Species preservations in an optimal harvest model with random prices

In this paper, we consider an optimal harvest model in which the objective is to maximize the expected return. The unit price of biomass is assumed constant until a random time when the price increases by a given amount. Furthermore, due to obvious environmental protection requirements, it is assumed that the fishery population is bounded from below for all time so as to reduce the danger of species extinction. Clearly, this problem is an optimal control problem in which a random parameter is involved. However, due to its special structure, it is shown that the problem is convertible into a deterministic optimal control problem and hence is solvable by an existing optimal control software package, MISER. The practical implication of several computed results obtained by this approach is discussed. They are also compared with other related results in the literature.     

The conservation and exploitation of vulnerable resources

The maximum principle of deterministic optimal control, which has proved to be a very useful tool in theoretical bioeconomics, is extended in this article to cover the optimal exploitation of a biological resource vulnerable to catastrophic collapse, the probability of which may depend in general on the state of the resource, the current control and time. A general formulation of the maximum principle for such stochastic problems is presented and a number of applications are outlined. These include: optimal harvesting of a fishery vulnerable to catastrophic collapse; optimal thinning of a forest vulnerable to fire; optimal expenditure and investment in forest fire protection and optimal consumption-pollution tradeoffs in an ecosystem vulnerable to pollution-related collapse. In addition an application of the method to a highly stylized behavioral ecology model is given.     

On open access and optimal landings tax

This paper develops two types of simple models on the dynamic interaction between the stock of fish and the effort expended by fishers: continuous-time/discrete-time models in which a landings tax is incorporated as a control variable available to the management authority. The continuous-time model can describe several ideal options of the optimal tax program; however, unfortunately, it is incapable of choosing the best option. Hence, using the alternative tractable discrete-time model and a computational method, the remaining task of determining a unique optimal tax program is accomplished. The fishery thus managed exhibits a regulated open access.     

Fish, Fact and Fantasy: a Long View

This paper suggests ways forward from the widely perceived present failures of fishery assessment and management. A history of fishery yield modelling is presented from the carefree days of the 1950s to the depressing series of stock collapses and depletions of the 1980s. Underlying this gruesome story has been the failure of management by quotas to arrest overcapacity in fishing power, the lack of robust and informative reference points and the inadequacy of methods dealing with some multispecies fisheries. The paper refines the use of the concept of Fext, defined as the minimum value of F in a self-regenerating yield model that leads to eventual extinction in a family of yield curves generated with a range of stock recruitment curves. Model reconstructions for North Sea cod and Icelandic herring make evident calamitous losses in catches forgone as result of the failure of rational management. An optimistic agenda that may achieve more effective fishery management in the future is presented. In some ways, we may have been trying to be too clever. A simple management system based on careful monitoring of fishing effort, biological targets such as F95, and exploitation of a diversity of fish resources may suffice to avert further disaster and hedge against uncertainty.     

Analytic solution of a dynamic pool model incorporating constant marginal cost and discount rates

A simple dynamic pool model is extended to describe the economics of a single-species fishery by incorporating constant marginal cost and discount rates. Assuming that the population has already come to equilibrium under an initial fishing mortality rate and that any change in that rate is to be sustained indefinitely, the model can be solved analytically to yield the optimal fishing mortality rate. When this rate is expressed as a proportion of the natural mortality rate, the solution takes the form of a third-degree polynomial whose coefficients are simple functions of four other parameters. The solution exhibits positive conservation effects as long as all four parameters are sufficiently high. These conservation effects may be great enough to warrant closing the fishery when the marginal cost rate exceeds a well-defined limit.     

Optimal harvesting strategies for a metapopulation

We consider optimal strategies for harvesting a population that is composed of two local populations. The local populations are connected by the dispersal of juveniles, e.g. larvae, and together form a metapopulation. We model the metapopulation dynamics using coupled difference equations. Dynamic programming is used to determine policies for exploitation that are economically optimal. The metapopulation harvesting theory is applied to a hypothetical fishery and optimal strategies are compared to harvesting strategies that assume the metapopulation is composed either of single unconnected populations or of one well-mixed population. Local populations that have high per capita larval production should be more conservatively harvested than would be predicted using conventional theory. Recognizing the metapopulation structure of a stock and using the appropriate theory can significantly improve economic gains.     

