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My second formally published paper, written with Peter Parsons and entitled ‘The analogy between factorial experimentation and balanced multi-point linkage tests’, 1 opens with the sentence ‘It was pointed out by Fisher 2 in the Bateson lecture that the factorial method of experimentation, now used extensively in agriculture and other fields of research, derives its name and structure from the simultaneous segregation of Mendelian characters’. As Fisher put it in his lecture, ‘I may mention a connection between our two subjects’, namely genetics and statistics, ‘which seems not to be altogether accidental’. He later says ‘What a beautifully controlled experiment, again, is put into the geneticist’s hands in a linkage test by simple backcross to a multiple recessive. Here each pair of allelomorphic genes should occur, though in different combinations, equally in each of the pairs of complementary genotypes which constitute his results. The first step to perfect control against viability disturbances, is then inherent in his material’. Fisher had defined what he called a ‘balanced’ multipoint linkage test in 1936 as one where there are both coupling and repulsion data for every possible pair of factors. 3 For a simple two-factor test, this would just mean having data from both the coupling (AB/ab ¼ ab/ab) and repulsion (Ab/aB ¼ ab/ab) double heterozygote backcrosses. In a later paper, 4 devoted to analysing a three-point linkage test in the mouse, he advocated using all four possible combinations of heterozygotes (ABC/abc, Abc/aBC, aBc/AbC and abC/ABc) to enable estimation of the recombination frequencies that would take into account the differential viabilities of the various genotypes, while at the same time enabling the estimation of these viability effects. This is clearly what he was referring to in the above quote and which he describes in more detail later in the lecture. In the 1949 paper, he pointed out that the results could be arranged in the form of a latin square, and it was this arrangement that Bodmer and Parsons 1 exploited in their factorial interpretation of such an experiment, something that Fisher must clearly have had in mind.

Commentary: Connections between genetics and statistics: a commentary on Fisher's 1951 Bateson lecture--'Statistical Methods in Genetics'