Optimal Management Of Renewable Resources Research Articles

The optimal management of renewable resources under the risk of potential regime shift

Complex dynamic systems can undergo changes in feedbacks between system components causing a rapid and persistent shift in system behavior (“regime shifts”), and potentially reduce welfare from declining provision of important ecosystem services. In this paper, we provide an analytical condition that determinfilefs whether the threat of a potential regime shift causes management to be more aggressive or more precautionary. In numerical simulations we find that aggressive management can occur for reasonable parameter values, which is counter prior results that the potential for harmful regime shift always leads to precautionary management.

Density dependent harvesting of a logistic population in a slowly varying environment

We apply a multiscale method to construct general analytic approximations for the solution of a harvested logistic system, where the system parameters vary slowly in time. Such approximations are a useful alternative to numerical solutions and are applicable to a range of parameter values. We consider two situations: subcritical harvesting, where the population survives; and supercritical harvesting, where it is driven to extinction. These approximations give excellent agreement with the numerical solutions of test cases. References J. R. Beddington and R. M. May. Harvesting natural populations in a randomly fluctuating environment. Science, 197:463--465, 1977. C. W. Clark. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. 2nd Edn. Wiley-Interscience, 2005. T. L. Cromer. Harvesting in a seasonal environment. Math. Comput. Model., 10(6):445--450, 1988. T. Grozdanovski. Multi-Scaling Methods Applied to Population Models. Ph.D. Thesis, RMIT University, 2009. T. Grozdanovski and J. J. Shepherd. Slow variation in the Gompertz model. ANZIAM J., 47:C451--C554, 2007. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1061 T. Grozdanovski, J. J. Shepherd and A. Stacey. Multiscaling analysis of a logistic model with slowly varying coefficients. Appl. Math. Lett., 22:1091--1095, Elsevier, 2009. doi:10.1016/j.aml.2008.10.002. T. Legovic and G. Peric. Harvesting population in a periodic environment. Ecol. Model., 24:221--229, 1984. J. D. Murray. Mathematical Biology I: An Introduction. 3rd Edn. Springer--Verlag, Berlin, 2007. S. Rosenblat. Population models in a periodically fluctuating environment. J. Math. Biol., 9:23--36, 1980.

Optimal management of renewable resources with Darwinian selection induced by harvesting

We present a bioeconomic analysis of the optimal long-term management of a genetic resource in the presence of selective harvesting. It is assumed that individuals possessing a particular gene have a lower natural mortality rate and are more valuable to capture. Highly selective harvesting may cause such a gene to lose its fitness advantage, and hence change the evolutionary path of the species. Results indicate that in a zero-cost harvesting regime, the decision to preserve the valuable gene depends on the natural rate of selection against less valuable individuals and the interest rate. On the other hand, the decision to let the less valuable gene become a significant fraction of the genes depends only on biological parameters. If marginal costs are positive, it is never optimal to let a valuable gene become extinct. Further, for some parameter values, the system exhibits multiple equilibriums. Therefore, optimal regulation may depend on initial conditions.

How to model marine reserves?

The safeguarding of resources is one of the principal subjects of halieutics studies. Among the solutions proposed to avert the disappearance of species, the setting in place of preservation (no take) reserves is often mentioned. Most work on this subject, theoretical as well as applied, was undertaken in recent years. In this paper, we seek to compare two different models presented in existing literature by highlighting their underlying assumptions. Both models were derived from what is often referred to as the “model of Schaefer–Clark” (reference to the work of the last author on Mathematical Bioeconomics: Clark [C.W. Clark, Mathematical Bioecomics: The Optimal Management of Renewable Resources, 2nd ed., John Wiley and Sons, New-York, 1990]). We show that various variations of this model lead to properties that can be very different.

On the Optimal Stochastic Impulse Control of Linear Diffusions

We consider a class of stochastic impulse control problems of linear diffusions arising in studies considering the determination of optimal dividend policies. This class of problems appears also in studies analyzing the optimal management of renewable resources. We state a set of weak conditions guaranteeing both existence and uniqueness of the boundary characterizing the optimal policy and its value. We also analyze two associated stochastic control problems and establish a general ordering for both the values and the marginal values of the considered stochastic control problems. In this way we extend previous findings obtained by relying on linear payoff characterizations.