Regional implementation of alternative entry control policies and their role in fisheries management

Abstract

This paper reviews and examines the development of the concept of entry control policies in fisheries management. With renewed expectations for U. S. fisheries surrounding the recent enactment of legislation that extends jurisdiction over living resources within 200 mi, optimal management of an open‐access resource becomes an increasingly important public policy problem. The paper reviews alternative entry control schemes and criteria in order to evaluate their effectiveness and suggests ways in which limited entry could be implemented incrementally. It is argued that the appropriate combination of alternative limited‐entry mechanisms should take into account regional variables that affect the feasibility of entry controls for each particular fishery. It is also postulated that exploitation of an open‐access resource such as a fishery implies certain types of political behavior and outcomes that are analogous to economic behavior and outcomes in a common‐property resource environment. These characteristics of an openaccess resource, along with physical characteristics, tend to inhibit severely the rate of development of clearly defined property rights that would enhance the overall efficiency of the resource industry. The rate of development of property rights in an open‐access resource is a function of the cost of defining and enforcing these rights. The paper urges further identification and analysis of these “transactions costs,” which are largely a function of the political environment.     

Individual-based movement behaviour in a simple marine reserve—fishery system: why predictive models should be handled with care

The problem of overexploitation and unsustainability is a major issue in global fisheries. Marine reserves or protected no-take zones have been suggested as a possible solution that would maintain yield and protect stocks indefinitely. A key factor in the effectiveness of a marine reserve—fishery system is the rate of exchange of biomass between reserve and fishery: if the rate of exchange is too low then the fishery is not viable, but if the rate of exchange is too high then stocks may be exploited unsustainably and the reserve is rendered ineffective. The rate of exchange is determined by both the physical design and shape of the reserve, and the movement and dispersal behaviour of both the adult and larval-stage fish. Previous models looking at optimal reserve design usually only consider a diffusive population scale movement and dispersal, even though most animal movement is more realistically modelled as being correlated at the individual level. In this article, a deliberately simple simulation of a theoretical marine reserve—fishery system is used to demonstrate the danger of making predictions using only a population-level simplistic diffusive movement model. Further predictions based on the population average of a more realistic correlated movement model are also shown to be inaccurate. This result is due to both the high levels of individual variability in movement behaviour, and the heterogeneity of the environment. This suggests that in future studies, individual-based (rather than population-level) simulations and models are likely to give more useful insights into the dynamics of the marine fishery environment. Guest editors: J. Davenport, G. Burnell, T. Cross, M. Emmerson, R. McAllen, R. Ramsay & E. Rogan Challenges to Marine Ecosystems     

Stock estimation, environmental monitoring and equilibrium control of a fish population with reserve area

For sustainable exploitation of renewable resources, the separation of a reserve area is a natural idea. In particular, in fishery management of such systems, dynamic modelling, monitoring and control has gained major attention in recent years. In this paper, based on the known dynamic model of a fish population with reserve area, the methodology of mathematical systems theory and optimal control is applied. In most cases, the control variable is fishing effort in the unreserved area. Working with illustrative data, first a deterministic stock estimation is proposed using an observer design method. A similar approach is also applied to the estimation of the effect of an unknown environmental change. Then it is shown how the system can be steered to equilibrium in given time, using fishing effort as an open-loop control. Furthermore, a corresponding optimal control problem is also solved, maximizing the harvested biomass while controlling the system into equilibrium. Finally, a closed-loop control model is applied to asymptotically control the system into a desired equilibrium, intervening this time in the reserve area.     

Age and growth of big skate (Raja binoculata) and longnose skate (R. rhina) in the Gulf of Alaska

In 2003, big skates, Raja binoculata, and longnose skates, Raja rhina, were the target of a commercial fishery around Kodiak Island in the Gulf of Alaska (GOA) for the first time. The sudden development of a fishery for these species prompted the need for improved life history information to better inform fishery managers. Due to the selective nature of the skate fishery, mostly larger individuals were captured. Back-calculation from skate vertebral measurements was used to estimate size-at-age for younger skates. Because back-calculated age-length data within individuals were highly correlated, bootstrap resampling methods were used to test for differences between male and female growth curves. Results from bootstrapping indicated that differences between male and female growth were statistically significant for both species. This investigation indicates that growth of big skates in the GOA (max size 178 cm total length, max age 15 years) is similar to that in California, but different from that in British Columbia. For longnose skates, our GOA results agree with those reported in British Columbia, but were considerably older (max size 130 cm, max age 25 years) than those reported in California, which may not be surprising because longnose skates in the present study were generally larger. This life history information suggests that both big and longnose skates are at risk of unsustainable exploitation by targeted fisheries.     

Extended fishery jurisdiction in canada and the united states

Abstract

The 200‐mi fishery zone is a reality presenting opportunities for coastal states to create new institutions or pursue new management strategies. The strategies followed by the United States and by Canada in the initial stages of their extended‐jurisdiction management programs have similarly stated goals yet offer a number of striking contrasts in development and application. These domestic fishery management programs are discussed in their sociolegal and historical contexts. The domestic legal authority for the management programs is reviewed, planning procedures and available sanctions are outlined, and the control of domestic and foreign fishing is discussed. Finally, an argument is advanced for greater participation in the development of fishery management plans and a possible system for implementation is suggested. It is concluded that the American management system is open, decentralized, and highly structured. In contrast, the Canadian system is closed, relatively centralized, and very flexible. Both approaches are considered extreme yet there is no evidence of the development of new procedures for management decision making.     

