what does the bible say?
Punctuated equilibrium is not in the Bible. The Bible is clear that creatures did not evolve, whether gradually or by punctuated equilibrium. Instead, the various "kinds" were created by God (Genesis 1:20–27).
The term "punctuated equilibrium" comes from an evolutionary theory that was postulated in 1974 as a way to explain gaps in the fossil record. According to Darwinism, all known species evolved slowly over millions of years, from a single-celled organism to the more complex forms we see today. In this way, gradual changes resulted in all the species of mammals, fish, birds, and reptiles that now exist. However, the fossil record does not prove this theory. any different species represented in fossils, some still living and some extinct, and there is a glaring absence of the transitional forms one would expect to see if species were evolving gradually over time. Punctuated equilibrium then is the idea that instead of species evolving gradually, as was originally postulated, the changes occurred sporadically and much more rapidly. However, within the evolutionary community there are major disagreements over the applicability of punctuated equilibrium.