Abstract

Darwin’s publication of The Origin of Species in 1859 situated biology firmly within the “probabilistic revolution” in the history of science. One consequence of this was an increased emphasis on probability and statistics in mathematical practice. The earliest attempts to test Darwin’s theory relied on statistical analyses of phenotypic traits in various species. With the rediscovery of Mendel’s work in the late nineteenth and early twentieth centuries, emphasis shifted to the development of genetical models based on combinatrics and discrete probability. The interplay between evolution and probability continues in the present, for example, in the development of coalescent theory and the study of Markov models on trees. We will survey this history, and we will discuss a few of the ideas underlying some of these mathematical models. We will also consider, and reject, certain probabilistic arguments presented by critics of evolutionary theory.