OPTIMAL IMPULSIVE HARVESTING OF A SINGLE-SPECIES WITH GOMPERTZ LAW OF GROWTH

2006 ◽  
Vol 14 (02) ◽  
pp. 303-314 ◽  
Author(s):  
YUJUAN ZHANG ◽  
ZHILONG XIU ◽  
LANSUN CHEN
Keyword(s):  
Global Attractivity ◽  
Population Level ◽  
Single Species ◽  
Maximum Sustainable Yield ◽  
Discrete Dynamical Systems ◽  
Optimal Harvesting ◽  
Sustainable Yield ◽  
Gompertz Law ◽  
Optimal Population ◽  
Impulsive Harvesting

In this paper we investigate the optimal harvesting problems of a single species with Gompertz law of growth. Based on continuous harvesting models, we propose impulsive harvesting models with constant harvest or proportional harvest. By using the discrete dynamical systems determined by the stroboscopic map, we discuss existence, stability and global attractivity of positive periodic solutions, and obtain the maximum sustainable yield and the corresponding optimal population level. At last, we compare the maximum sustainable yield of impulsive harvest with that of continuous harvest, and point out that proportional harvest is superior to constant harvest.

Optimal harvesting for a single-species population governed by Gompertz law: Influence of environmental fluctuation and limited harvesting capacity

2019 ◽  
Vol 12 (02) ◽  
pp. 1950018
Author(s):  
P. D. N. Srinivasu ◽  
Simon D. Zawka
Keyword(s):  
Control Variable ◽  
Optimal Solution ◽  
Single Species ◽  
Optimal Harvesting ◽  
Environmental Fluctuation ◽  
Gompertz Equation ◽  
Species Population ◽  
Gompertz Law ◽  
Binding Constraints ◽  
Single Species Population

This work presents an optimal harvesting problem associated with a single-species population governed by Gompertz law in a seasonally fluctuating environment. The influence of environmental fluctuation is accommodated by choosing the coefficients in the differential equation to be periodic functions with the same period and restriction on the harvesting effort is accommodated by considering binding constraints on the control variable. Hence, a linear optimal control problem has been considered where the state dynamics is governed by Gompertz equation and the control variable is subject to the binding constraints. With the help of maximum principle and the concept of blocked intervals, an optimal periodic solution has been obtained which is followed by the construction of optimal solution using the theory of most rapid approach. Important results of the study are demonstrated through numerical simulations.

scholarly journals Food for thought: pretty good multispecies yield

2016 ◽  
Vol 74 (2) ◽  
pp. 475-486 ◽  
Author(s):  
Anna Rindorf ◽  
Catherine Mary Dichmont ◽  
Phillip S. Levin ◽  
Pamela Mace ◽  
Sean Pascoe ◽  
...  
Keyword(s):  
Fisheries Management ◽  
Single Species ◽  
Maximum Sustainable Yield ◽  
Social Benefits ◽  
Sustainable Yield ◽  
Average Yield ◽  
Operational Management ◽  
Operating Space ◽  
Management Advice ◽  
Safe Operating

Abstract MSY principles for marine fisheries management reflect a focus on obtaining continued high catches to provide food and livelihoods for humanity, while not compromising ecosystems. However, maintaining healthy stocks to provide the maximum sustainable yield on a single-species basis does not ensure that broader ecosystem, economic, and social objectives are addressed. We investigate how the principles of a “pretty good yield” range of fishing mortalities assumed to provide >95% of the average yield for a single stock can be expanded to a pretty good multispecies yield (PGMY) space and further to pretty good multidimensional yield to accommodate situations where the yield from a stock affects the ecosystem, economic and social benefits, or sustainability. We demonstrate in a European example that PGMY is a practical concept. As PGMY provides a safe operating space for management that adheres to the principles of MSY, it allows the consideration of other aspects to be included in operational management advice in both data-rich and data-limited situations. PGMY furthermore provides a way to integrate advice across stocks, avoiding clearly infeasible management combinations, and thereby hopefully increasing confidence in scientific advice.

scholarly journals Achieving maximum sustainable yield in mixed fisheries: a management approach for the North Sea demersal fisheries

