Stability analysis of the population matrix model with two iteroparous species using the M-matrix

Abstract

In this paper, we study the growth of two iteroparous species in the same community focusing on species with two age classes. It is modeled using the Leslie population projection matrix. The two age classes in view are age classes in units of time such as months and years. We assume the species is only capable of giving birth once per unit of time. We also assume that the growth of both species is influenced by density-dependent growth factors that only occur in the first age class and harvesting in the second age class. We consider two different models, one with the same and the other with different levels of intraspecific and interspecific competition. In both models, we analyse the existence conditions and local asymptotic stability of each equilibrium point. The local asymptotic stability is analysed using M-matrix theory. The inherent net reproductive number is derived and its relationship to the equilibrium point is explored. The results show that models with the same levels of intraspecific and interspecific competition do not have co-existence equilibrium points and vice versa. Then, the inherent net reproduction number and the levels of intraspecific and interspecific competition affect the existence and local asymptotic stability for each equilibrium point.