Gaussian approximations for phylogenetic branch length statistics under stochastic models of biodiversity

Mathematical Biosciences

Volumn 209, Issue 1, 2007, Pages 108-123

  François, Olivier ^a   Mioland, Céline ^a  

^a CNRS   (France)

Author keywords

Branch length statistics; Branching processes; Gaussian approximations; Phylogenetic models; Tree shape statistics

Indexed keywords

BIODIVERSITY; STATISTICS; STOCHASTIC MODELS;

BRANCH LENGTH STATISTICS; BRANCHING PROCESSES; GAUSSIAN APPROXIMATIONS; PHYLOGENETIC MODELS; TREE SHAPE STATISTICS;

APPROXIMATION THEORY;

BIODIVERSITY; FRUIT; GAUSSIAN METHOD; PHYLOGENETICS; STOCHASTICITY;

ARTICLE; BIODIVERSITY; CHERRY; MATHEMATICAL MODEL; NORMAL DISTRIBUTION; PHYLOGENETIC TREE; PHYLOGENY; STOCHASTIC MODEL;

ANIMALS; BIODIVERSITY; BIRDS; COMPUTER SIMULATION; EVOLUTION, MOLECULAR; HIV-1; HUMANS; MODELS, GENETIC; PHYLOGENY; STOCHASTIC PROCESSES;

EID: 34547730867     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2007.01.005     Document Type: Article

References (51)