2016 ◽  
Vol 74 (2) ◽  
pp. 566-575 ◽  
Author(s):  
Clara Ulrich ◽  
Youen Vermard ◽  
Paul J. Dolder ◽  
Thomas Brunel ◽  
Ernesto Jardim ◽  
...  
Keyword(s):  
North Sea ◽  
Regional Scale ◽  
Single Species ◽  
Maximum Sustainable Yield ◽  
Management Approach ◽  
Sustainable Yield ◽  
Total Allowable Catch ◽  
The North ◽  
Trade Offs ◽  
The North Sea

Achieving single species maximum sustainable yield (MSY) in complex and dynamic fisheries targeting multiple species (mixed fisheries) is challenging because achieving the objective for one species may mean missing the objective for another. The North Sea mixed fisheries are a representative example of an issue that is generic across most demersal fisheries worldwide, with the diversity of species and fisheries inducing numerous biological and technical interactions. Building on a rich knowledge base for the understanding and quantification of these interactions, new approaches have emerged. Recent paths towards operationalizing MSY at the regional scale have suggested the expansion of the concept into a desirable area of “pretty good yield”, implemented through a range around FMSY that would allow for more flexibility in management targets. This article investigates the potential of FMSY ranges to combine long-term single-stock targets with flexible, short-term, mixed-fisheries management requirements applied to the main North Sea demersal stocks. It is shown that sustained fishing at the upper bound of the range may lead to unacceptable risks when technical interactions occur. An objective method is suggested that provides an optimal set of fishing mortality within the range, minimizing the risk of total allowable catch mismatches among stocks captured within mixed fisheries, and addressing explicitly the trade-offs between the most and least productive stocks.

Effects of predator–prey interactions and adaptive change on sustainable yield

2004 ◽  
Vol 61 (2) ◽  
pp. 175-184 ◽  
Author(s):  
Hiroyuki Matsuda ◽  
Peter A Abrams
Keyword(s):  
Feedback Control ◽  
Population Size ◽  
Single Species ◽  
Fishing Effort ◽  
Maximum Sustainable Yield ◽  
Adaptive Change ◽  
Sustainable Yield ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Abundance

We explore the effects on population size and yield of different levels of harvesting of a predator in a predator–prey system. We consider the consequences of adaptive change in the predator's foraging time (or effort) and feedback control of fishing effort. The predator may increase in population size with increasing fishing effort, either when the prey is characterized by a positive effect of its own population size on its own growth rate or when the prey is overexploited by the predator. The predator abundance at which the sustainable yield is maximized can be larger than the abundance without fishing. The effort that achieves maximum sustainable yield and the effort that maximizes predator abundance can both be close to the effort at which the stock collapses. Feedback control in the response to predator abundance may fail to achieve the desired abundance of the target stock or its prey even if the fishing effort is well controlled. These results suggest that developing policies for exploiting adaptive predator species in potentially cycling systems cannot be based on the stable single-species models often used in fisheries management.

A RESOURCE DEPENDENT FISHERY MODEL WITH OPTIMAL HARVESTING POLICY

2002 ◽  
Vol 10 (01) ◽  
pp. 1-13 ◽  
Author(s):  
BALRAM DUBEY ◽  
PEEYUSH CHANDRA ◽  
PRAWAL SINHA
Keyword(s):  
Single Species ◽  
Fish Population ◽  
Maximum Sustainable Yield ◽  
Equilibrium Density ◽  
Future Price ◽  
Optimal Harvesting ◽  
Biomass Density ◽  
Optimal Harvesting Policy ◽  
Yield Increase ◽  
Fishery Model

A dynamic model for a single-species fishery, which depends partially on a logistically growing resource with functional response, is proposed using taxation as control instrument to protect fish population from overexploitation. The analysis of the model shows that both the equilibrium density of fish population as well as the maximum sustainable yield increase as resource biomass density increases. The optimal harvesting policy is also discussed with the help of Pontryagin's Maximum Principle. It is found that for the optimum equilibrium value of resource biomass density, the total user's cost of harvest per unit effort must be equal to the discounted value of future price at the steady state.