Using grizzly bears to assess harvest-ecosystem tradeoffs in salmon fisheries

Implementation of ecosystem-based fisheries management (EBFM) requires a clear conceptual and quantitative framework for assessing how different harvest options can modify benefits to ecosystem and human beneficiaries. We address this social-ecological need for Pacific salmon fisheries, which are economically valuable but intercept much of the annual pulse of nutrient subsidies that salmon provide to terrestrial and aquatic food webs. We used grizzly bears, vectors of salmon nutrients and animals with densities strongly coupled to salmon abundance, as surrogates for "salmon ecosystem" function. Combining salmon biomass and stock-recruitment data with stable isotope analysis, we assess potential tradeoffs between fishery yields and bear population densities for six sockeye salmon stocks in Bristol Bay, Alaska, and British Columbia (BC), Canada. For the coastal stocks, we find that both bear densities and fishery yields would increase substantially if ecosystem allocations of salmon increase from currently applied lower to upper goals and beyond. This aligning of benefits comes at a potential cost, however, with the possibility of forgoing harvests in low productivity years. In contrast, we detect acute tradeoffs between bear densities and fishery yields in interior stocks within the Fraser River, BC, where biomass from other salmon species is low. There, increasing salmon allocations to ecosystems would benefit threatened bear populations at the cost of reduced long-term yields. To resolve this conflict, we propose an EBFM goal that values fisheries and bears (and by extension, the ecosystem) equally. At such targets, ecosystem benefits are unexpectedly large compared with losses in fishery yields. To explore other management options, we generate tradeoff curves that provide stock-specific accounting of the expected loss to fishers and gain to bears as more salmon escape the fishery. Our approach, modified to suit multiple scenarios, provides a generalizable method to resolve conflicts over shared resources in other systems.     

Fishery policy when considering the future opportunity of harvesting

Free access to a common pool of resource in a country may lead to over-exploitation and sacrifice future opportunities of harvesting. As such, the protection of a common fishery resource is worth investigating. In this paper we develop a two-period model and a multi-period model to analyze the optimal inter-temporal utilization of a finite resource of stock and propose to impose a tax on the harvest rate as an efficient mechanism with an aim at economic sustainability by incorporating the future opportunity of harvesting into the models as a major component of social objectives. The sensitivity analysis of the two-period model shows that (1) labor inputs for harvesting in Period 1 should be reduced, the biomass of fishery stock will increase, but the harvesting in Period 2 should be amplified and the biomass of fishery stock in Period 2 will not be affected if the current generation owns a higher valuation on the future opportunity of harvesting; (2) a higher internal regeneration rate leads to higher harvesting in each period and a higher level of fishery stock in Period 1, but an uncertain level of fishery stock in Period 2; (3) with a higher discount rate the harvesting in Period 1 should increase, but the harvesting in Period 2 should fall and the level of fishery stock in each period will be reduced; (4) a higher fish price in Period 1 leads to higher harvesting in Period 1, but reduced harvesting in Period 2. As a consequence, the level of fishery stock in each period will be reduced; (5) the effect of a change in fish prices in Period 2 on the harvesting and the level of fishery stock in Period 1 is uncertain, but the change in fish prices in Period 2 gives a positive effect on harvesting in Period 2 and a negative effect on the level of fishery stock in Period 2; (6) higher labor wages in Period 1 lead to lower harvesting, but a higher level of fishery stock in Period 1. This encourages an increase in harvesting in Period 2 and leads to a higher level of fishery stock in Period 2; and (7) a change of the labor wage in Period 2 affects the harvesting and the level of fishery stock in Period 1 indecisively, but it gives negative effects on the harvesting in Period 2 and positive effects on the level of fishery stock in Period 2.     

An ecological perspective on marine reserves in prey–predator dynamics

This paper describes a prey–predator type fishery model with prey dispersal in a two-patch environment, one of which is a free fishing zone and other is a protected zone. The existence of possible steady states, along with their local stability, is discussed. A geometric approach is used to derive the sufficient conditions for global stability of the system at the positive equilibrium. Relative size of the reserve is considered as control in order to study optimal sustainable yield policy. Subsequently, the optimal system is derived and then solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Numerical simulations are carried out to illustrate the importance of marine reserve in fisheries management. It is noted that the marine protected area enables us to protect and restore multi-species ecosystem. The results illustrate that dynamics of the system is extremely interesting if simultaneous effects of a regulatory mechanism like marine reserve is coupled with harvesting effort. It is observed that the migration of the resource, from protected area to unprotected area and vice versa, is playing an important role towards the standing stock assessment in both the areas which ultimately control the harvesting efficiency and enhance the fishing stock up to some extent.     

