Optimal Harvesting Policy Research Articles

Bioeconomic harvesting of a prey–predator fishery

This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-efforthypothesis. Here both the prey and the predator species obey the law of logistic growth. We have taken the predator functional response to prey density in such a form that each predator's functional response to the prey density approaches a constant as the prey population increases. Boundedness of the exploited system is examined. The existence of its steady states and their stability (local and global) are studied using Eigenvalue analysis. The existence of bionomic equilibria has been illustrated using a numerical example. The problem of determining the optimal harvesting policy is then solved by using Pontryagin's maximum principle.

Bioeconomic Modelling: An Application to the North-East- Atlantic Cod Fishery

This paper describes a single species model, which followed by two stages, a mature and an immature stage. Conditionsfor existence of equilibrium points and their stability are discussed. The model in this paper has been developed on theconcept of optimal management of resources based on the criterion of maximization of present values of net economicrevenues. Using the data from the North-East Atlantic cod fishery, the results of the optimal stock, harvest and effort levelare derived. Our simulation results show that optimal harvesting policy is much superior than the MSY policy and optimalpaths always take less time than the suboptimal path to reach the optimal steady state. Our analysis also shows that, if itis insisted that a closure is take place for one of the two sub-stocks,it will be optimal to reduce fishing on the immaturesub-stock rather than the mature sub-stock.

Asymptotic Convergence of Optimal Policies for Resource Management with Application to Harvesting of Multiple Species Forest

We study the long-term behavior of the optimal harvesting policies for a mixed forest composed by multiple species of different maturity ages. This model is a prototype for the exploitation of a finite resource such as land or space, which can be allocated to different activities that produce their revenue after certain delays at which the resource is liberated for reuse. We prove the existence and uniqueness of a sustainable state, and we discuss the conditions under which an optimal trajectory converges in the long run toward this state or toward the set of optimal periodic cycles. We also analyze different situations in which the convergence occurs in finite time.

Food chain model with optimal harvesting in fuzzy environment

A multispecies harvesting model with mutual interactions is formulated based on Lotka–Voltera model with three competing species which are affected not only by harvesting but also by the presence of prey, predator and the third species, which is super predator. In order to understand the dynamics of the system, it is assumed that the super predator follows the logistic growth. Further, there is demand for all the above three species in the market and hence harvesting of all species is performed. We derive the condition for global stability of the system using a suitable Lyapunov function. The possibility of existence of bioeconomic equilibrium is discussed. The optimal harvest policy is studied and the solution is derived under imprecise inflation in fuzzy environment using Pontryagin’s maximal principle. Finally some numerical examples are discussed to illustrate the model.

Optimal fishery harvesting rules under uncertainty

This paper derives the optimal fishery harvest policy in a real-option model with a stochastic logistic growth process, harvest-sensitive output price, and both fixed and variable harvesting costs. The policy specifies the harvest trigger and harvest size, while outputs from the model include the value of the fishery and the risk of extinction. The optimal policy is illustrated with data from the Pacific Halibut Fishery. For this particular case, the optimal policy recommends harvesting when the fish stock rises to about three-quarters the environmental carrying capacity, and the amount harvested should be approximately a quarter of the prevailing stock. This harvesting policy maximizes the value of the fishery, and importantly, the resulting risk of extinction is negligible. We also carry out some sensitivity analysis to see how the optimal policy (and the resulting fishery value and risk of extinction) change when the input parameters are varied, particularly the ecological parameters intrinsic growth rate and volatility of the stock, and also the economic parameters that have been ignored in previous papers (price sensitivity and fixed cost). If the optimal policy is followed, the risk of extinction will be negligible, except for very low growth rate and high volatility.