MSY needs no epitaph—but it was abused

2020 ◽  
Author(s):  
Daniel Pauly ◽  
Rainer Froese
Keyword(s):  
Maximum Sustainable Yield ◽  
Sustainable Yield

Abstract The maximum sustainable yield (MSY) concept is widely considered to be outdated and misleading. In response, fisheries scientists have developed models that often diverge radically from the first operational version of the concept. We show that the original MSY concept was deeply rooted in ecology and that going back to that version would be beneficial for fisheries, not least because the various substitutes have not served us well.

Production, Mortality, And Sustainable Yield Of Northwest Atlantic Harp Seals (Pagophilus groenlandicus)

1978 ◽  
Vol 35 (9) ◽  
pp. 1249-1261 ◽  
Author(s):  
G. H. Winters
Keyword(s):  
Population Size ◽  
Total Population ◽  
Historical Data ◽  
Maximum Sustainable Yield ◽  
Sustainable Yield ◽  
Natural Mortality ◽  
Northwest Atlantic ◽  
The Past ◽  
Relative Contribution ◽  
Pagophilus Groenlandicus

From recent and historical data the natural mortality rate of adult harp seals (Pagophilus groenlandicus) is estimated to be 0.10 which is within the range of previous estimates (0.08–0.11). New estimates of bedlamer and 0-group natural mortality rates were not significantly different from those of adult seals. Pup production estimates from survival indices agreed well with those from sequential population analyses and indicated a decline from about 350 000 animals in the early 1950s to about 310 000 animals in the early 1970s. Over the same period the 1+ population size declined from 2.5 to 1.1 million animals but has been increasing at the rate of 3%/yr since the introduction of quotas in 1972. The relative contribution of the "Front" production to total ("Front" plus Gulf) production during the past decade has fluctuated from 49 to 87%, the average of 64% being very similar to the 61% obtained previously. These fluctuations suggest some interchange between "Front" and Gulf adults and it is concluded that homing in the breeding areas is a facultative rather than obligatory aspect of seal behavior. Thus the heavier exploitation of the "Front" production is probably sufficiently diffused into the total population to avoid serious effects on "Front" production. The maximum sustainable yield of Northwest Atlantic seals harvested according to recent patterns is estimated to be 290 000 animals (80% pups) from a 1+ population size of 1.8 million animals producing 460 000 pups annually. The sustainable yield at present levels of pup production (335 000 animals) is calculated to be 220 000 animals which is substantially above the present TAC of 180 000 animals and coincides with present harvesting strategies designed to enable the seal hunt to increase slowly towards the MSY level. Key words: mortality, production, sustainable yield, population dynamics, marine mammal

scholarly journals Sustainable exploitation of temperate fish stocks

2009 ◽  
Vol 6 (1) ◽  
pp. 124-127 ◽  
Author(s):  
Henrik Sparholt ◽  
Robin M. Cook
Keyword(s):  
Species Interactions ◽  
Fishery Management ◽  
Regional Scale ◽  
Single Species ◽  
Fishing Effort ◽  
Theoretical Concept ◽  
Maximum Sustainable Yield ◽  
Production Model ◽  
The Status ◽  
Long Time

The theory of maximum sustainable yield (MSY) underpins many fishery management regimes and is applied principally as a single species concept. Using a simple dynamic biomass production model we show that MSY can be identified from a long time series of multi-stock data at a regional scale in the presence of species interactions and environmental change. It suggests that MSY is robust and calculable in a multispecies environment, offering a realistic reference point for fishery management. Furthermore, the demonstration of the existence of MSY shows that it is more than a purely theoretical concept. There has been an improvement in the status of stocks in the Northeast Atlantic, but our analysis suggests further reductions in fishing effort would improve long-term yields.

scholarly journals Optimal Harvesting Effort for Nonlinear Predictive Control Model for a Single Species Fishery

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Messaoud Bounkhel ◽  
Lotfi Tadj
Keyword(s):  
Predictive Control ◽  
Renewable Resource ◽  
Single Species ◽  
State Equation ◽  
Control Model ◽  
Optimal Harvesting ◽  
Solution Approach ◽  
Nonlinear Predictive Control ◽  
Nonlinear State ◽  
Resource System

We use nonlinear model predictive control to find the optimal harvesting effort of a renewable resource system with a nonlinear state equation that maximizes a nonlinear profit function. A solution approach is proposed and discussed and satisfactory numerical illustrations are provided.

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