How behavioral constraints may determine optimal sensory representations

The sensory-triggered activity of a neuron is typically characterized in terms of a tuning curve, which describes the neuron's average response as a function of a parameter that characterizes a physical stimulus. What determines the shapes of tuning curves in a neuronal population? Previous theoretical studies and related experiments suggest that many response characteristics of sensory neurons are optimal for encoding stimulus-related information. This notion, however, does not explain the two general types of tuning profiles that are commonly observed: unimodal and monotonic. Here I quantify the efficacy of a set of tuning curves according to the possible downstream motor responses that can be constructed from them. Curves that are optimal in this sense may have monotonic or nonmonotonic profiles, where the proportion of monotonic curves and the optimal tuning-curve width depend on the general properties of the target downstream functions. This dependence explains intriguing features of visual cells that are sensitive to binocular disparity and of neurons tuned to echo delay in bats. The numerical results suggest that optimal sensory tuning curves are shaped not only by stimulus statistics and signal-to-noise properties but also according to their impact on downstream neural circuits and, ultimately, on behavior.     

Combining control measures for more effective management of fisheries under uncertainty: quotas, effort limitation and protected areas

We consider combinations of three types of control measures for the management of fisheries when the input information for policy decisions is uncertain. The methods considered include effort controls, catch quotas and area closures. We simulated a hypothetical fishery loosely based on the Icelandic cod fishery, using a simple spatially explicit dynamic model. We compared the performance with respect to conserving the resource and economic return for each type of control measure alone and in combination. In general, combining more than one type of primary direct control on fishing provides a greater buffer to uncertainty than any single form of fishery control alone. Combining catch quota control with a large closed area is a most effective system for reducing the risk of stock collapse and maintaining both short and long-term economic performance. Effort controls can also be improved by adding closed areas to the management scheme. We recommend that multiple control methods be used wherever possible and that closed areas should be used to buffer uncertainty. To be effective, these closed areas must be large and exclude all principal gears to provide real protection from fishing mortality.     

Shortcomings of current fish transfer functions and a proposal for a new transfer function

One important component of almost all theoretical models in fishery is a fish transfer function. However, most of the current fish transfer functions have significant shortcomings. This paper contributes to the literature on fishery management by (1) showing some of shortcomings of commonly used fish transfer functions and proposing a new fish transfer function that is more appropriate to model net amount of fish transfer from one marine area to another; and (2) applying the proposed transfer function in an optimal harvest problem to assess the economic payoff from a switching reserve versus a fixed marine reserve. The findings indicate that a switching marine reserve appears to provide fishers with higher economic benefits than a fixed marine reserve. The payoff gain from a switching reserve appears to increase when the fish move less because of bio-ecological and territorial factors that impede the fish dispersal between marine areas.     

色林错渔业生产的现状与可持续利用的对策

色林错裸鲤（Gymnocypris selincuoensis)是藏北色林错湖泊中惟一的一种鱼类。本文介绍了色林错渔业的开发利用情况,并对色林错裸鲤最小捕捞年龄、捕捞强度、最小网目以及最佳年捕捞产量进行了探讨。从可持续发展的角度,我们认为对色林错鱼类资源的利用必须以保证现有湖泊生态系统的稳定为核心,在满足维持一个足够数量及年龄结构的繁殖群体的基础上,以获得最佳持续经济利益为目标。以往强调甚至采用的最大持续产量理论在高原极端环境条件下并不能作为鱼类资源利用的追求目标或确定渔产量的标准,而只能作为对其捕捞强度的参考。总的允许渔获量应当根据最适捕捞死亡率F0．2来确定。本文最后提出了色林错湖泊鱼类资源可持续利用的8条具体措施。     

Modelling the Impact of Marine Reserves on a Population with Depensatory Dynamics

In this study, we use a spatially implicit, stage-structured model to evaluate marine reserve effectiveness for a fish population exhibiting depensatory (strong Allee) effects in its dynamics. We examine the stability and sensitivity of the equilibria of the modelled system with regards to key system parameters and find that for a reasonable set of parameters, populations can be protected from a collapse if a small percentage of the total area is set aside in reserves. Furthermore, the overall abundance of the population is predicted to achieve a maximum at a certain ratio \(A\) of reserve area to fished area, which depends heavily on the other system parameters such as the net export rate of fish from the marine reserves to the fished areas. This finding runs contrary to the contested “equivalence at best” result when comparing fishery management through traditional catch or effort control and management through marine reserves. Lastly, we analyse the problem from a bioeconomics perspective by computing the optimal harvesting policy using Pontryagin’s Maximum Principle, which suggests that the value for \(A\) which maximizes the optimal equilibrium fishery yield also maximizes population abundance when the cost per unit harvest is constant, but can increase substantially when the cost per unit harvest increases with the area being harvested.