2021/11/07 by Jérémie Unterberger, Unterberger, J.
Biochemistry, Genetics and Molecular Biology · Mathematics · #60J74 #60K37 #82C35 #82M30 #92D15 #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #Populations and Evolution (q-bio.PE) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2111.04167
openalex publication_date 2021/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a general class of Markovian models describing the growth in a randomly fluctuating environment of a clonal biological population having several phenotypes related by stochastic switching. Phenotypes differ e.g. by the level of gene expression for a population of bacteria. The time-averaged growth rate of the population, Λ, is self-averaging in the limit of infinite times; it may be understood as the fitness of the population in a context of Darwinian evolution. The observation time T being however typically finite, the growth rate fluctuates. For T finite but large, we obtain the variance of the time-averaged growth rate as the maximum of a functional based on the stationary probability distribution for the phenotypes. This formula is general. In the case of two states, the stationary probability was computed by Hufton, Lin and Galla \citeHufLin2, allowing for an explicit expression which can be checked numerically.