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Revisiting the Logistic Growth with Random Disturbances

Paweł Klimasara — 2019

Mathematica Applicanda

The logistic growth population model still can help explain ecological phenomena. We consider a simple 1-dimensional model of savanna introduced by D’Odorico, Laio, and Ridolfi [A probabilistic analysis of fire-induced tree-grass coexistence in savannas. The American Naturalist 167, 2006] which is in fact a model of tree-grass coexistence driven by stochastic fire. We provide an appropriate stochastic process for this model and study it using the stochastic semigroup theory. Finally, we give the...

A model for random fire induced tree-grass coexistence in savannas

Paweł Klimasara;  Marta Tyran-Kamińska — 2018

Mathematica Applicanda

Tree-grass coexistence in savanna ecosystems depends strongly on environmental disturbances out of which crucial is fire. Most modeling attempts in the literature lack stochastic approach to fire occurrences which is essential to reflect their unpredictability. Existing models that actually include stochasticity of fire are usually analyzed only numerically. We introduce minimalistic model of tree-grass coexistence where fires occur according to stochastic process. We use the tools of linear semigroup...

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