CAPITAL THEORETIC ANALYSIS OF A HOLLING–TANNER-TYPE PREY–PREDATOR FISHERY WITH TAXATION AS A CONTROL INSTRUMENT

The level of fishing effort expands or contracts in a dynamic reaction model of a fishery accordingly as the net economic revenue (i.e. perceived rent) to the fishermen is positive or negative. A dynamic reaction model reflects this dynamic interaction between the perceived rent and the effort in a fishery. The combined harvesting of a prey–predator fishery is assumed to be regulated by an external authority by imposing a tax per unit biomass of both the species. The fishing effort is taken to be a dynamic variable of time, which is proportional to the instantaneous capital invested in the fishery. The steady states of the system along with their local as well as global stability are considered. The optimal harvesting policy with the tax as a control instrument is discussed. The results are numerically discussed and graphically illustrated. Sensitivity analysis of the parameters is carried out. The paper ends with concluding remarks.

OPTIMAL CONTROL FOR A PREDATOR-PREY SYSTEM WITH AGE-DEPENDENT

This paper is concerned with optimal harvesting policy for predator-prey system of three species with age-dependent. The existence and uniqueness of non-negative solution of the system are proved using the fixed pint theorem. The existence of optimal control strategy is discussed, optimality conditions are derived by means of normal cone and Dubovitskii–Milyutin's general theory. Our results extend some known criteria.

Bionomic exploitation of a ratio-dependent predator–prey system

The present article deals with the problem of combined harvesting of a Michaelis–Menten-type ratio-dependent predator–prey system. The problem of determining the optimal harvest policy is solved by invoking Pontryagin's Maximum Principle. Dynamic optimization of the harvest policy is studied by taking the combined harvest effort as a dynamic variable. Computer simulations are carried out to illustrate our analytical findings. Biological and bioeconomical interpretations of the results are explained critically.

Escapement goal analysis and stock reconstruction of sockeye salmon populations (Oncorhynchus nerka) using life-history models

We compare life-history models with the Beverton–Holt approach of escapement goal analysis. We model the life history of a sockeye salmon ( Onchorhynchus nerka ) population from a spawning stage, through juvenile and adult stages, and ending with adults that return to spawn. We fit models to data by statistically comparing predicted and observed numbers of four dominant adult ages. Posterior estimates of parameters from Markov chain Monte Carlo simulations are then used to assess optimal harvest policies. We search for policies that produce the highest average yield. We find that it is possible to detect density dependence with a life-history model where analysis of Beverton–Holt stock–recruitment relationship fails to do so. We find that Beverton–Holt relationships produce policies and long-term yield estimates that are inconsistent with empirical trends. Conversely, we find that optimal spawning stock sizes and maximum sustained yield estimates using the life-history model estimate are consistent with the historical behavior of fisheries examined. Adding smolt data to the analysis does not substantially change predicted optimal spawning stock size, but decreases the variance in estimated posterior parameter distributions and policy variable distributions.

MODELING AND ANALYSIS OF A HARVESTING FISHERY MODEL IN A TWO-PATCH ENVIRONMENT

In this paper, a harvesting fishery model in a two-patch environment: one free-fishing zone and the other one reserved zone where fishing is strictly prohibited, is proposed and analyzed. The existence of possible biological steady states, along with their local stability, instability and global stability is discussed. The existence of bioeconomic equilibrium is derived. An optimal harvesting policy is also given by applying pontryagin's maximum principle.

Harvesting of a prey–predator fishery in the presence of toxicity

In this model we discuss the bioeconomic harvesting of a prey–predator fishery in which both the species are infected by some toxicants released by some other species. Here both the species are harvested where we use the usual catch-per-unit-effort hypothesis. The dynamical behaviour of the exploited system is examined. The possibility of existence of a bionomic equilibrium is considered. The optimal harvesting policy is studied by using Pontryagin’s maximal principle. Some numerical examples and the corresponding solution curves are studied to illustrate the results of the model. Finally, the existence of limit cycle is discussed.

