Work

A hybrid reaction-diffusion system to shed light on ecological transitions between boreal and temperate forests

Year: 2026

Type: article

Abstract: Understanding how forest ecosystems respond to megafires arising from climate change is a major challenge, as forests are well known to be an important reserve of carbon and biodiversity. In this paper, we present a new hybrid model that combines a continuous and deterministic mechanism governed by reaction-diffusion equations modeling the biological evolution of the forest, coupled with a discrete and probabilistic process reproducing the impact of forest fires. This original model allows us to study the competition and the ecological transitions between the temperate forest and the boreal forest. We prove that the hybrid model admits relevant equilibrium states of extinction, coexistence and invasion, and generates global solutions. We perform a complete stability analysis of the extinction equilibrium, establishing a non trivial parameter regime where the deterministic component of the model is unstable, with a stabilization under the action of the probabilistic process. We show that well chosen trajectories of the model can reach an invasion equilibrium where the temperate forest colonizes the boreal forest. We also prove that the model is able to reproduce spatial heterogeneity with the formation of patterns corresponding to enclaves of temperate forest within the boreal forest.

Source: Discrete and Continuous Dynamical Systems - S

DOI: 10.3934/dcdss.2026167

Authors: Sully Mak, Guillaume Cantin, Benoît Delahaye

Institutions: École Centrale de Nantes, Centre National de la Recherche Scientifique, Laboratoire des Sciences du Numérique de Nantes, Nantes Université

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

SDGs: Life on land, Climate action

Open Access status: diamond

Funder: Agence Nationale de la Recherche