Optimal impulsive control in periodic ecosystem

In this paper, the impulsive exploitation of single species modelled by periodic Logistic equation is considered. First, it is shown that the generally periodic Kolmogorov system with impulsive harvest has a unique positive solution which is globally asymptotically stable for the positive solution. Further, choosing the maximum annual biomass yield as the management objective, we investigate the optimal harvesting policies for periodic logistic equation with impulsive harvest. When the optimal harvesting effort maximizes the annual biomass yield, the corresponding optimal population level, and the maximum annual biomass yield are obtained. Their explicit expressions are obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. In particular, it is proved that the maximum biomass yield is in fact the maximum sustainable yield (MSY). The results extend and generalize the classical results of Clark [Mathematical Bioeconomics: The Optimal Management of Renewable Resources, Wiley, New York, 1976] and Fan [Optimal harvesting policy for single population with periodic coefficients, Math. Biosci. 152 (1998) 165–177] for a population described by autonomous or nonautonomous logistic model with continuous harvest in renewable resources.

Gilpin–Ayala model with spatial diffusion and its optimal harvesting policy

In this paper we consider spatially nonhomogeneous Gilpin-Ayala diffusive equation suffered from exploitation with spatially variable harvesting effort E(x):@[email protected][email protected]+r(x)u1-(uK(x))^@q-E(x)u,(t,x)@?(0,~)[email protected],u(0,x)[email protected](x),[email protected][email protected],@[email protected]?n=0,[email protected]?(0,~),[email protected][email protected][email protected],which describes the growth of the single-species with Neumann boundary condition and initial value condition. We investigate the global stability of equilibrium solution and optimal harvesting policy. It is found that in the case of ordinary differential equation, our results generalize the spatially homogeneous equations discussed in [C.W. Clark, Mathematical Bio-economics: The Optimal Management of renewable Resources, Wiley, New York, 1976; C.W. Clark, Mathematical Bio-economics: The Optimal Management of Renewable Resources, second ed., Wiley, New York, 1990; M. Fan, K. Wang, Optimal harvesting policy for single population with periodic coefficients, Math. Biosci. 152 (1998) 165; H. Li, A class of single-species models with periodic coefficients and their optimal harvesting policy, J. Biomath. 14(4) (1999) 293], our brief results also generalize the corresponding results in [H. Li, Logistic model for single-species with spatial diffusion and its optimal harvesting policy, J. Biomath. 14(3) (1999) 293] when @q=1.

Can marine protected areas enhance both economic and biological situations?

This paper investigates impacts of the creation of Marine Protected Areas (MPAs), in both economic and biological perspectives. The economic indicator is defined as the sum of discounted benefits derived from exploitation of the resource in the fishery sector, assumed to be optimally managed. The biological indicator is taken as the stock density of the resource. The basic fishery model (C.W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources, second ed., John Wiley and Sons, New York, 1990) will serve as a convenient benchmark in comparing results with those that are derived from a model of two patchy populations (cf. R. Hannesson, Marine reserves: what would they accomplish, Mar. Resour. Econ. 13 (1998) 159). In the latter, a crucial characteristic is the migration coefficient with describes biological linkages between protected and unprotected areas. A set of situations where both economic and biological criteria are enhanced, after introducing a MPA, is presented. These results are obtained with the help of numerical simulations. To cite this article: D. Ami et al., C. R. Biologies 328 (2005).

Optimal management of multiple renewable resource stocks: An application to Minke whales

Most bioeconomic models of efficient renewable resource management are constructed for a single harvesting ground. A bioeconomic model is developed in this paper to study the optimal management of renewable resources that are found in spatially distinct harvesting grounds. The model is applied to Minke whale management. Important inter-regional substitution effects are shown to exist. In addition, comparison with previous studies shows that multiple stock management is necessary for efficient management. Finally, the current Minke whale moratorium is shown to be inefficient unless significant nonmarket values exist.

Mathematical Bioeconomics: The Optimal Management of Renewable Resources.

