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Habitat loss causes long extinction transients in small trophic chains

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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 driven by the climate crisis or anthropogenic actions (habitat destruction, deforestation, or defaunation), it is important to study how dynamics can proceed till equilibria. This article investigates the 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 dynamical study of a small food chain system given by three trophic levels: primary producers, i.e., vegetation, herbivores, and predators. Our models reveal how habitat loss pushes vegetation towards tipping points, how the presence of herbivores in small habitats could promote ecosystem's extinction (ecological meltdown), or how the loss of predators produce a cascade effect (trophic downgrading). Mathematically, these systems exhibit many of the possible local bifurcations: saddle-node, transcritical, Andronov-Hopf, together with a global bifurcation given by a heteroclinic bifurcation. The associated transients are discussed, from the ghost dynamics to the critical slowing down tied to the local and global bifurcations. Our work highlights how the increase of ecological complexity (trophic levels) can imply more complex transitions. This article shows how the pernicious effects of perturbations (i.e., habitat loss or hunting pressure) on ecosystems could not be immediate, producing extinction delays. These theoretical results suggest the possibility that some ecosystems could be currently trapped into the (extinction) ghost of their stable past.

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Habitat loss causes long extinction transients in small trophic chains