In this paper we develop a mathematical model for a harvested marine biological stock. The stock consists of two discretely separated sub-stocks which are connected by the dispersal of individuals, and hence forms a metapopulation structure. The model assumes that the production function of each stock follows a logistic equation, hence the full system of the stocks governed by a couple of logistic equations. We find the formula of the maximum sustainable yield (MSY) for each sub-stock, which is extendable to a metapopulation with several discretely separated sub-populations. We also give a numerical simulation to illustrate the application of the formula for two-patch case, based on the quasi maximum sustainable yield. The simulation shows that ignoring the existence of the coupling of the system resulting in a lower total harvest from the population. This indicates a financial lost potential arising from an inappropriate recognition of a metapopulation structure in a fishery industry.
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Research Article| February 21 2014
Marine biological metapopulation with coupled logistic growth functions: The MSY and quasi MSY
AIP Conf. Proc. 1587, 51–56 (2014)
H. Husniah, A. K. Supriatna; Marine biological metapopulation with coupled logistic growth functions: The MSY and quasi MSY. AIP Conf. Proc. 21 February 2014; 1587 (1): 51–56. https://doi.org/10.1063/1.4866532
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