Abstract
The question of long term survival of species in a model governed by a system of four autonomous differential equations is considered. The criteria used is the ecologically realistic one of permanence that is populations with all initial values positive must remain positive, greater than some fixed positive numbers. We propose and analyse a four species mathematical model in which mutualism occurs with prey. The present work is in continuation of the work of Rai and Singh (J Int Acad Phys Sci 12:151–172, 2008), in which we have discussed stability analysis along with boundedness of solutions of initial value problems. Here we will discuss conditions for permanence of all the species with special reference to reversal of outcome due to presence of mutualist in a competitive ecosystem.
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