Influence of intraspecific density dependence on a three-species food chain with and without external stochastic disturbances

Abstract

Natural population dynamics are very complicated. Previous theory has shown that this phenomenon can be explained by the stochastic behavior arising from stochastic disturbances of external environment factors and the highly complex and chaotic behavior generating from nonlinearities in population itself, which is considered as a leading one. However, recently many studies theoretically show that ecological factors such as immigration, omnivory, habitat-heterogeneity may impede and control chaos. In this paper, we investigate the role of intraspecific density dependence (IDD), another important ecological factor, in the dynamics of two versions (deterministic and stochastic) of a food chain. We find that the addition of IDD to a deterministic three-species food chain model stabilizes the food chain system, leading chaotic and periodic dynamics to a steady state and especially making the very famous ‘teacup’ chaotic attractor disappear, and that the addition of it to a stochastic one at most results in a reduction in amplitude and frequency of dynamical fluctuations and can never eliminate the stochastic behavior. Our results contribute to investigations of the relative importance of the intrinsic factors and extrinsic environmental factors in determining population size fluctuations. Also, they give a better understanding of the essential difference between chaos and stochasticity.