Finding the best resolution for the kingman–tajima coalescent: Theory and applications

Journal of Mathematical Biology

Volumn 70, Issue 6, 2015, Pages 1207-1247

  Sainudiin, Raazesh ^a   Stadler, Tanja ^b   Véber, Amandine ^c  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

^b ETH ZURICH   (Switzerland)

^c CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Computationally efficient and statistically sufficient inference; N Coalescent resolutions; Tree shape statistics

Indexed keywords

ALGORITHM; BIOLOGICAL MODEL; BIOLOGY; BIOSTATISTICS; HUMAN; MARKOV CHAIN; MATHEMATICAL PHENOMENA; MUTATION; PHYLOGENY; POPULATION GENETICS; PROBABILITY; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA;

ALGORITHMS; BIOSTATISTICS; COMPUTATIONAL BIOLOGY; GENETICS, POPULATION; HUMANS; MARKOV CHAINS; MATHEMATICAL CONCEPTS; MODELS, GENETIC; MODELS, STATISTICAL; MUTATION; PHYLOGENY; PROBABILITY;

EID: 84938269799     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-014-0796-5     Document Type: Article

References (39)

1. Aldous DJ (2001) Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today. Stat Sci 16(1):23–34
2. Bahlo M, Griffiths R (1996) Inference from gene trees in a subdivided population. Theor Pop Biol 57:79–95
3. Beaumont M, Zhang W, Balding D (2002) Approximate Bayesian computation in population genetics. Genetics 162:2025–2035
4. Beaumont M, Robert C, Marin JM, Cornuet J (2009) Adaptivity for ABC algorithms: the ABC–PMC scheme. Biometrika 96(4):983–990
5. Birkner M, Blath J (2008) Computing likelihoods for coalescents with multiple collisions in the infinitely many sites model. J Math Biol 57:435–465
6. Colless DH (1982) Review of phylogenetics: the theory and practice of phylogenetic systematics. Syst Zool 31:100–104
7. Del Moral P (2004) Feynman–Kac formulae: genealogical and interacting particle systems with applications. Springer, New York
8. Doucet A, Johansen AM (2009) A tutorial on particle filtering and smoothing: fifteen years later. In: Crisan D, Rozovsky B (eds) The Oxford handbook of nonlinear filtering. Oxford University Press, Oxford
9. Etheridge AM (2011) Some mathematical models from population genetics. Lecture notes in mathematics 2012. Springer, Berlin
10. Fisher R (1930) The genetical theory of natural selection. Clarenson, Oxford
11. Ford D, Matsen E, Stadler T (2009) A method for investigating relative timing information on phylogenetic trees. Syst Biol 58(2):167–183
12. Fu YX (1995) Statistical properties of segregating sites. Theor Pop Biol 48:172–197
13. Griffiths R, Tavare S (1994) Ancestral inference in population genetics. Stat Sci 9:307–319
14. Griffiths R, Tavare S (1996) Markov chain inference methods in population genetics. Math Comput Model 23:141–158
15. Iorio M, Griffiths R (2004) Importance sampling on coalescent histories I. Adv Appl Prob 36:417–433
16. Kemeny J, Snell J (1960) Finite Markov chains. D. van Nostrand Company Inc, Princeton
17. Kendall DG (1975) Some problems in mathematical genealogy. In: Gani J (ed) Perspectives in probability and statistics. Academic Press, New York, pp 325–345
18. Kingman JFC (1982a) The coalescent. Stoch Proc Appl 13:235–248
19. Kingman JFC (1982b) On the genealogy of large populations. J Appl Probab 19:27–43
20. Kolmogorov A (1942) Sur l’estimation statistique des paramètres de la loi de gauss. Bull Acad Sci URSS Ser Math 6:3–32
21. Le Cam L (1964) Sufficiency and approximate sufficiency. Ann Math Stat 35:1419–1455
22. Leuenberger C, Wegmann D (2009) Bayesian computation and model selection without likelihoods. Genetics 184:243–252
23. Marin JM, Pudlo P, Robert CP, Ryder RJ (2012) Approximate Bayesian computational methods. Stat Comput 22(6):1167–1180. doi:10.1007/s11222-011-9288-2
24. Marjoram P, Molitor J, Plagnol V, Tavare S (2003) Markov chain Monte Carlo without likelihoods. Proc Natl Acad Sci USA 100:15324–15328
25. McKenzie A, Steel M (2000) Distribution of cherries for two models of trees. Math Biosci 164:81–92
26. Pritchard J, Seielstad M, Perez-Lezaun A, Feldman M (1999) Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Mol Biol Evol 16:1791–1798
27. Ralph P, Coop G (2013) The geography of recent genetic ancestry across Europe. PLoS Biol 11(5): e1001555
28. Sackin MJ (1975) “Good” and “bad” phenograms. Syst Zool 21:225–226
29. Sainudiin R, Thornton K, Harlow J, Booth J, Stillman M, Yoshida R, Griffiths R, McVean G, Donnelly P (2011) Experiments with the site frequency spectrum. Bull Math Biol 73(4):829–872
30. Semple C, Steel M (2003) Phylogenetics. Oxford University Press, Oxford
31. Sisson S, Fan Y, Tanaka M (2007) Sequential Monte Carlo without likelihoods. Proc Natl Acad Sci USA 104:1760–1765
32. Slatkin M (2002) A vectorized method of importance sampling with applications to models of mutation and migration. Theor Pop Biol 62:339–348
33. Stephens M, Donnelly P (2000) Inference in molecular population genetics. J R Stat Soc B 62:605–655
34. Tajima F (1983) Evolutionary relationship of DNA sequences in finite populations. Genetics 105:437–460
35. Tajima F (1989) Statistical method for testing the neutral mutation hypothesis by DNA polymorphism. Genetics 123:585–595
36. Tavaré S (1983) Line-of-descent and genealogical processes, and their applications in population genetics models. Theor Pop Biol 26:119–164
37. Watterson GA (1975) On the number of segregating sites in genetical models without recombination. Theor Pop Biol 7:256–276
38. Weiss G, von Haeseler A (1998) Inference of population history using a likelihood approach. Genetics 149:1539–1546
39. Wright S (1931) Evolution in Mendelian populations. Genetics 16:97–159