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UID:859@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150923T160000
DTEND;TZID=Europe/Paris:20150923T170000
DTSTAMP:20150908T140000Z
URL:https://www.i2m.univ-amu.fr/evenements/adaptive-walks-following-a-movi
 ng-optimum-mal-adaptation-and-population-extinction/
SUMMARY: (...): Adaptive walks following a moving optimum: (Mal)adaptation 
 and population extinction
DESCRIPTION:: We analyze a stochastic process describing an evolving popula
 tion adapting to a gradually changing environment with a moving phenotypic
  optimum. Our main simplifying assumption is that beneficial mutations tha
 t escape stochastic loss are fixed instantaneously. Adaptation thus resemb
 les a jump process. Taking the limit of small jumps enables us to derive a
 nalytical approximations for the mean degree of maladaptation (how far the
  population lags behind the optimum) and its variance. Simulations show th
 at this approximation is accurate as long as the mean lag is greater than 
 the size of a typical mutation. Furthermore\, in the small-jumps limit\, t
 he process converges to an Ornstein-Uhlenbeck process around the long-term
  mean. Using published results about first-passage times of OU processes\,
  we derive an approximation for the time until maladaptation becomes so se
 vere that the population is in danger of extinction. This time has an appr
 oximately exponential distribution with a mean that decreases exponentiall
 y with the inverse of the speed of environmental change relative to the ra
 te and size of new mutations. We also derive a critical rate of environmen
 tal change\, beyond which the mean degree of adaptation is to poor to allo
 w population survival. (joint work with Elma Nassar and Etienne Pardoux\, 
 I2M)Webpage
CATEGORIES:Séminaire,Mathématiques-Évolution-Biologie
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DTSTART:20150329T030000
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