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Analytic and computational methods developed within statistical physics havefound applications in numerous disciplines. In this letter, we use such methodsto solve a long-standing problem in statistical genetics. The problem, posed byHaldane and Waddington [J.B.S. Haldane and C.H. Waddington, Genetics 16,357-374 (1931)], concerns so-called recombinant inbred lines (RILs) produced byrepeated inbreeding. Haldane and Waddington derived the probabilities of RILswhen considering 2 and 3 genes but the case of 4 or more genes has remainedelusive. Our solution uses two probabilistic frameworks relatively unknownoutside of physics: Glauber's formula and self-consistent equations of theSchwinger-Dyson type. Surprisingly, this combination of statistical formalismsunveils the exact probabilities of RILs for any number of genes. Extensions ofthe framework may have applications in population genetics and beyond.

Statistical physics methods provide the exact solution to a long-standing problem of genetics