"Piecewise deterministic Markov processes in ecology and evolution"Aguirre, LeonardoEcological systems are commonly understood as complexes of various subsystems whose respective dynamics may unfold through different kinds of mechanisms. Some of these mechanisms produce gradual state changes, such as physical growth of organisms, changes in temperature or approximately continuous abundance changes in large populations, while others act as abrupt state jumps, such as reproduction and death events in populations of low abundance. The former sort of mechanism can be conveniently captured in (deterministic) ODE models, while the latter has lead to (stochastic) Markov jump processes. While each of these two model classes has a long track record in their respective domain, there are scenarios which require an integration of gradual and abrupt mechanisms, for instance when metabolic state variables of a species are coupled to propensities of reproduction or death events. The model class of piecewise deterministic Markov processes (PDMPs) meets this demand by coupling ODE and Markov jump mechanisms in a fairly flexible way while still lending itself to rigorous mathematical approaches such as system size expansion or large deviation principles. Conceived about 40 years ago PDMPs have recently been attracting more and more attention in fields such as cell biology and can be expected to become a powerful tool also for ecology in order to integrate dynamics across scales. In this mini-symposium we would like to give several perspectives on the state-of-the-art in PDMPs as they relate to ecology and evolution. Talks should cover the following topics: • Recent applications of PDMPs to problems of ecology and evolution as well as successful cell biology applications that have obvious ties to ecological scenarios. • Mathematical methods such as system size expansion, WKB large deviation principle etc. • Future perspectives such as model integration, thermodynamics of complex systems, universal scaling laws etc. |
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