Introduction. 1. Elementary Dynamics of Exploited Populations. 1.1 The Logistic Growth Model. 1.2 Generalized Logistic Models: Depensation. 1.3 Summary and Critique. 2. Economic Models of Renewable-Resource Harvesting. 2.1 The Open-Access Fishery. 2.2 Economic Overfishing. 2.3 Biological Overfishing. 2.4 Optimal Fishery Management. 2.5 The Optimal Harvest Policy. 2.6 Examples Based on the Schaefer Model. 2.7 Linear Variational Problems. 2.8 The Possibility of Extinction. 2.9 Summary and Critique. 3. Capital-Theoretic Aspects of Resource Management. 3.1 Interest and Discount Rates. 3.2 Capital Theory and Renewable Resources. 3.3 Nonautonomous Models. 3.4 Applications to Policy Problems: Labor Mobility in the Fishery. 4. Optimal Control Theory. 4.1 One-Dimensional Control Problems. 4.2 A Nonlinear Fishery Model. 4.3 Economic Interpretation of the Maximum Principle. 4.4 Multidimensional Optimal Control Problem. 4.5 Optimal Investment in Renewable-Resource Harvesting. 5. Supply and Demand: Nonlinear Models. 5.1 The Elementary Theory of Supply and Demand. 5.2 Supply and Demand in Fisheries. 5.3 Nonlinear Cost Effects: Pulse Fishing. 5.4 Game-Theoretic Models. 5.5 Transboundary Fishery Resources: A Further Application of the Theory. 5.6 Summary and Critique. 6. Dynamical Systems. 6.1 Basic Theory. 6.2 Dynamical Systems in the Plane: Linear Theory. 6.3 Isoclines. 6.4 Nonlinear Plane-Autonomous Systems. 6.5 Limit Cycles. 6.6 Gause's Model of Interspecific Competition. 7. Discrete-Time and Metered Models. 7.1 A General Metered Stock-Recruitment Model. 7.2 The Beverton-Holt Stock-Recruitment Model. 7.3 Depensation Models. 7.4 Overcompensation. 7.5 A Simple Cohort Model. 7.6 The Production Function of a Fishery. 7.7 Optimal Harvest Policies. 7.8 The Discrete Maximum Principle. 7.9 Dynamic Programming. 8. The Theory of Resource Regulation. 8.1 A Behavioral Model. 8.2 Optimization Analysis. 8.3 Limited Entry. 8.4 Taxes and Allocated Transferable Quotas. 8.5 Total Catch Quotas. 8.6 Summary and Critique. 9. Growth and Aging. 9.1 Forestry Management: The Faustmann Model. 9.2 The Beverton-Holt Fisheries Model. 9.3 Dynamic Optimization in the Beverton-Holt Model. 9.4 The Case of Bounded F. 9.5 Multiple, Cohorts: Nonselective Gear. 9.6 Pulse Fishing. 9.7 Multiple Cohorts: Selective Gear. 9.8 Regulation. 9.9 Summary and Critique. 10. Multispecies Models. 10.1 Differential Productivity. 10.2 Harvesting Competing Populations. 10.3 Selective Harvesting. 10.4 A Diffusion Model: The Inshore-Offshore Fishery. 10.5 Summary and Critique. 11. Stochastic Resource Models. 11.1 Stochastic Dynamic Programming. 11.2 A Stochastic Forest Rotation Model. 11.3 Uncertainty and Learning. 11.4 Searching for Fish. 11.5 Summary and Critique. Supplementary Reading. References. Index.

Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Colin W. Clark

<i>Mathematical Bioeconomics: The Optimal Management of Renewable Resources</i>. Colin W. Clark

Optimal management of renewable resources with growing demand and stock externalities

In an equilibrium framework, optimal management of renewable resources in the presence of growing demand or externalities leads to steady states that differ from those characterized by rate of interest equals rate of change in growth plus rate of change in prices. Measures to reach an optimum with externalities other than direct controls are found to be critically mediated by the costs of harvesting.

The Optimal Management of Transboundary Renewable Resources

This paper investigates the question of the optimal management of renewable resources jointly owned by two states. A dynamic model of fisheries is combined with Nash's theory of two-person co-operative games. Conflicts in the management strategies of the two states arising from differences in perceptions of the social rate of discount, fishing effort costs, and consumer preferences are examined. Cases are considered in which the two partners can and cannot make side or transfer payments to one another. It is concluded that side payments greatly ease the resolution of resource management conflicts. La gestion optimale de ressour-ces renouvelables trans-nationales. Ce memoire examine le problmy renewable resources / 357 should be extended to cover transboundary resources involving several countries. That however, would be the subject of another paper.

Mathematical Bioeconomics: The Optimal Management of Renewable Resources (Colin W. Clark)

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistoryPublished online: 17 February 2012Publication DataISSN (print): 0036-1445ISSN (online): 1095-7200Publisher: Society for Industrial and Applied MathematicsCODEN: siread

Mathematical Bioeconomics. The Optimal Management of Renewable Resources.

Mathematical Bioeconomics. The Optimal Management of Renewable Resources.

Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Colin W. Clark

Previous articleNext article No AccessNew Biological BooksMathematical Bioeconomics: The Optimal Management of Renewable Resources. Colin W. Clark Kenneth E. F. WattKenneth E. F. Watt Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Quarterly Review of Biology Volume 52, Number 4Dec., 1977 Published in association with Stony Brook University Article DOIhttps://doi.org/10.1086/410255 Views: 2Total views on this site PDF download Crossref reports no articles citing this article.

Mathematical Bio-Economics: The Optimal Management of Renewable Resources

Mathematical Bio-Economics: The Optimal Management of Renewable Resources