Combined effects of intra- and inter-specific non-monotonic functions on the stability of a two-species system

Although either interspecific or intraspecific non-monotonic functions have been found to influence stability of community and ecological networks, population models considering both interspecific and intraspecific non-monotonic functions have not been investigated. In this study, by using graphic stability analysis, we found a two-species model with both intra- and inter-specific non-monotonic functions could produce multiple equilibria; the probability of producing stable equilibrium points was larger than that using the models with only intraspecific non-monotonic functions, but lower than that using the models with only interspecific non-monotonic functions. Our results further confirmed that dome-shaped interspecific non-monotonic function was a stabilizing force, while dome-shaped intraspecific non-monotonic function was a destabilizing force; the former should be more favored by natural selection than the latter. Besides, limit cycles were also detected in this two-species system. We appeal for more efforts in studying the ecological non-monotonicity in both theoretical and empirical studies by considering multiple-species systems and various non-monotonic interaction forms.