A Brief History of Evolutionary Modeling

One of the first mathematical models in evolutionary biology was Dusing’s analysis of sex ratio, published in 1884 (see Edwards 1998, 2000). This showed how the rarer sex tended to leave more offspring, so that populations tend toward equal proportions of males and females (pp. 506 and 603). Francis Galton introduced the idea of regression, in order to describe the inheritance of continuous traits; this was developed by Karl Pearson into a sophisticated theory that showed how selection shapes the distribution of quantitative traits (pp. 20–21). Soon after the rediscovery of Mendel’s work in 1900, discrete inheritance was analyzed, with calculations of how the proportions of different genotypes change over the generations. The eminent mathematician G.H. Hardy (1908) showed how the frequencies of diploid genotypes depend on the allele frequencies when there is random mating; the German physician Wilhelm Weinberg (1908) discovered this independently and explored the consequences of Mendelian inheritance in a series of papers during the early twentieth century. Around the same time, the first ecological models were developed by Alfred J. Lotka, Vito Volterra, and others, showing how population growth could be checked by competition (see Kingsland 1985).

These various strands came together in the 1920s and 1930s when much of population genetics was developed. As we saw in Chapter 1, the early theory made a major contribution to the synthesis between Mendelian genetics and Darwinian evolution (p. 30). Most important was the demonstration that natural selection could act rapidly and could easily account for even the fastest examples of evolutionary change. In the first half of the 20th century, population genetics was applied to specific problems: measuring inbreeding, improving methods for artificial selection, and analyzing geographic variation (Chapter 16). Most of the mathematical methods that we use now, and which we review in this chapter, were developed around this time.