Gander, Martin J. Mazza, Christian Rummler, Hansklaus 2007-04-30 Organisms are known to adapt to regularly varying environments. However, in most cases, the fluctuations of the environment are irregular and stochastic, alternating between favorable and unfavorable regimes, so that cells must cope with an uncertain future. A possible response is population diversification. We assume here that the cell population is divided into two groups, corresponding to two phenotypes, having distinct growth rates, and that cells can switch randomly their phenotypes. In static environments, the net growth rate is maximized when the population is homogeneously composed of cells having the largest growth rate. In random environments, growth rates fluctuate and observations reveal that sometimes heterogeneous populations have a larger net growth rate than homogeneous ones, a fact illustrated recently through Monte-Carlo simulations based on a birth and migration process in a random environment. We study this process mathematically by focusing on the proportion <i>f</i>(<i>t</i>) of cells having the largest growth rate at time <i>t</i>, and give explicitly the related steady state distribution π. We also prove the convergence of empirical averages along trajectories to the first moment Ε_π(f), and provide efficient numerical methods for computing Ε_π(f) application/pdf https://folia.unifr.ch/global/documents/300503 https://folia.unifr.ch/documents/300503/files/J._Math._Biol._2007_.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00285-007-0083-9 info:eu-repo/semantics/openAccess License undefined Journal of Mathematical Biology. - 2007, vol. 55, no. 2, p. 249-269 gene expression fluctuating environment steady state info:eu-repo/classification/udc/51 Stochastic gene expression in switching environments http://purl.org/coar/resource_type/c_6501