On Wright-Fisher diffusion and its relatives

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2007, Issue 11, 2007, Pages

  Huillet, Thierry ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

Mutational and evolutionary processes (theory); Phylogeny (theory); Population dynamics (theory)

Indexed keywords

EID: 38049001097     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2007/11/P11006     Document Type: Article

References (17)

1. Blythe R A and McKane A J 2007 Stochastic models of evolution in genetics, ecology and linguistics J. Stat. Mech. P07018
2. Crow J F and Kimura M 1970 An Introduction to Population Genetics Theory (New York: Harper & Row)
3. Dynkin E B 1965 Markov Processes (Die Grundlehren der Mathematischen Wissenschaften Bände 121) vol I (New York: Academic) (Berlin: Springer) (Translated with the authorization and assistance of the author by J Fabius, V Greenberg, A Maitra and G Majone)
4. Dynkin E B 1965 Markov Processes (Die Grundlehren der Mathematischen Wissenschaften Bände 122) vol II (New York: Academic) (Berlin: Springer) (Translated with the authorization and assistance of the author by J Fabius, V Greenberg, A Maitra and G Majone)
5. Ethier S N and Kurtz T G 1986 Markov Processes. Characterization and Convergence (Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics) (New York: Wiley)
6. Ewens W J 2004 Mathematical Population Genetics. I. Theoretical Introduction (Interdisciplinary Applied Mathematics vol 27) 2nd edn (New York: Springer)
7. Feller W 1952 The parabolic differential equations and the associated semi-groups of transformations Ann. Math. 55 468
8. Gillespie J H 1991 The Causes of Molecular Evolution (New York: Oxford University Press)
9. Griffiths R C 2003 The frequency spectrum of a mutation, and its age, in a general diffusion model Theor. Popul. Biol. 64 241
10. Karlin S and Taylor H M 1981 A Second Course in Stochastic Processes (New York: Academic/Harcourt Brace Jovanovich)
11. Kingman J F C 1982 The coalescent Stoch. Process. Appl. 13 235
12. Mandl P 1968 Analytical Treatment of One-Dimensional Markov Processes (Die Grundlehren der Mathematischen Wissenschaften Band 151) (Prague: Academia Publishing House of the Czechoslovak Academy of Sciences) (New York: Springer)
13. Maruyama T 1977 Stochastic Problems in Population Genetics (Springer Lecture Notes in Biomathematics vol 17) (Berlin: Springer)
14. Nagylaki T 1989 Anecdotal, historical and critical commentaries on genetics Gustave Malécot and the transition from classical to modern population genetics Genetics 122 253
15. Neuhauser C and Krone S M 1997 The genealogy of samples in models with selection Genetics 145 519
16. Simon D and Derrida B 2006 Evolution of the most recent common ancestor of a population with no selection J. Stat. Mech. P05002
17. Tavaré S 2004 Ancestral inference in population genetics Lectures on Probability Theory and Statistics, Saint-Flour 2001 (Springer Lecture Notes in Mathematics vol 1837) (Berlin: Springer) pp1-188