Adaptive walks following a moving optimum: (Mal)adaptation and population extinction

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Date(s) - 23/09/2015
16 h 00 min - 17 h 00 min


We analyze a stochastic process describing an evolving population adapting to a gradually changing environment with a moving phenotypic optimum. Our main simplifying assumption is that beneficial mutations that escape stochastic loss are fixed instantaneously. Adaptation thus resembles a jump process. Taking the limit of small jumps enables us to derive analytical approximations for the mean degree of maladaptation (how far the population lags behind the optimum) and its variance. Simulations show that 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, the 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 severe that the population is in danger of extinction. This time has an approximately exponential distribution with a mean that decreases exponentially with the inverse of the speed of environmental change relative to the rate and size of new mutations. We also derive a critical rate of environmental change, beyond which the mean degree of adaptation is to poor to allow population survival. (joint work with Elma Nassar and Etienne Pardoux, I2M)

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