Mass Extinctions and Punctuated Equilibria in a Simple Model of Evolution

Abstract

Darwin’s theory is a concise formulation of some general observations for the evolution of life on earth. In contrast to the laws of physics, which are expressed as mathematical equations relating to physical observable quantities, there are no Darwin’s equations describing biological evolution in the language of rigorous mathematics, as my colleague and friend Henrik Flyvbjerg once eloquently pointed out. Therefore, it is a highly important matter to determine if Darwin’s theory gives an essentially complete description of life on earth, or if some other principles have to be included. Darwin’s theory concerns evolution at the smallest scale, microevolution. We do not know the consequences of his theory for evolution on the largest scale, macroevolution, so it is difficult to confront, and possibly falsify, the theory by observations on the fossil record.