However, it seems that the most significant evolutionary changes, the ‘major evolutionary transitions’ described by John Maynard Smith and Eoer Szathmary, were quite radical. The transition from procaryotic to eucaryotic cells, for instance, led to the possibility for complex plants and animals to evolve, where before there were only primitive single-celled organisms. Lyn Margulis has argued that this transition was an instance of symbiogenesis, the combination of two existing life forms into a single one. The mitochondrion, which distinguishes eucaryotic cells, was thought to be a free-living procaryote which was consumed by another procaryote; rather than being digested, it was incorporated, leading to a new type of organism. This leap was radical, probably impossible in any slow, accretive mechanism.

Sewall Wright’s notion of fitness landscape comes to mind, too, the notions of adaptive peaks and fitness valleys to be crossed. A species becomes highly adapted to a particular environment To adapt to some other environment, it must cross a fitness valley, meaning change in a way which makes it less fit for a time, as a necessary step towards becoming highly adapted in the new environment.

That brings to mind Rene Thom’s catastrophe theory, or Thomas Kuhn’s idea of a paradigm shift. Both describe processes which evolve slowly. However, there are occasionally radical changes (’catastrophes’ or ‘paradigm shifts’) which disrupt the ordinary dynamics into some other regime. It’s noteworthy that these two modes of change, accretive and radical, go hand in hand; generally one cannot exist without the other.