Franck POMMEREAU (PR Univ. Evry, IBISC équipe COSMO) intervient dans le cadre du séminaire MeFoSyLoMa Paris-Saclay du vendredi 11 octobre 2019.
Titre: Formal modelling and analysis of ecosystems
Several concepts have recently been proposed to understand long-term ecosystem dynamics. These include basins of attraction expressing resilience and tipping points expressing sharp changes in ecosystem’s behavior, which are increasingly being used in ecology. Yet these temporal features remain difficult to identify and quantify, as models usually focus on part of the ecosystem behaviour only. We propose an original family of models designed to comprehensively characterize ecosystem dynamics over the long term. Such models are based on discrete systems borrowed from theoretical computer sciences. We developed a qualitative model based on Petri nets, made up of a relational graph (interaction network) which was then rigorously handled with transition rules. Unlike traditional models and graph theory approaches, such rules may strongly modify the graph structure (i.e. a dynamical topology). We illustrated such Petri nets in a theoretical ecosystem chosen as an insect (termite) colony to show their added values. This ecosystem, made of abiotic and biotic components and processes, was explored in all its possible trajectories and then analyzed. Several temporal features were easily detected and quantified, such as basins (i.e. strongly connected states), tipping points (critical transitions along trajectories) and various kinds of collapses (functioning systems whose structures were nevertheless frozen). It is expected that Petri nets developed for more realistic ecosystems would provide original insights into their overall behavior.