论文标题
鲍威尔对以稳定状态的人口的概括
Generalization of Powell's results to population out of steady state
论文作者
论文摘要
自鲍威尔的开创性工作以来，人口增长率之间的关系，生成时间的概率分布和细胞年龄的分布已经以稳定的指数增长状态而闻名。在这里，我们将这些关系概括为包括批处理培养和母机实验的不稳定（瞬态）状态。特别是，我们得出了时间依赖性的欧拉 - 洛特卡方程（将生成时间分布与人口增长率相关），并概括平均生成时间和人口加倍时间之间的不平等。为此，我们使用了Lebowitz和Rubinow提出的模型，其中每个细胞的年龄和发电时间都描述了。我们表明，只要这些附加变量的集成将模型降低为lebowitz-rubinow形式，我们的结果对于使用其他状态变量除了使用其他状态变量的更复杂模型仍然有效。作为这种形式主义的应用，我们计算出表型特征（细胞年龄，生成时间）的适应性景观，而人群的适应性景观并未成倍增长。我们澄清说，细胞年龄作为表型性状的已知适应性景观公式是与确切的时间依赖性公式的近似值。
Since the seminal work of Powell, the relationships between the population growth rate, the probability distributions of generation time, and the distribution of cell age have been known for the bacterial population in a steady state of exponential growth. Here, we generalize these relationships to include an unsteady (transient) state for both the batch culture and the mother machine experiment. In particular, we derive a time-dependent Euler-Lotka equation (relating the generation time distributions to the population growth rate) and a generalization of the inequality between the mean generation time and the population doubling time. To do this, we use a model proposed by Lebowitz and Rubinow, in which each cell is described by its age and generation time. We show that our results remain valid for a class of more complex models that use other state variables in addition to cell age and generation time, as long as the integration of these additional variables reduces the model to Lebowitz-Rubinow form. As an application of this formalism, we calculate the fitness landscapes for phenotypic traits (cell age, generation time) in a population that is not growing exponentially. We clarify that the known fitness landscape formula for the cell age as a phenotypic trait is an approximation to the exact time-dependent formula.
