MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Statistical physics methods provide the exact solution to a long-standing problem of genetics
Areejit Samal and Olivier MartinAbstract
Analytic and computational methods developed within statistical physics have found applications in numerous disciplines. In this letter, we use such methods to solve a long-standing problem in statistical genetics. The problem, posed by Haldane and Waddington [J.B.S. Haldane and C.H. Waddington, Genetics 16, 357-374 (1931)], concerns so-called recombinant inbred lines (RILs) produced by repeated inbreeding. Haldane and Waddington derived the probabilities of RILs when considering 2 and 3 genes but the case of 4 or more genes has remained elusive. Our solution uses two probabilistic frameworks relatively unknown outside of physics: Glauber's formula and self-consistent equations of the Schwinger-Dyson type. Surprisingly, this combination of statistical formalisms unveils the exact probabilities of RILs for any number of genes. Extensions of the framework may have applications in population genetics and beyond.
- Received:
- 24.07.14
- Published:
- 11.08.14
- PACS:
- 02.50.Cw, 05.40.-a, 02.50.Sk