« Darwin regarded differences within species and differences among species as ontologically related. He replaced the ideal entities, species, with the material entities, individuals and populations, as the proper objects of study. Darwin's revolutionary insight was that the differences among individuals within a species are converted into differences among species in space and time. The problematic of evolutionary theory then became - and remains to the present day - to provide the mechanism for this transformation. » [Richard Levins and Richard Lewontin, The dialectical biologist]
Rare events are by definition difficult to observe, and their numerical study is all the more complex. A class of methods, "population dynamics algorithms" allowed progress in this area. The idea is to simulate not one, but a large number of copies of the system, each playing the role of an 'individual' possessing a certain 'genome' (the configuration); these individuals are subject to 'mutation' (noise) and 'selection' (birth/death). This selection makes it possible to make typical, in the population dynamics, the rare event in which we are interested in the dynamics of the original system. Population dynamics are in exact correspondence with models of biological phenomena in genetics and ecology – studied in mathematics. The aim of the workshop is to exploit this correspondence to put in contact researchers of different communities, in order to (i) export modern tools and concepts from the theory of large deviations and algorithms to biological models, so as to understand its hidden characteristics; (ii) conversely to import mathematical tools from probability theory to improve the existing algorithms of the theory of large deviations.
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