collected inside and outside the fishery are contrasted via the validation of a relatively simple decision‐making model (presented in this paper) coupled with other “operation models” of higher complexity.
• If the “catch‐to‐stock” parameter cannot be reasonably assessed (), the fishery managers may rely upon the lower bound of stationary stock size, which depends on economic and biological factors (such as the present and future economic values of the exploited fish stock, its marginal productivity, and underlying dynamics of biological growth).

     

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.     

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.     

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 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).     

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.     

Harvesting in a pelagic fishery: The case of Northern Chile

This paper analyses the pelagic fishery of Northern Chile, estimating harvesting functions that contribute to understand why rather poor incentives to exit may predominate in pelagic fisheries, despite scarcer fish stocks. Our results show that pervessel catch's stock sensitivity (the catchtobiomass elasticity value) varies negatively with stock levels. Stock levels preceding a marked fall into biological overfishing would have been associated to biomass elasticities lower than the unitary value. This suggests that during catch bonanza periods, catchperunitofeffort would fail to detect a rapidly declining stock trend, increasing the risk of fishing collapse. Moreover, external economies in search efforts would have reduced the incentives to exit, particularly for the smaller vessels in our sample. Finally, we find evidence of either constant or increasing marginal returns in the use of pervessel fishing effort, which suggests that inefficiency in production has resulted from direct restrictions upon fishing effort. Overall, our findings provide consistent evidence that enhances the necessity of more efficient regulations upon harvesting in pelagic fisheries.     

STANDARDIZATION OF CATCH-PER-UNIT-EFFORT FOR SHORT-TERM TRENDS IN CATCHABILITY

Examination of daily catch–per–unit–effort (CPUE) information on Pacific halibut revealed sharp declines that could not be explained by natural and fishing mortality. Catchability may have decreased during a fishing period because of local depletions of fish, changes in fish behavior, and other causes. Mathematical models of CPUE with a short–term catchability function of time or effort were based on a generalization of the DeLury method. A method of standardization was developed to account for the length of a fishing period and to correct for catchability. The effort model was best for Pacific halibut data and the application showed that standardization of CPUE is necessary to have a valid index of abundance when short–term changes in catchability occur.     

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.     

Sustainable Yield Analysis in a Multicohort Single-species Fishery: A Mathematical Programming Approach

The concept of sustainable yield, i.e. the fish catch that can be maintained in the long run from a fishery in a steady state, is widely used in fisheries management. In traditional methods of sustainable yield analysis, based on the Schaefer model of a fish stock, the age structure of the stock is ignored. Approaches based on the Beverton-Holt multicohort fish population model take account of age structure but assume that instantaneous natural and fishing mortality rates are constant throughout the year. Using a fish population model in which this assumption is not required, a mixed integer programming model is developed for the analysis of a multicohort single-species fishery in a steady state. This new method of sustainable yield analysis is demonstrated using data for the western mackerel fishery. Comparisons with results from other studies of this fishery are presented.     

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.     

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.     

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.     

SHARING THE NORTHEAST ARCTIC COD: POSSIBLE EFFECTS OF CLIMATE CHANGE

ABSTRACT. The Northeast Arctic cod inhabits the exclusive economic zones of Norway and Russia and migrates extensively between these zones. The stock is shared evenly between the two countries, with a small allocation to third countries. Higher temperatures in the Barents Sea and the Norwegian Sea are expected to affect the stock, probably increasing its size and leading to a larger share inhabiting the Russian economic zone. It is also conceivable that some spawning will begin to take place off the coast of Russia in addition to the spawning that now occurs exclusively in Norwegian waters. This paper looks at the implication of this for the division of the stock between the two countries. It is found that a greater presence of the stock in the Russian zone would strengthen rather than weaken the Norwegian bargaining position if the unit cost of fish is not sensitive to the size of the stock. If, on the other hand, the fishing costs are proportional to fishing mortality, Norway's position would be weakened almost on par with the fall in its share of the stock. The paper uses a Beverton‐Holt year class model with a Ricker recruitment function. The recruitment function is hump‐shaped, implying that a too large spawning stock is harmful for recruitment. Strong density‐dependence in the survival of eggs and larvae is a possible reason for this. It is shown that, for a stock being limited by carrying capacity at the pre‐recruit stage rather than the post‐recruit stage, one may expect a strongly asymmetric curve for sustainable yield as a function of total biomass. The biomass of an exploited population might possibly exceed the biomass of a pristine population under those circumstances.     

AN INDIVIDUAL-BASED FISHERY MODEL AND ASSESSING FISHERY STABILITY

ABSTRACT. The stability of a fishery system was investigated using two forms of a stochastic computer simulation model that was individually based in terms of the fishing boats. Fish catch was partitioned among boats according to two catch processes: an unranked process in which all boats had equal ability to catch fish and a ranked catch model in which a boat's ability to catch fish depended on its wealth. Stock size, total catch, fleet size and individual boat wealth were modeled over a series of years. In the unranked catch model the fish stock size and fleet size were significantly more variable than in the ranked catch 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.     

