Exact computation of growth-rate fluctuations in random environment [article]

J. Unterberger
2022 arXiv   pre-print
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
more » ... 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 , allowing for an explicit expression which can be checked numerically.
arXiv:2111.04167v2 fatcat:vzm7p2ivjjdu7lwq4fse3mjcba