Marine biological metapopulation with coupled logistic growth functions: The MSY and quasi MSY

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.