Varieties as incipient species: Darwin's numerical analysis

Abstract

Charles Darwin claimed but little aptitude for mathematics. In his autobiography he lamented: "I attempted mathematics, and even went during the summer of 1828 with a private tutor (a very dull man) to Barmouth, but I got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps of algebra."' Thus, although it seems highly unlikely that the name Darwin will ever be associated with the phrase "numerical analysis,"2 Darwin worked most diligently from the summer of 1857 through the spring of 1858 on a massive tabulation and mathematical analysis of botanical data which he viewed as "one of the most important arguments I have yet met with"3 in support of his conjecture that varieties were incipient species. The idea of using numerical data in botanical studies of relationships of genera, species, and varieties by no means originated with Darwin. In fact, many of his contemporaries made use of such data in testing ideas that were definitely similar to those he would later adopt. For example, Alphonse de Candolle in his GCographie biologique raisonne'e compiled extensive data that he utilized in drawing conclusions concerning, among other things, the geographically common species in various