The interplay of phenotypic variability and fitness in finite microbial populations

Abstract

<jats:p>In isogenic microbial populations, phenotypic variability is generated by a combination of stochastic mechanisms, such as gene expression, and deterministic factors, such as asymmetric segregation of cell volume. 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, despite its relevance to many natural scenarios. We show that the outcome of competition between multiple microbial species can be determined from the distribution of phenotypes in the culture using a generalization of the well-known Euler–Lotka equation, which relates the steady-state distribution of phenotypes to the population growth rate. We derive a generalization of the Euler–Lotka equation for finite cultures, which relates the distribution of phenotypes among cells in the culture to the exponential growth rate. Our analysis reveals that in order to predict fitness from phenotypes, it is important to understand how distributions of phenotypes obtained from different subsets of the genealogical history of a population are related. To this end, we derive a mapping between the various ways of sampling phenotypes in a finite population and show how to obtain the equivalent distributions from an exponentially growing culture. Finally, we use this mapping to show that species with higher growth rates in exponential growth conditions will have a competitive advantage in the finite culture.</jats:p>

Modeling the impact of single-cell stochasticity and size control on the population growth rate in asymmetrically dividing cells

“…Eq 3 can also be shown to apply in the case of finite population sizes using the transport equation approach outlined in Ref. [17]. Our current approach provides the additional benefit of predicting the ratio of cell types m present in the population at a single time-point, given the distribution of interdivision times.…”

Non-genetic variability: survival strategy or nuisance?

“…In this section, we introduce their model and main results. In the next section, we show how the self-consistent equation explored by Levien et al [33] can be used to generalize the work of Lin et al [19].…”

The “friend and foe” of deterministic and stochastic cell-cell variations

“…the changes in population growth rate to modulations in lineage diversity S. In other words, we consider the increase in population growth rate ∆ G = G(a, ξ) − G(a = 0, ξ = 0), where ξ denotes noise, and where lineage entropy is controlled via noise level ξ and asymmetry a. Using the Euler-Lotka model of population growth, we related the population diversity resulting from the combined existence of ADS and noise (with the probability density of doubling times f full (T ADS , T ξ )) to population growth G(a, ξ) [27][28][29]. Since the distributions of noise and ADS-induced doubling times are statistically independent (Table S1) we found a simplified expression for G(a, ξ) by expanding each of these distributions in statistical cumulants and applying series inversion [30,31] (SI Sec.…”