Gauging genetic odds after repeated inbreeding

Cross pollination of two individual plants produces an offspring with two sets of chromosomes. The figure shows three genes, each having a pair of chromosome segments called alleles. One set of alleles, labeled a₁, a₂, and a₃, comes from the mother plant, and the other, labeled A₁, A₂, and A₃, comes from the father. Self pollinate the offspring (F₁) and the next generation’s (F₂’s) sets mix up the a and A alleles. Repeat the procedure for many generations and you end up with a recombinant inbred line (RIL), a plant with identical sets of alleles. Such plants are widely used in agriculture to locate the genes responsible for particular traits. In 1931 biologists John Haldane and Conrad Waddington worked out the probabilities for producing RILs for two and three genes. By reaching into their...