多层级进化的标度律：群体内与群体间进化的平衡如何决定
A scaling law of multilevel evolution: how the balance between within- and among-collective evolution is determined
AI总结：
本研究通过数学分析和模拟揭示，在层级组织的生命系统中，群体内与群体间进化的平衡遵循标度律$Nm^α$为常数，为理解欺骗与利他主义的进化条件提供了新见解。
摘要：
众多生命系统具有层级组织结构，其中可复制的组分被分组为可繁殖的集体——例如，细胞器被分组为细胞，细胞被分组为多细胞生物。在这样的系统中，进化可以在两个层面运作：群体间进化倾向于促进集体内组分之间的无私合作（称为利他主义），而群体内进化则倾向于促进集体内组分之间的欺骗行为。因此，群体内与群体间进化的平衡对这些系统的适应性产生深远影响。在此，我们通过数学分析和多个群体遗传学模型的计算机模拟，研究了这种平衡如何依赖于集体的大小（记为$N$）和组分的突变率（$m$）。我们首先证实了一个先前的结果：增加$N$或$m$会加速群体内进化相对于群体间进化的进程，从而促进欺骗行为的进化。此外，我们表明，当群体内与群体间进化恰好相互平衡时，以下标度关系普遍成立：$Nm^α$为常数，其中标度指数$α$取决于多个参数，如选择强度以及利他主义是二元性状还是数量性状。这一关系表明，尽管$N$和$m$对群体内与群体间进化的平衡具有数量上不同的影响，但如果$m$以适当的指数进行缩放，它们的影响将变得相同。因此，我们的结果为在层级组织的复制系统中欺骗或利他主义进化的条件提供了新的见解。
英文摘要：
Numerous living systems are hierarchically organised, whereby replicating components are grouped into reproducing collectives -- e.g., organelles are grouped into cells, and cells are grouped into multicellular organisms. In such systems, evolution can operate at two levels: evolution among collectives, which tends to promote selfless cooperation among components within collectives (called altruism), and evolution within collectives, which tends to promote cheating among components within collectives. The balance between within- and among-collective evolution thus exerts profound impacts on the fitness of these systems. Here, we investigate how this balance depends on the size of a collective (denoted by $N$) and the mutation rate of components ($m$) through mathematical analyses and computer simulations of multiple population genetics models. We first confirm a previous result that increasing $N$ or $m$ accelerates within-collective evolution relative to among-collective evolution, thus promoting the evolution of cheating. Moreover, we show that when within- and among-collective evolution exactly balance each other out, the following scaling relation generally holds: $Nm^α$ is a constant, where scaling exponent $α$ depends on multiple parameters, such as the strength of selection and whether altruism is a binary or quantitative trait. This relation indicates that although $N$ and $m$ have quantitatively distinct impacts on the balance between within- and among-collective evolution, their impacts become identical if $m$ is scaled with a proper exponent. Our results thus provide a novel insight into conditions under which cheating or altruism evolves in hierarchically-organised replicating systems.
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