Habitat loss causes long transients in small trophic chains

Abstract

Transients in ecology are extremely important since they determine how equilibria are approached. The debate on the dynamic stability of ecosystems has been largely focused on equilibrium states. However, since ecosystems are constantly changing due to climate conditions or to perturbations such as the climate crisis or anthropogenic actions (habitat destruction, deforestation, or defaunation), it is important to study how dynamics can proceed till equilibria. In this contribution we investigate dynamics and transient phenomena in small food chains using mathematical models. We are interested in the impact of habitat loss in ecosystems with vegetation undergoing facilitation. We provide a thorough dynamical study of a small food chain system given by three trophic levels: vegetation, herbivores, and predators. The dynamics of the vegetation alone suffers a saddle-node bifurcation, causing extremely long transients. The addition of a herbivore introduces a remarkable number of new phenomena. Specifically, we show that, apart from the saddle node involving the extinction of the full system, a transcritical and a supercritical Hopf-Andronov bifurcation allow for the coexistence of vegetation and herbivores via non-oscillatory and oscillatory dynamics, respectively. Furthermore, a global transition given by a heteroclinic bifurcation is also shown to cause a full extinction. The addition of a predator species to the previous systems introduces further complexity and dynamics, also allowing for the coupling of different transient phenomena such as ghost transients and transient oscillations after the heteroclinic bifurcation. Our study shows how the increase of ecological complexity via addition of new trophic levels and their associated nonlinear interactions may modify dynamics, bifurcations, and transient phenomena.