The adaptive radiation of animals often follows mass extinctions. How does this support the punctuated equilibrium theory?

The adaptive radiation of animals often follows mass extinctions. How does this support the punctuated equilibrium theory? When some animals suddenly become extinct, other animals can slowly and uniformly evolve to fill the empty niches left from the extinct animals. The remaining members of extinct species will quickly evolve to fill in the empty spots in the ecosystem, but this will be followed by a long period lacking speciation. When animals become extinct, species that were closely related to them will experience convergent evolution. When some animals suddenly become extinct, oth