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454 Statistical geneticsStewart, 1971) provided a general approach for simple pedigrees. Extensionof this approach to complex pedigree structures (Cannings et al., 1978) andto more general trait models (Cannings et al., 1980) was a major advance instatistical genetics of the 1970s, enabling inference of gene ancestry in humanpopulations (Thompson, 1978), the computation of risk probabilities in thecomplex pedigrees of genetic isolates (Thompson, 1981) and the analysis ofgene extinction in the pedigrees of endangered species (Thompson, 1983).Statistical genetics is fundamentally a latent variable problem. The underlyingprocesses of descent of DNA cannot be directly observed. The observeddata on individuals result from the types of the DNA they carry at certaingenome locations, but these locations are often unknown. In 1977, the EMalgorithm (Dempster et al., 1977) was born. In particular cases it had existedmuch earlier, in the gene-counting methods of Ceppelini et al. (1955), in thevariance component methods of quantitative genetics (Patterson and Thompson,1971) and in the reconstruction of human evolutionary trees (Thompson,1975), but the EM algorithm provided a framework unifying these examples,and suggesting approaches to maximum likelihood estimation across a broadrange of statistical genetics models.39.3 The 1980s: Genetic maps and hidden MarkovmodelsThe statistical methodology of human genetic linkage analysis dates back tothe 1930s work of J.B.S. Haldane (1934) and R.A. Fisher (1934), and the likelihoodframework for inferring and estimating linkage from human family datawas established in the 1950s by work of C.A.B. Smith (1953) and N.E. Morton(1955). However, genetic linkage findings were limited: there were no geneticmarker maps.That suddenly changed in 1980 (Botstein et al., 1980), with the arrivalof the first DNA markers, the restriction fragment polymorphisms or RFLPs.For the first time, there was the vision we now take for granted, of geneticmarkers available at will throughout the genome, providing the frameworkagainst which traits could be mapped. This raised new statistical questions inthe measurement of linkage information (Thompson et al., 1978). The developmentof DNA markers progressed from RFLP to (briefly) multilocus variablenumber of tandem repeat or VNTR loci used primarily for relationshipinference (Jeffreys et al., 1991; Geyer et al., 1993) and then to STR (shorttandem repeat or microsatellite) loci(Murrayetal.,1994);seeTable39.2.These DNA markers, mapped across the genome, brought a whole new frameworkof conditional independence to the computation of linkage likelihoods(Lander and Green, 1987; Abecasis et al., 2002). Rather than the conditionalindependence in the transmission of DNA from parents to offspring, the rel-