Courant Institute of Mathematical Sciences, New York University, New York, NY 10012.
Institute for Molecules and Materials, Radboud University, NL-6525 AJ Nijmegen, The Netherlands.
Proc Natl Acad Sci U S A. 2021 Jan 26;118(4). doi: 10.1073/pnas.2015665118.
A mathematical analysis of the evolution of a large population under the weak-mutation limit shows that such a population would spend most of the time in stasis in the vicinity of saddle points on the fitness landscape. The periods of stasis are punctuated by fast transitions, in ln time ( , effective population size; , selection coefficient of a mutation), when a new beneficial mutation is fixed in the evolving population, which accordingly moves to a different saddle, or on much rarer occasions from a saddle to a local peak. Phenomenologically, this mode of evolution of a large population resembles punctuated equilibrium (PE) whereby phenotypic changes occur in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but the phenotype does not change substantially. Theoretically, PE has been linked to self-organized criticality (SOC), a model in which the size of "avalanches" in an evolving system is power-law-distributed, resulting in increasing rarity of major events. Here we show, however, that a PE-like evolutionary regime is the default for a very simple model of an evolving population that does not rely on SOC or any other special conditions.
在弱突变极限下，对大群体演化的数学分析表明，这样的群体在适应度景观的鞍点附近会处于停滞状态。停滞期会被快速转变打断，转变时间为 ln 时间（ ，有效种群大小； ，突变的选择系数），当一个新的有利突变在进化种群中被固定时，种群就会相应地移动到不同的鞍点，或者在极少数情况下从鞍点移动到局部峰值。从现象上看，这种大群体的演化模式类似于间断平衡（PE），其中表型变化以快速爆发的方式发生，而在这些爆发之间则是更长时间的停滞期，在此期间会积累突变，但表型不会发生实质性变化。从理论上讲，PE 与自组织临界性（SOC）有关，SOC 是一个模型，其中进化系统中的“雪崩”大小呈幂律分布，导致重大事件的罕见性增加。然而，我们在这里表明，对于一个不依赖 SOC 或任何其他特殊条件的简单进化群体模型，PE 样的演化状态是默认状态。
