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Dynamics and management of stage-structured fish stocks
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, China)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. (IceLab)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria)
2013 (English)In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 75, no 1, 1-23 p.Article in journal (Refereed) Published
Abstract [en]

With increasing fishing pressures having brought several stocks to the brink of collapse, there is a need for developing efficient harvesting methods that account for factors beyond merely yield or profit. We consider the dynamics and management of a stage-structured fish stock. Our work is based on a consumer-resource model which De Roos et al. (in Theor. Popul. Biol. 73, 47-62, 2008) have derived as an approximation of a physiologically-structured counterpart. First, we rigorously prove the existence of steady states in both models, that the models share the same steady states, and that there exists at most one positive steady state. Furthermore, we carry out numerical investigations which suggest that a steady state is globally stable if it is locally stable. Second, we consider multiobjective harvesting strategies which account for yield, profit, and the recovery potential of the fish stock. The recovery potential is a measure of how quickly a fish stock can recover from a major disturbance and serves as an indication of the extinction risk associated with a harvesting strategy. Our analysis reveals that a small reduction in yield or profit allows for a disproportional increase in recovery potential. We also show that there exists a harvesting strategy with yield close to the maximum sustainable yield (MSY) and profit close to that associated with the maximum economic yield (MEY). In offering a good compromise between MSY and MEY, we believe that this harvesting strategy is preferable in most instances. Third, we consider the impact of harvesting on population size structure and analytically determine the most and least harmful harvesting strategies. We conclude that the most harmful harvesting strategy consists of harvesting both adults and juveniles, while harvesting only adults is the least harmful strategy. Finally, we find that a high percentage of juvenile biomass indicates elevated extinction risk and might therefore serve as an early-warning signal of impending stock collapse.

Place, publisher, year, edition, pages
Springer, 2013. Vol. 75, no 1, 1-23 p.
Keyword [en]
Stage structure, Selective harvest, Pareto efficiency, MEY, MSY, Early-warning signal
National Category
Computational Mathematics
URN: urn:nbn:se:umu:diva-66412DOI: 10.1007/s11538-012-9789-yISI: 000313723900001OAI: diva2:607384
Available from: 2013-02-22 Created: 2013-02-19 Last updated: 2015-03-16Bibliographically approved

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Meng, XinzhuLundström, Niklas L.P.Bodin, MatsBrännström, Åke
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Department of Mathematics and Mathematical StatisticsDepartment of Ecology and Environmental Sciences
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