Advances in Applied Probability

Phenotypic diversity and population growth in a fluctuating environment

Clément Dombry, Christian Mazza, and Vincent Bansaye

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Organisms adapt to fluctuating environments by regulating their dynamics, and by adjusting their phenotypes to environmental changes. We model population growth using multitype branching processes in random environments, where the offspring distribution of some organism having trait tT in environment eE is given by some (fixed) distribution Yt,e on N. Then, the phenotypes are attributed using a distribution (strategy) πt,e on the trait space T. We look for the optimal strategy πt,e, tT, eE, maximizing the net growth rate or Lyapounov exponent, and characterize the set of optimal strategies. This is considered for various models of interest in biology: hereditary versus nonhereditary strategies and strategies involving or not involving a sensing mechanism. Our main results are obtained in the setting of nonhereditary strategies: thanks to a reduction to simple branching processes in a random environment, we derive an exact expression for the net growth rate and a characterization of optimal strategies. We also focus on typical genealogies, that is, we consider the problem of finding the typical lineage of a randomly chosen organism.

Article information

Adv. in Appl. Probab., Volume 43, Number 2 (2011), 375-398.

First available in Project Euclid: 21 June 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K37: Processes in random environments 62D25

Branching process in a random environment phenotypic diversity Lyapounov exponent optimal strategy extinction typical genealogy


Dombry, Clément; Mazza, Christian; Bansaye, Vincent. Phenotypic diversity and population growth in a fluctuating environment. Adv. in Appl. Probab. 43 (2011), no. 2, 375--398.

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