Lenski实验的一个基于个体的模型，以及相对适合度的减速
An individual-based model for the Lenski experiment, and the deceleration of the relative fitness
摘要：
Lenski实验研究了细菌种群的长期进化。它的设计允许直接比较进化株与其创始祖先的生殖适应性。Wiser等人（2013）观察到，相对适合度随时间呈次线性增加，这种行为通常归因于克隆干扰或上位性等效应。在本文中，我们提出了一个基于个人的概率模型，捕捉Lenski实验的设计的基本特征。我们假设，每个有益的突变增加了一个固定的量，这对应于在连续时间（日内）模型的一部分上位性的情况下，个体繁殖率，但导致在离散时间（日间）模型的一部分上位性效应。使用近临界Galton-Watson过程的近似，我们证明了在排除克隆干扰的模型参数上的一些假设下，经过适当的重新缩放，相对适应度过程在大人口限制下收敛到幂律函数。
英文摘要：
The Lenski experiment investigates the long-term evolution of bacterial populations. Its design allows the direct comparison of the reproductive fitness of an evolved strain with its founder ancestor. It was observed by Wiser et al. (2013) that the relative fitness over time increases sublinearly, a behaviour which is commonly attributed to effects like clonal interference or epistasis. In this paper we present an individual-based probabilistic model that captures essential features of the design of the Lenski experiment. We assume that each beneficial mutation increases the individual reproduction rate by a fixed amount, which corresponds to the absence of epistasis in the continuous-time (intraday) part of the model, but leads to an epistatic effect in the discrete-time (interday) part of the model. Using an approximation by near-critical Galton-Watson processes, we prove that under some assumptions on the model parameters which exclude clonal interference, the relative fitness process converges, after suitable rescaling, in the large population limit to a power law function.
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