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 lnN_e/s time (N_e, effective population size; s, 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.

对弱突变限制下大量种群进化的数学分析表明，这样的种群大部分时间都在适应度景观的鞍点附近处于停滞状态。在 ln N _e /s时间 ( N _e , 有效种群大小; s，突变的选择系数），当一个新的有益突变在进化种群中固定时，它相应地移动到不同的鞍，或者在更罕见的情况下从鞍移动到局部峰值。从现象学上讲，这种大量种群的进化模式类似于标点平衡 (PE)，其中表型变化发生在快速爆发中，这些变化被更长的停滞间隔分开，在此期间突变积累但表型没有实质性变化。从理论上讲，PE 与自组织临界 (SOC) 相关联，在该模型中，不断发展的系统中“雪崩”的大小呈幂律分布，导致重大事件越来越罕见。然而，我们在这里展示，