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Research talks;Dynamical Systems and Ordinary Differential Equations;Partial Differential Equations

Evolutionary rescue (ER) is the process by which a population, initially destined to extinction due to environmental stress, avoids extinction via adaptive evolution. One of the widely observed pattern of ER (especially in the study of antibiotic resistance) is that it is more likely to occur in mild than in strong stress. This may be due either to purely demographic effects (extinction is faster in strong stress) or to evolutionary effects (adaptation is harder in strong stress). Disentangling the two and predicting the likelihood of ER has important medical or agronomic implications, but also has a strong potential for empirical testing of eco-evolutionary theory, as ER experiments are widespread (at least in microbial systems) and fairly rapid to perform.
Here, I will present results from three recent articles [1-3] where we considered the probability of ER, and the distribution of extinction times, in a classic phenotype-fitness landscape: Fisher’s geometric model (FGM). In our (classic) version of the FGM, fitness is a quadratic function of traits, with an optimum that depends on the environment. This model has received some empirical support with respects to its ability to reproduce or even predict patterns of context dependence in mutation effects on fitness (be it environmental or genetic context).
In our FGM-ER scenario, a population is initially adapted to the current optimum (either a clone or at mutation selection balance). The environment shifts abruptly and the optimum position, plus possibly peak height and width are modified. We follow the evolutionary and demographic response to this change, assuming a density-independent demography (which we approximate by continuous branching process CB process or Feller process).
In spite of its simplicity, the FGM displays fairly distinct behaviors depending on the relative strength of selection and mutation: this yields different approaches to deal with the FGM-ER scenario. I will thus present the different approaches we have used so far: from the strong selection, weak mutation regime to the weak mutation strong selection regime, and discuss possible extensions at the transition between these regimes.
Evolutionary rescue (ER) is the process by which a population, initially destined to extinction due to environmental stress, avoids extinction via adaptive evolution. One of the widely observed pattern of ER (especially in the study of antibiotic resistance) is that it is more likely to occur in mild than in strong stress. This may be due either to purely demographic effects (extinction is faster in strong stress) or to evolutionary effects ...

35K58 ; 35Q92 ; 37N25 ; 60G99

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- v; 107 p.

Hokkaido University technical report series in mathematics

Localisation : Colloque 1er étage (HOKK)

équation aux dérivées partielles # onde progressive # équation de chaleur # incandescence # système dynamique

76B15 ; 35K58 ; 35Q35 ; 35K35 ; 76B47 ; 39A11 ; 35J60 ; 35K51

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- v; 97 p.
ISBN 978-1-4704-3626-1

Memoirs of the American Mathematical Society , 1255

Localisation : Collection 1er étage

équation aux dérivées partielles # équation de chaleur # énergie supercritique

35B32 ; 35B35 ; 35B44 ; 35J61 ; 35K58

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- vii; 167 p.
ISBN 978-1-107-47739-1

London mathematical society lecture note series , 0419

Localisation : Collection 1er étage

problème de Cauchy # équation semi-linéaire parabolique # équation aux dérivées partielles # continuité de lipschitz # principe du maximum # principe du minimum

35-02 ; 35K58 ; 35B40

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- x; 272 p.
ISBN 978-1-4419-5541-8

Springer monographs in mathematics

Localisation : Ouvrage RdC (BARB)

opérateur monotone # équation différentielle non linéaire # équation d'évolution non linéaire # système dissipatif # média poreux # équation de réaction-diffusion # équation de Navier-Stokes

34G20 ; 35-02 ; 34G25 ; 47H05 ; 47H06 ; 47H20 ; 47J35 ; 35K58 ; 35L71 ; 35J87 ; 35K86

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