Bio-economics of a renewable resource in a seasonally varying environment

Castilho, César; Pichika, Srinivasu D. N.

doi:10.1016/j.mbs.2006.09.011

Cited by 25 publications

(13 citation statements)

References 15 publications

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“…" Mangel et al (2002) examine problems with the standard definition of maximum sustainable yield when there are large fluctuations in environmental conditions using the California commercial squid fishery as an example. 3 An unpublished paper from the mathematical population dynamic literature by Castilho and Srinivasu (2005) goes over some of the same ground as Parma (1990) with respect to the implications of a time varying growth rate for optimal management. There are many population dynamic models that have growth rates that are predictable functions of identifiable factors such as environmental conditions (Mallet et al 1999).…”

Section: Introductionmentioning

confidence: 99%

Fisheries Management Under Cyclical Population Dynamics

Carson

Granger

Jackson

et al. 2008

Environ Resource Econ

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Cycles in environmental conditions (e.g., sea-surface temperature) directly impact fish growth. This paper extends the classical Gordon-Schaefer fishery model by replacing the constant growth rate with a cyclical growth rate. The optimal harvest rate is shown to fluctuate, but the cycle of the harvest rate lags the cycle of the biological growth function with the highest harvest rate occurring after biological conditions start to decline. Simulations contrast various fishing policies and illustrate the proclivity to crash a fishery if it is wrongfully managed as if there is a constant growth rate with i.i.d. environmental shocks. Finally, we show that small cyclical fluctuations in one species can result in large fluctuations in the optimal harvest rate of another species if the fish species are interlinked through predator-prey relationships.

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Section: Introductionmentioning

confidence: 99%

Fisheries Management Under Cyclical Population Dynamics

Carson

Granger

Jackson

et al. 2008

Environ Resource Econ

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“…A great number of works are dedicated to systems with renewable resources, for example [1][2][3]. The base of the mathematical apparatus consists of differential equations in which the sought for function is dependent on time.…”

Section: Introductionmentioning

confidence: 99%

Application of Functional Operators with Shift to the Study of Renewable Systems When the Reproductive Process Is Described by Integrals with Degenerate Kernels

Karelin¹,

Tarasenko²,

Gonzalez-Hernandez³

2013

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We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive processes as a linear expression or as a shift summand. In this work, the reproductive term is represented using an integral with a degenerate kernel. A cyclic model of evolution of the system with a renewable resource is developed. We propose a method for solving the balance equation and we determine an equilibrium state of the system. Having applied this model, we can investigate problems of natural systems and their resource production.

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“…There has been considerable study in recent years on optimal management of renewable resources from various perspectives (see, e.g., [1][2][3][4][5]). The need for sustenance of the resources for future generations is the motivating factor for most of the studies in this area.…”

Section: Introductionmentioning

confidence: 99%

Asymptotically periodic solution and optimal harvesting policy for Gompertz system

Zeng

2011

Nonlinear Analysis: Real World Applications

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Bio-economics of a renewable resource in a seasonally varying environment

Cited by 25 publications

References 15 publications

Fisheries Management Under Cyclical Population Dynamics

Fisheries Management Under Cyclical Population Dynamics

Application of Functional Operators with Shift to the Study of Renewable Systems When the Reproductive Process Is Described by Integrals with Degenerate Kernels

Asymptotically periodic solution and optimal harvesting policy for Gompertz system

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