Journal of Mathematics and Statistics

ON RESERVES, STABILITY AND THE MAXIMUM SUSTAINABLE YIELD PROBLEM

Arild Wikan

DOI : 10.3844/jmssp.2013.325.333

Journal of Mathematics and Statistics

Volume 9, Issue 4

Pages 325-333

Abstract

Due to the fact that several species of commercial interest have been overexploited throughout the years it is important to understand how harvest and other factors like introducing reserves influence the dynamic behaviour of a population with respect to stability and possible extinction. Therefore, simple one-population models are analysed and it is shown that harvest acts in a strong stabilizing fashion in the sense that it may transfer a population which exhibits chaotic oscillations to a state where the equilibrium population is stable. Moreover, if we divide the habitat of the population into a reserve and a harvest zone we find that increased harvest as well as migration between the two areas act stabilizing but that the former turns out to be the dominating one. If age structure is included in the population model harvest may not necessarily play the same role, especially if the number of age classes become large. Regarding MSY, we demonstrate that it is indeed possible to obtain the same MSY in the case where the habitat is split into a reserve and a harvest zone as in case of no reserve.

Copyright

© 2013 Arild Wikan. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.