2DkcTXceO

452 Statistical geneticsTABLE 39.1The changing study designs and data structures and relationship to developingstatistical approaches.Date Data Design/Structure Statistical Approach1970s pedigrees; evolutionary trees Latent variables and EM1980s genetic maps HMM methodslinkage analysisGraphical models1990s more complex traits Monte Carlo likelihood; MCMCmore complex pedigrees Complex stochastic systems2000s large scale association mapping FDR, p ≫ n2010s descent of genomes; IBD MC realization of latent structureIt is often commented, how, in an earlier era, genome science and statisticalscience developed in parallel. In 1922, Fisher started to develop likelihoodinference (Fisher, 1922a), while in the same year his first example of maximumlikelihood estimation was of estimating genetic recombination frequencies indrosophila (Fisher, 1922b). His first use of the term variance was in developingthe theory of genetic correlations among relatives (Fisher, 1918), while analysisof variance was established in Fisher (1925). In parallel, Wright (1922)was also developing the theory of the dependence structure of quantitativegenetic variation among related individuals, leading to the theory of path coefficients(Wright, 1921) and structural equation modeling (Pearl, 2000). Thechanges in genetics and genomics, statistical science, and both molecular andcomputational technologies over the last 40 years (1970–2010) are arguablymany times greater than over the preceding 40 (1930–1970), but the samecomplementary developments of statistics and genetics are as clear as thoseof Fisher and Wright; see Table 39.1. Moreover the basic scientific questionsremain the same: Where are the genes? What do they do? How do they do it?39.2 The 1970s: Likelihood inference and theEM algorithmThe basic models of genetics are fundamentally parametric. The dependencestructure of data on a pedigree dates to Elston and Stewart (1971) and isshown in Figure 39.1(a). First, population-level parameters provide the probabilitiesof genotypes G (F ) of founder members, across a small set of marker(M) or trait (T ) loci. Parameters of the process of transmission of DNA fromparents to offspring then determine the probabilities of the genotypes (G)