ASSESSING COMPONENTS OF UNCERTAINTY IN VPA ABUNDANCE AND MORTALITY ESTIMATES USING AN ALTERNATIVE EXPLOITATION RATE‐BASED ALGORITHM

Abstract Using an exploitation rate (not fishing mortality) based virtual population analysis (VPA) algorithm, which is itself a generalization of the Pope approximation to the original VPA equations, I show how to derive variance estimates for the key VPA outputs (recruitment, SSB, exploitation rates) given variance information on the key inputs (catch‐at‐age/terminal exploitation rates). Given the alternative VPA algorithm permits closed‐form solutions for the outputs in terms of the inputs, the delta method is employed to obtain the variance estimates, removing the need for complex simulation techniques. Using North Sea herring data as an example, the method’s utility is demonstrated by exploring the impact of aging error in the catch data and tuning error on the precision of estimates of SSB, recruitment and exploitation rates, and the parameters of the stock‐recruit relationship.     

FISHERY BENEFITS OF FULLY PROTECTED MARINE RESERVES: WHY HABITAT AND BEHAVIOR ARE IMPORTANT

ABSTRACT. Fully protected marine reserves, areas that are closed to all fishing, have attracted great interest for their potential to benefit fisheries. A wide range of models suggest reserves will be most effective for species that are relatively sedentary as adults but produce offspring that disperse widely. Adult spawning stocks will be secure from capture in reserves, while their offspring disperse freely into fishing grounds. Such species include animals like reef fish, mollusks and echino‐derms, and models typically indicate that when they are over‐fished, catches will be higher with reserves than without. By contrast, the same models suggest that reserves will be ineffective for animals that are mobile as adults species like cod, tuna or sharks. They remain vulnerable to fishing whenever they move outside reserves. Unfortunately, most models lack sufficient realism to effectively gauge reserve effects on migratory species. They usually assume that individuals are homogeneously distributed in a uniform sea and move randomly. They also assume that fishers hunt at random. Neither is true. For centuries, fishers have targeted places and times when their quarry are most vulnerable to capture. Protecting these sites could have disproportionately large effects on stocks. Furthermore, models rarely take into account possible benefits from improvements in habitat within reserves. Such changes, like increased biomass and complexity of bottom‐living organisms, could alter fish movement patterns and reduce natural mortality rates in ways that enhance reserve benefits. We present a simple model of reserve effects on a migratory fish species. The model incorporates spatial variation in vulnerability to capture and shows that strategically placed reserves can offer benefits in the form of increased spawning stock and catch, especially when fishing intensities are high. We need to develop a new generation of models that incorporate habitat and behaviour to better explore the utility of reserves for mobile species. Migratory behavior does not preclude reserves from benefiting a species, but it demands that we apply different principles in designing them. We must identify critical sites to species and develop reserve networks that focus protection on those places.     

Evaluating impacts of fish stock enhancement and biodiversity conservation actions on the livelihoods of small‐scale fishers on the Beijiang River,China

Inappropriate development and overexploitation have seriously degraded aquatic resources in China. Stakeholders identified three fish stock enhancement and biodiversity conservation scenarios for the Beijiang River: S1, increased fish restocking; S2, no fishing season and habitat conservation; and S3, strict pollution control. Potential impacts of these actions on the livelihoods of fishers were evaluated using applied economic modeling. Baseline costs and benefits came from logbooks from 30 fishers and a survey of 90 households in three villages. The financial net benefit for a household was US$1583 (￥11,160) annually, representing a 142% and 387% return on capital and operating costs, respectively. Larger catches associated with S1 and S2 generated a net benefit of US$1651 and US$1822, respectively. Strict pollution control resulting in higher catches (+20%) and lower operating costs (?20%) would increase the net benefit by 15.9% to US$1835 annually. Pollution control would benefit other resource users and is a prerequisite for ecological restoration. Recommendations for Resource Managers

• Stringent pollution control measures are essential to conserve aquatic biodiversity and enhance the livelihoods of fishers but will require considerable public and private sector investment.
• Enhanced fish stocks in the Beijiang River could benefit poor livelihoods but may not be sufficient to lift households out of poverty, aged fishers require government assistance to diversify their livelihoods, access alternative urban employment, and survive with dignity.
• Adopting the economic modeling approach presented here could enable responsible authorities to simultaneously evaluate fish stock enhancement and biodiversity conservation options.
• Broader application of the approach presented here could help ensure small‐scale inland fisheries are managed sustainably and aquatic ecosystems are restored and protected by 2020, in line with Target 6 of the United Nations’ Convention on Biological Diversity Strategic Plan for Biodiversity.