A predator-prey model for two-species populations with nonlinear interactions and implications for fisheries management.

Abstract

A predator-prey interaction model is proposed for studying management implications of two fish species populations with nonlinear interactions. Nonlinear interactions seem more plausibl than linear ones in natural pupulations. The present model is built up by adding second order interactive terms to the Lotka-Volterra type linear model proposed by LARKIN. The prey isocline, which is a curve satisfying the equation dN1/dt=0 in the N1 (prey population density)-N2 (predator population density) plane, is classified into the four types based on the shape of the isocline. The predator isocline is also classified into the four types. The present model with the elliptic predator and prey isoclines, can be used to represent all the types of isoclines and can show the general nature of various nonlinear interactions. The responses to exploitation of the present nonlinear predator-prey system are qualitatively different from those of the original linear system. The equilibrium catches may suddenly decline from positive levels to zero even if fishing pressure increases continuously. Such a catastrophic phenomenon is caused by the destabilization of the system. If the single-species MSY (maximum sustainable yield) policies are practiced wihtout taking into account the stability of the system, populations may be threatened with sudden collapses. The MSY policies for populations with nonlinear interactions may be quite dangerous.