Abstract Current evolutionary biology models usually assume that a phenotype undergoes gradual change. This is in stark contrast to biological intuition, which indicates that change can also be punctuated—the phenotype can jump. Such a jump could especially occur at speciation, i.e., dramatic change occurs that drives the species apart. Here we derive a Central Limit Theorem for punctuated equilibrium. We show that, if adaptation is fast, for weak convergence to normality to hold, the variability in the occurrence of change has to disappear with time.

中文翻译：

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间断平衡的中心极限定理

摘要 当前的进化生物学模型通常假设表型会经历逐渐变化。这与生物学直觉形成鲜明对比，生物学直觉表明变化也可以被打断——表型可以跳跃。这种跳跃尤其可能发生在物种形成时，即发生导致物种分离的巨大变化。在这里，我们推导出间断平衡的中心极限定理。我们表明，如果适应速度很快，为了保持对常态的弱收敛，变化发生的可变性必须随时间消失。