The genealogical tree of a chromosome

Journal of Statistical Physics

Volumn 94, Issue 3-4, 1999, Pages 277-298

  Derrida, B ^a   Jung Muller, B ^b,c  

^a LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

^c AGROPARISTECH   (France)

Author keywords

Random genealogies; Spin chain; Steady state

Indexed keywords

EID: 0033072666     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004560700396     Document Type: Article

References (17)

1. R. L. Cann, M. Stoneking, and A. C. Wilson, Mitochondrial DNA and human evolution, Nature 325:31 (1987).
2. R. Hudson, Gene genealogies and the coalescent process, Oxford Surveys in Evolutionnary Biology, Vol. 7, p. 1, D. Futuyma and J. Antonovics, eds. (Oxford University Press, 1991).
3. P. Donnelly and S. Tavaré, Coalescents and genealogical structure under neutrality, Annu. Rev. Genet. 29:401 (1995).
4. J. F. Kingman, The coalescent, Stoch. Proc. Appl. 13:235 (1982).
5. R. Hudson, Properties of a neutral allel model with intragenic recombination, Theor. Pop. Biol. 23:183 (1983).
6. C. Wiuf and J. Hein, On the number of ancestors to a DNA sequence, Genetics 147:1459 (1997).
7. M. Mézard, G. Parisi, N. Sourlas, G. Toulouse, and M. Virasoro, Replica symmetry breaking and the nature of the spin glass phase, J. Physique 45:843 (1984).
8. M. Mézard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, 1987).
9. B. Derrida and H. Flyvbjerg, Statistical properties of randomly broken objects and of multivalley structures in disordered systems, J. Phys. A 20:5273 (1987).
10. B. Derrida, From random walks to spin glasses, Physica D 107:186 (1997).
11. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
12. B. Derrida and L. Peliti, Evolution in a flat fitness landscape, Bull. Math. Biol. 53:355 (1990).
13. P. G. Higgs, Frequency distributions in population genetics parallel those in statistical physics, Phys. Rev. E 51:95 (1995).
14. L. Frachebourg, I. Ispolatov, and P. L. Krapivsky, Extremal properties of random systems, Phys. Rev. E 52:R5727 (1995).
15. M. S. McPeek and T. P Speed, Modeling interference in genetic recombination, Genetics 139:1031 (1995).
16. G. S Roeder, Sex and the single cell, Proc. Natl. Acad. Sci. USA 92:10450 (1995).
17. S. Ohno, The Maltusian parameter of ascents: what prevents the exponential increase of one's ancestors? Proc. Natl. Acad. Sci. USA 93:15276 (1996).