OPTIMAL HARVESTING PROBLEM FOR AN AGE-DEPENDENT n-DIMENSIONAL COMPETING SYSTEM WITH DIFFUSION

In this work, optimal harvesting policy for an age-dependent and spatial diffusion n-dimensional competing species is discussed. The existence and uniqueness of non-negative solution to the system are investigated by using the fixed point theorem. The existence of optimal control strategy is discussed and optimality conditions are obtained. Our results extend some known criteria.

Optimal harvesting for an age-dependent n-dimensional food chain model

This paper is concerned with optimal harvesting policy for an age-dependent n-dimensional food chain model. The existence and uniqueness of non-negative solution of the system are proved using the fixed point theorem. By Mazur’s theorem, the existence of optimal control strategy is demonstrated and optimality conditions derived by means of normal cone.

The optimal harvesting problem with a land market: a characterization of the asymptotic convergence

We study the asymptotic behavior of the optimal harvesting policies for a multiple species forest with a land market, i.e., any fraction of the land can be traded at any time stage. We prove the existence of sustainable states and we discuss the conditions under which any optimal trajectory converges in the long run towards one of these states or towards the set of optimal periodic cycles. We also discuss briefly a more general problem that includes costs of converting land between the different species.

Optimal harvesting considering biological and economic objectives

Most examinations of optimal harvesting policies have considered only biological objectives, yet it is increasingly recognized that a primary objective of many fisheries is economic profitability. Using Bayesian risk analysis, we compare policies that combine fish harvesting, the revenue brought in by fish sales, the cost of harvesting and processing, and processing and fishing capacity to find policies that maximize biological yield and economic profit to the processing and harvesting sectors for a major Pacific salmon (Oncorhynchus spp.) fishery in Bristol Bay, Alaska. We show that although average catch is maximized by a fixed escapement policy, total revenue is maximized by a policy that includes some harvesting at stock sizes below that required to produce maximum average catch. In addition, there is a wide range of policies that provide 90% of the maximum for any of the biological and economic objectives considered. Economic profitability is enhanced by limitations on processing and harvesting capacity.

On selective harvesting of an inshore‐offshore fishery: a bioeconomic model

AbstractIn the present paper, a bioeconomic model is developed for the selective harvesting of a single species, inshore‐offshore fishery, assuming that the growth of the species is governed by the Gompertz law. The dynamical system governing the fishery is studied in depth; the local and global stability of its non‐trivial steady state are examined. Existence of a bionomic equilibrium is established under different parametric considerations. The optimal harvest policy is discussed by invoking Pontryagin's Maximum Principle. Lastly, the results are illustrated with the help of a numerical example. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A ratio‐dependent predator–prey model with stage structure and optimal harvesting policy

AbstractIn this paper, a ratio‐dependent predator–prey model with stage structure and harvesting is investigated. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence and stability are performed. By constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. The existence possibilities of bioeconomic equilibria have been examined. An optimal harvesting policy is also given by using Pontryagin's maximal principle. Copyright © 2007 John Wiley & Sons, Ltd.

Optimal harvesting for a population dynamics problem with age-structure and diffusion

In this work, optimal harvesting policy for the predator-prey system of three species with age-dependent and diffusion is discussed. Existence and uniqueness of non-negative solution to the system are investigated by using the fixed point theorem. The existence of optimal control strategy is discussed and optimality conditions are obtained. Our results extend some known criteria.

Optimal harvesting policy for inshore-offshore fishery model with impulsive diffusion *

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.

A bioeconomic model of a single-species fishery with a marine reserve

This study examines the impact of the creation of marine protected areas (MPAs), from both economic and biological perspectives. In particular, we examine the effects of protected patches and harvesting on resource populations. We conclude that protected patches are an effective means of conserving resource populations, even though extinction cannot be prevented in all cases. We discuss the dynamic optimization of a harvest policy by choosing E( t), the harvesting effort, as the dynamic variable. We also discuss the optimal equilibrium harvest policy and explain the biological and bioeconomic interpretations of the results.