There is an ongoing debate amongst evolutionists between those who believe in
We translate Darwin's two hypotheses of random small variations and natural selection
Darwin's gradualism and those who support Eldredge and Gould's punctuated equilibria.
According to the latter the fossil record shows long periods of equilibrium punctuated by
brief periods of relatively rapid evolution.
into mathematics in the simplest possible way, and deduce punctuated equilibria. Thus
Eldredge and Gould's theory is a consequence of, rather than a contradiction to,
Darwin's theory. Moreover the model also explains speciation and canalisation,
and multiple speciation at the punctuation points, showing why multiple speciation is
more generic than bifurcation. It also shows how these are related to the creation of
abrupt frontiers, and invasions of territory.