Cell division times in microbial populations display significant fluctuations. These fluctuations impact the population growth rate in a non-trivial way. If fluctuations are uncorrelated among different cells, the population growth rate is predicted by the Euler-Lotka equation, which is a classic result in mathematical biology. However, cell division times can present significant correlations, due to physical properties of cells that are passed from mothers to daughters. In this paper, we derive an equation remarkably similar to the Euler-Lotka equation which is valid in the presence of correlations. Our exact result is based on large deviation theory and does not require particularly strong assumptions on the underlying dynamics. We apply our theory to a phenomenological model of bacterial cell division. We find that the discrepancy between the growth rate predicted by the Euler-Lotka equation and our generalized version is relatively small, but large enough to be measurable in experiments.

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相关细胞分裂的广义Euler-Lotka方程

微生物种群中的细胞分裂时间显示出明显的波动。这些波动以不平凡的方式影响着人口增长率。如果不同细胞之间的波动不相关，则可以通过Euler-Lotka方程预测种群增长率，这是数学生物学中的经典结果。但是，由于从母体传给子代的细胞的物理特性，细胞分裂时间可能呈现出显着的相关性。在本文中，我们导出了一个与Euler-Lotka方程非常相似的方程，该方程在存在相关性的情况下有效。我们的精确结果基于大偏差理论，不需要对基础动力学进行特别强的假设。我们将我们的理论应用于细菌细胞分裂的现象学模型。