1. Agapow P.M., and Purvis A. Power of eight tree shape statistics to detect non-random diversification: a comparison by simulation of two models of cladogenesis. Syst. Biol. 51 (2002) 866-872
2. Aldous D.J. Probability distributions on cladograms. In: Aldous D.J., and Pemantle R. (Eds). Random Discrete Structures. IMA Volumes Math. Appl vol. 76 (1996), Springer, Berlin 1-18
3. Aldous D.J. Stochastic models and descriptive statistics for phylogenetic trees, from Yule to Today. Stat. Sci. 16 (2001) 23-34
4. Aldous P., and Popovic L. A critical branching process model for biodiversity. Adv. Appl. Prob. 37 (2005) 1094-1115
5. Baldi P., Rinott Y., and Stein C. A normal approximation for the number of local maxima of a random function on a graph. Probability, Statistics, and Mathematics (1989), Academic Press, Boston 59-81
6. Baldi P., and Rinott Y. On normal approximations of distributions in terms of dependency graphs. Ann. Probab. 17 (1989) 1646-1650
7. Blum M.G.B., and François O. Minimal clade size and external branch length under the neutral coalescent. Adv. Appl. Prob. 37 (2005) 647-662
8. Blum M.G.B., and François O. On statisticals tests of phylogenetic tree imbalance: the Sackin and other indices revisited. Math. Biosci. 195 (2005) 141-153
9. Blum M.G.B., and François O. Which random processes describe the Tree of Life? A large scale study of phylogenetic tree imbalance. Syst. Biol. 55 (2006) 685-691
10. Blum M.G.B., François O., and Janson S. The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance. Ann. Appl. Probab. 16 (2006) 2195-2214
11. Bortolussi N., Durand E., Blum M.G.B., and François O. ApTreeshape: Statistical analysis of phylogenetic treeshape. Bioinformatics 22 (2006) 363-364
12. A. Caliebe, R. Neininger, M. Krawczak, U. Rösler, The length of external branches in coalescent trees, in: 33rd European Mathematical Genetics Meeting, EMGM05, Annals of Human Genetics, vol. 69, 2005, p. 764.
13. Colless D.H. Review of phylogenetics: the theory and practice of phylogenetic systematics. Syst. Zool. 31 (1982) 100-104
14. Durrett R. Probabilistic Models of DNA Sequences (2002), Springer Verlag, New York
15. Durrett R. Probability: Theory and Examples. third ed. (2005), Duxbury Press, Belmont, CA
16. Ewens W.J. Mathematical Population Genetics (1978), Springer, New York
17. Felsenstein J. Inferring Phylogenies (2003), Sinauer Associates, Sunderland, MA
18. Faith D.P. Conservation evaluation and phylogenetic diversity. Biol. Conservat. 61 (1992) 1
19. Fu Y.X., and Li W.H. Statistical tests of neutrality of mutations. Genetics 133 (1993) 93-709
20. Harding E.F. The probabilities of rooted tree- shapes generated by random bifurcation. Adv. Appl. Prob. 3 (1971) 4-77
21. Harris T.E. The Theory of Branching Processes (1964), Springer Verlag, Berlin
22. Harvey P.H., Brown A.J.L., Smith J.M., and Nee S. New Uses for New Phylogenies (1996), Oxford University Press, Oxford, UK
23. Hein J., Schierup M.H., and Wiuf C. Gene Genealogies, Variation and Evolution: A Primer in Coalescent Theory (2005), Oxford University Press, Oxford, UK
24. Hey J. Using phylogenetic trees to study speciation and extinction. Evolution 46 (1992) 627-640
25. Kingman J.F.C. The coalescent. Stoch. Proc. Appl. 13 (1982) 235-248
26. Kirkpatrick M., and Slatkin M. Searching for evolutionary patterns in the shape of a phylogenetic tree. Evolution 47 (1993) 1171-1181
27. Mace G.M., Gittleman J.L., and Purvis A. Preserving the Tree of Life. Science 300 (2003) 1707-1709
28. McKenzie A., and Steel M. Properties of phylogenetic trees generated by Yule-type speciation models. Math. Biosci. 170 (2000) 91-112
29. Mooers A.Ø., and Heard S.B. Inferring evolutionary process from phylogenetic tree shape. Quart. Rev. Biol. 72 (1997) 1-54
30. A.Ø. Mooers, L.J. Harmon, M.G.B. Blum, D.H.J. Wong, S.B. Heard, Some models of phylogenetic tree shape, in: O. Gascuel, M. Steel (Eds.), Reconstructing Evolution: New Mathematical and Computational Advances, Oxford University Press, Oxford, 2007, in press.
31. Moore B.R., Chan K.M.A., and Donoghue M.J. Detecting diversification rate variation in supertrees. In: Bininda-Edmonds O.R.P. (Ed). Phylogenetic Supertrees: Combining Information to Reveal the Tree of Life, Computational Biology vol. 3 (2004), Kluwer Academic Publishers, Netherlands 487-533
32. Moran P.A.P. Random processes in genetics. Proc. Camb. Philos. Soc. 54 (1958) 60-72
33. Nee S., May R.M., and Harvey P.H. The reconstructed evolutionary process. Philos. Trans. Roy. Soc. Lond. B 344 (1994) 305-311
34. Nee S., Barraclough T.G., and Harvey P.H. Temporal changes in biodiversity: detecting patterns and identifying causes. In: Gaston K. (Ed). Biodiversity (1996), Oxford University Press, Oxford, UK 230-252
35. Nee S., and May R.M. Extinction and the loss of evolutionary history. Science 278 (1997) 692-694
36. Nordborg M. Coalescent theory. In: Balding D.J., et al. (Ed). Handbook of Statistical Genetics (2003), Wiley, New York 179-208
37. Paradis E., Claude J., and Strimmer K. APE: analyses of phylogenetics and evolution in R language. Bioinformatics 20 (2004) 289-290
38. Popovic L. Asymptotic genealogy of a critical branching process. Ann. Appl. Probab. 14 (2004) 2120-2148
39. Purvis A., and Hector A. Getting the measure of biodiversity. Nature 405 (2000) 212-219
40. Pybus O.G., and Harvey P.H. Testing macro-evolutionary models using incomplete molecular phylogenies. Proc. R. Soc. Lond. B 267 (2000) 2267-2272
41. Rinott Y., and Rotar V. Normal approximations by Stein's method. Decisions Econ. Finance 23 (2000) 15-29
42. Rosenberg N.A. The mean and variance of the numbers of r-pronged nodes and r-caterpillars in Yule-generated genealogical trees. Ann. Combinatorics 10 (2006) 129-146
43. Sackin M.J. Good and bad phenograms. Syst. Zool. 21 (1972) 225
44. Shao K., and Sokal R.R. Tree balance. Syst. Zool. 39 (1990) 266
45. Sibley C.G., and Ahlquist J.E. Phylogeny and Classification of Birds: A Study in Molecular Evolution (1990), Yale University Press, New Haven
46. C. Stein, Approximate computation of expectations, in: S.S. Gupta (ed.), Institute of Mathematical Statistics Lecture Notes-Monograph Series vol. 7, Hayward California, 1986.
47. Strimmer K., and Pybus O.G. Exploring the demographic history of DNA sequences using the generalized skyline plot. Mol. Biol. Evol. 18 (2001) 2298-2305
48. S. Tavaré, Ancestral inference in population genetics, in: Lectures on Probability Theory and Statistics, Lecture Notes Math. 1837, Springer, Berlin, 2004, pp. 1-188.
49. Yule G.U. A mathematical theory of evolution, based on the conclusions of Dr. J.C. Willis. Philos. Trans. Roy. Soc. Lond. Ser. B 213 (1924) 21-87
50. Yusim K., Peeters M., Pybus O.G., Bhattacharya T., Delaporte E., Mulanga C., Muldoon M., Theiler J., and Korber B. Using HIV-1 sequences to infer historical features of the AIDS epidemic and HIV evolution. Philos. Trans. R. Soc. Lond. B 356 (2001) 855-866
51. Wollenberg K., Arnold J., and Avise J.C. Recognizing the forest for the trees: testing temporal patterns of cladogenesis using a null model of stochastic diversification. Mol. Biol. Evol. 13 (1996) 833-849