Evolutionary dynamics in non-Markovian models of microbial populations
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Abstract
In the past decade, great strides have been made to quantify the dynamics of single-cell growth and division in microbes. In order to make sense of the evolutionary history of these organisms, we must understand how features of single-cell growth and division influence evolutionary dynamics. This requires us to connect processes on the single-cell scale to population dynamics. Here, we consider a model of microbial growth in finite populations which explicitly incorporates the single-cell dynamics. We study the behavior of a mutant population in such a model and ask: can the evolutionary dynamics be coarse-grained so that the forces of natural selection and genetic drift can be expressed in terms of the long-term fitness? We show that it is in fact not possible, as there is no way to define a single fitness parameter (or reproductive rate) that defines the fate of an organism even in a constant environment. This is due to fluctuations in the population averaged division rate. As a result, various details of the single-cell dynamics affect the fate of a new mutant independently from how they affect the long-term growth rate of the mutant population. In particular, we show that in the case of neutral mutations, variability in generation times increases the rate of genetic drift, and in the case of beneficial mutations, variability decreases its fixation probability. Furthermore, we explain the source of the persistent division rate fluctuations and provide analytic solutions for the fixation probability as a multi-species generalization of the Euler-Lotka equation.
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This Zenodo record is a permanently preserved version of a PREreview. You can view the complete PREreview at https://prereview.org/reviews/10250501.
This paper provides a theoretical framework to understand the effect of single cell growth and division on evolutionary dynamics via population dynamic studies. It connects processes of single cell scale to population dynamics. By first developing a comprehensive model incorporating Stochastic Differential Equations for evolution of rare mutations in an evolving population and linking this model to single cell scale using population growth dynamics equations, the authors develop a predictive theory of microbial evolution. In particular, they provide a theory for predicting conditions for genetic drift and fixation probabilities of mutants in a large population. Their work is exceptional as …
This Zenodo record is a permanently preserved version of a PREreview. You can view the complete PREreview at https://prereview.org/reviews/10250501.
This paper provides a theoretical framework to understand the effect of single cell growth and division on evolutionary dynamics via population dynamic studies. It connects processes of single cell scale to population dynamics. By first developing a comprehensive model incorporating Stochastic Differential Equations for evolution of rare mutations in an evolving population and linking this model to single cell scale using population growth dynamics equations, the authors develop a predictive theory of microbial evolution. In particular, they provide a theory for predicting conditions for genetic drift and fixation probabilities of mutants in a large population. Their work is exceptional as it focuses on division rate fluctuations without assuming age distribution to be in a steady state or discrete age classes. They also demonstrate that such approximations aren't valid for physiologically relevant models of microbial growth. By generalization of continuous time Moran processes, derived for physiological models of growth, division and cell age control, the authors derive Fokker-Plank equations for the genotype frequencies. This is then used to predict equations and conditions for fixation probabilities and genetic drift under Neutral and Adaptive evolution strategies. Generally classical theory predicts linear increase in fitness with time by relying on selection coefficient, however, their model shows the insufficiency of this coefficient because of non-linear fitness trajectories in long-term evolutionary dynamics.
The paper is comprehensive in theory however, it lacks experimental support and validation.
Competing interests
The author declares that they have no competing interests.
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