Data from: Optimal lineage principle for age-structured populations

We present a formulation of branching and aging processes that allows distributions along lineages to be studied within populations, and provides a new interpretation of classical results in the theory of aging. We establish a variational principle for the stable age distribution along lineages. Using this optimal lineage principle, we show that the response of a population’s growth rate to age-specific changes in mortality and fecundity – a key quantity which was first calculated by Hamilton – is given directly by the age distribution along lineages. We apply our method also to the Bellman-Harris process, in which both mother and progeny are rejuvenated at each reproduction event, and show that this process can be mapped to the classic aging process such that age statistics in the population and along lineages are identical. Our approach provides both a theoretical framework for understanding the statistics of aging in a population, and a new method of analytical calculations for populations with age structure. We discuss generalizations for populations with multiple phenotypes, and more complex aging processes. We also provide a first experimental test of our theory applied to bacterial populations growing in a microfluidics device.

本研究提出了分支与衰老过程的理论形式化表述，使得我们可以在种群层面研究谱系沿线上的分布特征，并为衰老理论中的经典结论提供全新的阐释视角。我们针对谱系沿线上的稳定年龄分布建立了变分原理。借助这一最优谱系原理，我们证明：种群增长率对年龄特异性死亡率与繁殖力变化的响应——这一由汉密尔顿首次推导得到的关键量化指标——可直接由谱系沿线上的年龄分布给出。我们还将所提方法应用于贝尔曼-哈里斯过程（Bellman-Harris process），该过程中每次生殖事件都会使母代与子代均重置年龄，我们证明该过程可映射至经典衰老过程，使得种群内与谱系沿线上的年龄统计特征完全一致。本研究不仅为理解种群内衰老的统计特征提供了理论框架，同时也为具有年龄结构的种群提供了一种全新的解析计算方法。我们还讨论了针对多表型种群与更复杂衰老过程的推广拓展。此外，我们针对在微流控装置（microfluidics device）中培养的细菌种群开展了本理论的首次实验验证。