Genealogies in simple models of evolution

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2013, Issue 1, 2013, Pages

  Brunet, Éric ^a   Derrida, Bernard ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

population dynamics (theory); stochastic processes (theory)

Indexed keywords

EID: 84874462104     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2013/01/P01006     Document Type: Article

References (58)

1. Chang J 1999 Recent common ancestors of all present-day individuals Adv. Appl. Probab. 31 1002
2. Kingman J F C 1982 The coalescent Stoch. Proc. Appl. 13 235
3. Kingman J F C 1982 On the genealogy of large populations J. Appl. Probab. 19 27
4. Hudson R R 1991 Gene genealogies and the coalescent process Oxford Surv. Evol. Biol. 7 1
5. Donnelly P and Tavare S 1995 Coalescents and genealogical structure under neutrality Annu. Rev. Genet. 29 401
6. Brunet É, Derrida B, Mueller A H and Munier S 2006 Noisy traveling waves: effect of selection on genealogies Europhys. Lett. 76 1
7. Brunet É, Derrida B, Mueller A H and Munier S 2007 Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization Phys. Rev. E 76 041104
8. Bolthausen E and Sznitman A S 1998 On Ruelle's probability cascades and an abstract cavity method Commun. Math. Phys. 197 247
9. Derrida B, Manrubia S and Zanette D 2000 On the genealogy of a population of biparental individuals J. Theor. Biol. 203 303
10. Brunet É and Derrida B 2012 How genealogies are affected by the speed of evolution Phil. Mag. 92 255
11. Nordborg M 2001 Coalescent theory Handbook of Statistical Genetics ed D J Balding, M Bishop and C Cannings (Chichester: Wiley) pp 179-212
12. Berestycki N 2009 Recent progress in coalescent theory Ensaios Matemat. 16 1
13. Pitman J 1999 Coalescents with multiple collisions Ann. Probab. 27 1870
14. Durrett R and Schweinsberg J 2005 A coalescent model for the effect of advantageous mutations on the genealogy of a population Stoch. Proc. Appl. 115 1628
15. Huillet T and Möhle M 2012 On the extended Moran model and its relation to coalescents with multiple collisions Theor. Popul. Biol. at press
16. Tavare S 1984 Line-of-descent and genealogical processes, and their applications in population-genetics models Theor. Popul. Biol. 26 119
17. Simon D and Derrida B 2006 Evolution of the most recent common ancestor of a population with no selection J. Stat. Mech. P05002
18. Sherrington D and Kirkpatrick S 1975 Solvable model of a spin-glass Phys. Rev. Lett. 35 1792
19. Kirkpatrick S and Sherrington D 1978 Infinite-ranged models of spin-glasses Phys. Rev. B 17 4384
20. Mézard M, Parisi G, Sourlas N, Toulouse G and Virasoro M A 1984 Replica symmetry breaking and the nature of the spin-glass phase J. Physique 45 843
21. Mézard M, Parisi G and Virasoro M A 1987 Spin Glass Theory and Beyond (World Scientific Lecture Notes in Physics) vol 9 (Singapore: World Scientific)
22. Parisi G 1979 Infinite number of order parameters for spin-glasses Phys. Rev. Lett. 43 1754
23. Parisi G 1980 The order parameter for spin glasses: a function on the interval 0-1 J. Phys. A: Math. Gen. 13 1101
24. Parisi G 1983 Order parameter for spin-glasses Phys. Rev. Lett. 50 1946
25. Schweinsberg J 2005 Coalescent process obtained from supercritical Galton-Watson processes Stoch. Proc. Appl. 106 107
26. O'Fallon B D, Seger J and Adler F R 2010 A continuous-state coalescent and the impact of weak selection on the structure of gene genealogies Mol. Biol. Evol. 27 1162
27. Griffiths R C 1980 Lines of descent in the diffusion-approximation of neutral Wright-Fisher models Theor. Popul. Biol. 17 37
28. Etheridge A 2011 Some Mathematical Models from Population Genetics (Lecture Notes in Mathematics) (Berlin: Springer)
29. Möhle M and Sagitov S 2001 A classification of coalescent processes for haploid exchangeable population models Ann. Probab. 29 1547
30. Ewens W J 1972 The sampling theory of selectively neutral alleles Theor. Popul. Biol. 3 87
31. Tajima F 1983 Evolutionary relationship of DNA sequences in finite populations Genetics 105 437
32. Fu Y X and Li W H 1997 Estimating the age of the common ancestor of a sample of DNA sequences Mol. Biol. Evol. 14 195
33. Degnan J H and Salter L A 2005 Gene tree distributions under the coalescent process Evolution 59 24
34. Derrida B and Peliti L 1991 Evolution in a flat fitness landscape Bull. Math. Biol. 53 355
35. Rosenberg N A and Nordborg M 2002 Genealogical trees, coalescent theory and the analysis of genetic polymorphisms Nature Rev. Genet. 3 380
36. Prignano L and Serva M 2009 Genealogical trees from genetic distances Eur. Phys. J. B 69 20
37. Serva M 2005 On the genealogy of populations: trees, branches and offspring J. Stat. Mech. P07011
38. Derrida B 1997 From random walks to spin glasses Physica D 107 186
39. d Ann. Probab. 17 1333
40. Limic V and Sturm A 2006 The spatial Λ-coalescent Electron. J. Probab. 11 363
41. Brunet E, Derrida B and Simon D 2008 Universal tree structures in directed polymers and models of evolving populations Phys. Rev. E 78 061102
42. Bak P and Sneppen K 1993 Punctuated equilibrium and criticality in a simple model of evolution Phys. Rev. Lett. 71 4083
43. Kessler D A, Levine H, Ridgway D and Tsimring L 1997 Evolution on a smooth landscape J. Stat. Phys. 87 519
44. Desai M M, Fisher D S and Murray A W 2007 The speed of evolution and maintenance of variation in asexual populations Curr. Biol. 17 385
45. Rouzine I M, Brunet E and Wilke C O 2008 The traveling wave approach to asexual evolution: Muller's ratchet and speed of adaptation Theor. Popul. Biol. 73 24
46. Yu F and Etheridge A 2008 Rate of adaptation of large populations Evolutionary Biology from Concept to Application ed P Pontarotti (Berlin: Springer) pp 3-27
47. Brunet É, Derrida B, Mueller A H and Munier S 2006 A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts Phys. Rev. E 73 056126
48. Rohde D, Olson S and Chang J 2004 Modelling the recent common ancestry of all living humans Nature 431 562
49. Munier S 2009 private communication
50. Kesten H 1978 Branching brownian motion with absorption Stoch. Proc. Appl. 7 9
51. Derrida B and Simon D 2007 The survival probability of a branching random walk in presence of an absorbing wall Eur. Phys. Lett. 78 60006
52. Berestycki J, Berestycki N and Schweinsberg J 2010 The genealogy of branching brownian motion with absorption arXiv:1001.2337
53. Maillard P 2011 Branching brownian motion with selection of the N right-most particles: an approximate model arXiv:1112.0266
54. Jain K and Krug J 2005 Evolutionary trajectories in rugged fitness landscapes J. Stat. Mech. P04008
55. Neuhauser C and Krone S 1997 The genealogy of samples in models with selection Genetics 145 519
56. Barton N H and Etheridge A M 2004 The effect of selection on genealogies Genetics 166 1115
57. Neher R A, Shraiman B I and Fisher D S 2010 Rate of adaptation in large sexual populations Genetics 184 467
58. Hudson R R and Kaplan N L 1988 The coalescent process in models with selection and recombination Genetics 120 831