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.     

EFFECT OF FISH MOVEMENT AND FLEET SPATIAL BEHAVIOR ON MANAGEMENT OF FISH SUBSTOCKS

I investigated the questions (i) how much movement of fish between areas within a stock is required before the areas can be managed jointly instead of separately and (ii) how is the trade-off between separate and joint management affected by the spatial behavior of the fishing fleet? I addressed these questions using a simulation model of a fishery on a stock that is divided into two areas (substocks) between which fish can move. Under joint management, fleet spatial behavior is characterized by its “switching level,” or the biomass level in the currently fished area at or below which the fleet will switch to the other area. Catch levels were calculated under both separate and joint management for a range of movement rates and switching levels. I also studied the effect of differences in natural mortality rates between the two areas. When the natural mortality rates were the same for the two areas, (i) separate management resulted in higher catch than joint management, (ii) joint management only approached the catch of separate management when movement rate of fish between the two areas was very high, (iii) the difference between separate and joint management was greatest when (a) the switching level of the joint fleet was low (i.e., inertia was high) and (b) the joint fleet had a preference for one area. When natural mortality rate was different in the two areas, and (i) the joint fleet did not prefer one area, (a) separate management produced higher catches at low fish movement rates while joint management produced higher catches at high movement rates and (b) switching level had no effect on catch, and (ii) when the fleet had a preference for the area with the higher natural mortality rate, separate management resulted in higher catches than joint management, and the difference increased with increasing fish movement rate. These simulations suggest that the relative merits of separate and joint management of two areas depends on the assumptions one makes about the spatial behavior of the fishing fleet. This behavior is as important as movement of fish between the areas, which is normally assumed to be the overriding determinant of the relative merits of separate and joint management.     

BENEFITS AND RISKS OF INCREASED SPATIAL RESOLUTION IN THE MANAGEMENT OF FISHERY METAPOPULATIONS UNDER UNCERTAINTY

Abstract Stock assessments and harvest guidelines are typically based on the concept of a “fish stock,” which may encompass a very large area. The presence of discrete subpopulations within managed fish stocks presents risks and opportunities for fishery management. Failure to manage catch at the same scale as the true population structure can lead to extirpation of discrete subpopulations and to declines in the productivity of the larger metapopulation. However, it may be difficult and costly to assess and manage stocks at a finer spatial scale, and there is likely greater uncertainty about the size of substocks than about the aggregate stock. We use a two‐area simulation model to compare the performance of fishery management at different spatial resolutions when there is uncertainty about growth, the size of the total population, and the relative size of the subpopulations. We show that relative benefits of finer scale management, in terms of profits and risks of depleting subpopulations, depend on a number of biological, technical, and economic factors. In some cases it may be both less risky and more profitable to manage the fishery with a single total allowable catch, even when there are biologically separate fish populations in the two areas.     

THE EFFECT OF DECREASING SYSTEM SIZE ON BIRTH AND DEATH MODELS OF OPEN-ACCESS FISHERIES AND PREDATOR-PREY ECOSYSTEMS

Birth and death simulation, developed by Pielou, is a form of Markov stochastic process for describing the time evolution of populations. Applied to modelling the human element of a fishery, it expresses two features of fishing effort dynamics absent in systems of differential equations: (1) discreteness of events, such as a fishing trip or entry of a vessel into the fleet, and (2) demography stochasticity, expressed as randomness in the time occurrence of successive events. Birth and death simulation is based on randomly selecting the waiting time between events from a negative exponential distribution, derived under the assumption of Markov. Histograms from commercial landings data of waiting times between events of boats returning to port in a Nova Scotia fishery yielded good agreement with the predicted negative exponential. Algorithms are presented for stochastically modelling two processes: (1) catch and (2) the open-access hypothesis for changes in fleet size in response to changing levels of profit. The solutions qualitatively diverge from that predicted by differential equations: As the numbers of vessels and fish schools decline (i.e., as the system size scale shrinks), a birth and death formulation predicts increasing instability of the predator-prey cycle solution about the deterministically stable open-access equilibrium. Open-access models are a form of predator-prey model. In choosing the minimum wilderness preserve area needed to sustain a population of top predators, numbered in the low hundreds, a predator-prey model formulated with differential equations could underestimate instability and thus the risk of extinction, when the discreteness and randomness of predator-prey birth, death, and capture events is significant.     

