On the degradation of forest ecosystems by extreme events: Statistical Model Checking of a hybrid model

In this paper, we study the vulnerability of forest ecosystems perturbed by extreme events, such as those arising from climate change. To investigate the complex interactions between the biological dynamics of the forest and the climatic activity, we construct an original hybrid model, obtained by coupling a continuous reaction-diffusion system, which describes the spatio-temporal dynamics of the forest ecosystem, with a discrete probabilistic process, which models the possible occurrences of extreme events. Properties of ecological interest are considered: invariance of the persistence equilibrium, attraction to the extinction equilibrium and emergence of degraded states. Those properties of the hybrid model are verified through an extension of the Statistical Model Checking framework. We establish the existence of a threshold above which the persistence equilibrium of the forest ecosystem is compromised and give a numerical assessment of this threshold in terms of the probability and intensity of extreme events. We also present non-trivial parameter conditions for which the forest ecosystem converges to a degraded savanna-like state.

Automated summary

In this paper, we investigate the vulnerability of forest ecosystems to extreme events caused by climate change. We propose an original hybrid model that combines a continuous reaction-diffusion system with a discrete probabilistic process to capture the complex interactions between biological dynamics and climatic activity. The model is analyzed using the Statistical Model Checking framework, showing the existence of a threshold that compromises the persistence equilibrium of the forest ecosystem and providing numerical assessments of this threshold in terms of extreme event probability and intensity. We also identify parameter conditions that lead to a degraded savanna-like state in the forest ecosystem.