Acta Biotheoretica

, Volume 62, Issue 3, pp 355–369 | Cite as

Viability Analysis of Fisheries Management on Hermaphrodite Population

Regular Article

Abstract

We study the viability domains of bio-economic constraints for fishing model of hermaphrodite population, displaying three stages, juvenile, female and male. The dynamic of this model is subject to two constraints: an ecological constraint ensuring the stock perennity, and an economic constraint ensuring a minimum revenue for fishermen. Using viability kernel, we find out a viability domain which simultaneously guarantees a minimum stock level and a minimum income for fleets.

Keywords

Harvesting models Viability kernel Hermaphrodite population 

References

  1. Alonzo SH, Mangel M (2004) The effects of size-selective fisheries on the stock dynamics of and sperm limitation in sex-changing fish. Fish Bull 102:1–13Google Scholar
  2. Armsworth PR (2001) Effects of fishing on a protogynous hermaphrodite. Can J Fish Aquat Sci 58(11):568–578CrossRefGoogle Scholar
  3. Aubin J-P (1991) Viability theory. Birkhäuser, BostonGoogle Scholar
  4. Aubin J-P (1997) Dynamic economic theory: a viability approach. Studies in economic theory, vol 5. Springer, Berlin, HeidelbergGoogle Scholar
  5. Brusle J (1985) Synopsis of biological data on the groupers Epinephelus aeneus (Geoffrey Saint Hilaire, 1809) and Epinephelus guaza (Linnaeus, 1758) of the Atlantic Ocean and Mediterranean sea. FAO Fish Synop 129:1–69Google Scholar
  6. Cartigny P, Gómez W, Salgado H (2008) The spatial distribution of small- and large-scale fisheries in a marine protected area. Ecol Model 212(3):513–521CrossRefGoogle Scholar
  7. Clark CW (1979) Mathematical bioeconomics: The optimal management of renewable resources. Willey Interscience Publication, Willey, New YorkGoogle Scholar
  8. Doyen L, Béné C (2003) Sustainability of fisheries through marine reserves: a robust modeling analysis. J Environ Manag 69:1–13CrossRefGoogle Scholar
  9. Ferchichi A, BenMiled S, Jerry M (2012) Optimal strategy of fishing problem on hermaphrodite population. JP J Appl Math 4(1 and 2):9–25Google Scholar
  10. Huntsman GR, Schaaf WE (1994) Simulation of the impact of fishing on reproduction of a protogynous grouper, the graysby. N Am J Fish Manag 14:41–52CrossRefGoogle Scholar
  11. Jerry M, Raissi N, Rapaport A (2011) A viability analysis for an explicit inshore–offshore model. J Appl Math 1(1):41–60Google Scholar
  12. Jerry M, Rapaport A, Cartigny P (2010) Can protected areas potentially enlarge viability domains for harvesting management? Nonlinear Anal Real World Appl 11(2):720–734CrossRefGoogle Scholar
  13. Liu M, Sadovy Y (2004) The influence of social factors on adult sex change and juvenile sexual differentiation in a diandric, protogynous epinepheline, Cephalopholis boenak (Pisces, Serranidae). J Zool 264(3):239–248CrossRefGoogle Scholar
  14. Miled SB, Kebir A, Hbid ML (2010) Mathematical modeling describing the effect of fishing and dispersion on hermaphrodite population dynamics. Math Model Nat Phenom 5(6):159–179CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.ENIT-LAMSINUniversité de Tunis El ManarTunisTunisia
  2. 2.Polydisciplinary Faculty of Beni MellalUniversity of Sultan Moulay SlimaneBeni MellalMorocco
  3. 3.Pasteur Institute of TunisUniversité de Tunis El ManarTunisTunisia

Personalised recommendations