Phyletic Gradualism or Punctuated Equilbrium?

Sean Davis is asking journalists:

…do you believe in phyletic gradualism or punctuated equilbrium?

My answer: Let's do both!

Phyletic gradualism is based on the idea that nature does not make jumps. Punctuated equilibrium is based on the idea that almost all the time, species aren't changing. Oddly enough both theories are compatible with each other in the presence of change. The Cantor function (also known as the “Devil's Staircase”) increases from 0 to 1 even though it is both continuous (the equivalent of phyletic gradualism) and the first derivative is defined and zero almost everywhere (the equivalent of punctuated equilibrium).