Quantifying phenotypic variability and fitness in finite microbial populations

In isogenic microbial populations, phenotypic variability is generated by a combination of intrinsic factors, specified by cell physiology, and environmental factors. Here we address the question: how does phenotypic variability of a microbial population affect its fitness? While this question has previously been studied for exponentially growing populations, the situation when the population size is kept fixed has received much less attention. We show that in competition experiments with multiple microbial species, the fitness of the population can be determined from the distribution of phenotypes, provided all variability is due to intrinsic factors. We then explore how robust the relationship between fitness and phenotypic variability is to environmental fluctuations. We find that this relationship breaks down in the presence of environmental fluctuations, and derive a simple formula relating the average fitness of a population to the phenotype distribution and fluctuations in the instantaneous population growth rate. Using published experimental data we demonstrate how our formulas can be used to discriminate between intrinsic and environmental contributions to phenotypic diversity.