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 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.     

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.     

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.     

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.     

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 Size and Composition of a Road Transport Fleet

The paper starts with a discussion of the simple fleet size problem. It is shown that this simple problem can be formulated as a linear program.The second part of the paper consists of an actual case study. The fleet concerned is faced with highly seasonal demand which can be met by the firm's own vehicles or by outside hire. There are two types of vehicle, both of which are available in six different sizes. Linear programming was used to find the optimum size and composition of the company fleet. The results, which were substantially implemented, recommended a smaller company fleet and concentration on larger and more flexible vehicles.     

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.     

Regional economic impacts of fish resources utilization from the Barents Sea: Trade-offs between economic rent,employment and income

A multi-objective programming model has been developed to investigate the trade-offs among regional employment, regional income, and economic rent of the North Norwegian cod fisheries in the Barents Sea, where all vessels are regulated by an individual quota system. Fishery managers are confronted with the problem on how best to allocate the total allowable catch (TAC) among four vessel groups. It is apparent that depending on how fishery managers view the importance of each objective, the desirable allocation of TAC will differ. Therefore, the trade-offs information can be very useful to fishery managers indicating the relative “expensiveness” of trading one objective with another. Decision maps are generated depicting how the trade-offs between two objectives are affected by the third objective. Compromise solutions taking into account all three objectives will allocate the TAC to satisfy the maximum capacity of both the factory trawlers and the small-scale vessels with the remaining TAC distributed to the coastal fleet and fresh fish trawlers.     

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.     

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).

     

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.     

Vehicle Scheduling with Timed and Connected Calls: A Case Study

A manual method was developed for scheduling the vehicle fleet of a contract transport undertaking. The main requirements were observance of time limits on individual calls and the ability to allocate pairs or groups of related calls to the same vehicle. These objectives were achieved by introducing an initial allocation of calls to vehicles prior to sequential routing of the calls. The allocation was based on a model relating work density (calls per unit area) to vehicle loading (calls per unit of vehicle time), and on fact-finding research on the main parameters of calling time, travelling speed and distance. This relationship was embodied in a visual scheduling aid for use by the route planners. Implementation was successful and resulted in about 15 per cent of vehicle time being made available for additional revenue-earning work without increase in fleet size. When utilized this represented an effective saving in operating costs of about 12 per cent.     

Fleet Structures Model: Predictive Modelling of the UK Sea-Fishing Fleet

The Fleet Structures Model is a predictive computer model under development by the Sea Fish Industry Authority. Its purpose is to simulate aspects of the structure and operation of the UK sea-fishing fleet in order to make comparative appraisals of fleet-management policy scenarios under varying assumptions about the behavioural environment. The model operates in yearly incremental steps, providing feedback between the fleet operation, the expected changes in fleet structure, fish prices and the state of fish stocks. It is an analytic model, and is mainly deterministic with stochastic elements. Implementation is in programs written in Pascal. This paper presents an overview of the model, and highlights aspects of its development and implementation.     

The impact of fleet size on performance-based incentive management

Performance-based contracting (PBC) is envisioned to lower the asset ownership cost while ensuring desired system performance. System availability, widely used as a performance metric in such contracts, is affected by multiple factors such as equipment reliability, spares stock, fleet size, and service capacity. Prior studies have either focussed on ensuring parts availability or advocating the reliability allocation during design. This paper investigates a single echelon repairable inventory model in PBC. We focus on reliability improvement and its interaction with decisions affecting service time, taking into account the operating fleet size. The study shows that component reliability in a repairable inventory system is a function of the operating fleet size and service rate. A principal-agent model is further developed to evaluate the impact of the fleet size on the incentive mechanism design. The numerical study confirms that the fleet size plays a critical role in determining the penalty and cost sharing rates when the number of backorders is used as the negative incentive scheme.