Yule and evolution (1924)

Abstract

Society who had published in 1922 a book entitled Age and Area, A Study in Geo-graphical Distribution and Origin of Species. He had studied the distribution of species among different genera in the classification of plants and animals. The data that he had compiled showed that most genera contained only one species, that fewer and fewer genera contained higher numbers of species and that there were still a few genera containing a great number of species. Table 15.1 shows the data concerning snakes, lizards and two families of beetles (the Chrysomelidae and the Cerambycinae). The 1,580 species of lizards known at the time had been classified in 259 genera, 105 genera containing only one species, 44 only two species, 23 only three species, etc., and two genera containing more than one hundred species. For other families of animals and plants, the distribution of genera according to the number of species they contain had a very similar shape. Yule suggested that Willis should try to plot his data in a graph with logarithmic scales. This gave a striking result (Fig. 15.2): the logarithm of the number Q n of genera containing n species decreases more or less linearly with log(n). In other words, there are constants α > 0 and β > 0 such that Q n α n −β : the distribution follows a " power law " . In his 1924 article, Yule looked for a mathematical model of evolution that could explain such a statistical distribution. Table 15.1 Data compiled by Willis.