A Central Limit Theorem for Punctuated Equilibrium

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 can 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 hold, dramatic change has to be a rare event. AMS subject classification: 60F05, 60J70, 60J85, 62P10, 92B99