Quantifying phenotypic variability and fitness in finite microbial populations

Abstract

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.

Adaptive strategy in Kelly's horse races model

“…(6) This theoretical prediction is shown in Figure 2 for a time t 0 respecting the condition for (5). By taking the derivative of ( 6) with respect to time, one obtains the following expression for t :…”

“…This value of information quantifies the quality of the strategies adopted by individuals in a population when faced with unpredictably varying environments [4]. In these conditions, it is sometimes advantageous for individuals to accept a reduction of their short-term reproductive success, in exchange for longer-term risk reduction, a strategy known as bet-hedging [5]. Such a strategy is employed for instance by cells to cope with antibiotics or by plants to cope with a fluctuating climate [6].…”

A large deviation principle linking lineage statistics to fitness in microbial populations

“…A key determinant of fitness in microbial populations is the population growth rate [1][2][3]. For organisms such as Escherichia coli which undergo binary fission, the exponential growth rate of the population is determined by single-cell properties such as generation time, defined as the time from cell birth to division.…”

“…The relationship between this distribution and the population growth rate, Λ, has been the subject of numerous studies. A key result is the Euler-Lotka equation [1][2][3][13][14][15],…”

“…There are numerous other mechanisms which can generate correlations between mother and daughter cells. For example, environmental fluctuations can induce positive correlations between mother and daughter cells [3,13].…”