Distance measures in terms of substitution processes

Theoretical Population Biology

Volumn 55, Issue 2, 1999, Pages 166-175

  Baake, Ellen ^a   Von Haeseler, Arndt ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AMINO ACID SEQUENCE; GENETIC DISTANCE; MODEL; NUCLEOTIDE SEQUENCE; PHYLOGENY;

EID: 0033117920     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1006/tpbi.1998.1395     Document Type: Article

References (31)

1. Akin E. The Geometry of Population Genetics. Lecture Notes in Biomathematics. 31:1979;Springer, New York.
2. Antonelli P. L., Strobeck C. The geometry of random drift. I. Stochastic distance and diffusion. Adv. Appl. Prob. 9:1977;238-249.
3. Baake E. Math. Biosci. 154:1998;1-21.
4. Bandelt H.-J., Dress A. Reconstructing the shape of a tree from observed dissimilarity data. Adv. Appl. Math. 7:1986;309-343.
5. Barry D., Hartigan J. A. Asynchronous distance between homologous DNA sequences. Biometrics. 43:1987;261-276.
6. Benzer S. On the topography of the genetic fine structure. Proc. Natl. Acad. Sci. USA. 47:1961;403-415.
7. Chang J. T. Full reconstruction of Markov models on evolutionary trees: Identifiability and consistency. Math. Biosci. 137:1996a;51-73.
8. Chang J. T. Inconsistency of evolutionary tree topology reconstruction methods when substitution rates vary across characters. Math. Biosci. 134:1996b;189-215.
9. Felsenstein J. Evolutionary trees from DNA sequences: A maximum likelihood approach. J. Mol. Evol. 17:1981;368-376.
10. Golding B. Estimates of DNA and protein sequence divergence: An examination of some assumptions. Mol. Biol. Evol. 1:1983;125-142.
11. Gu X., Li W.-H. Bias-corrected paralinear and LogDet distances and tests of molecular clocks and phylogenies under nonstationary nucleotide frequencies. Mol. Biol. Evol. 13:1996a;1375-1383.
12. Gu X., Li W.-H. A general additive distance with time-reversibility and rate variation among nucleotide sites. Proc. Natl. Acad. Sci. USA. 93:1996b;4671-4676.
13. Karlin K. S., Taylor H. M. A First Course in Stochastic Processes. 1975;Academic Press, London.
14. Karlin K. S., Taylor H. M. A Second Course in Stochastic Processes. 1981;Academic Press, London.
15. Kelly C., Rice J. Modelling nucleotide evolution: A heterogenous rate analysis. Math. Biosci. 133:1996;85-109.
16. Kemeny J. G., Snell J. L. Finite Markov Chains. 1981;Springer, New York.
17. Lake J. A. Reconstructing evolutionary trees from DNA and protein sequences: Paralinear distances. Proc. Natl. Acad. Sci. USA. 91:1994;1455-1459.
18. Lanave C., Preparata G., Saccone C., Serio G. A new method for calculating evolutionary substitution rates. J. Mol. Evol. 20:1984;86-93.
19. Lockhart P., Steel M., Hendy M., Penny D. Recovering evolutionary trees under a more realistic model of sequence evolution. Mol. Biol. Evol. 11:1994;605-612.
20. Miller W. Symmetry Groups and Their Applications. 1972;Academic Press, London.
21. Rzhetsky A., Nei M. Tests of applicability of several substitution models for DNA sequence data. Mol. Biol. Evol. 12:1995;131-151.
22. Saitou N., Nei M. The neighbor-joining method: A new method for reconstructing phylogenetic trees. Mol. Biol. Evol. 4:1987;406-425.
23. Shahshahani S. A new mathematical framework for the study of linkage and selection. Memoirs Am. Math. Soc. 211:1979.
24. Steel M., Hendy M., Penny D. Technical Report. 1993.
25. Steel M., Székely L., Hendy M. Reconstructing trees when sequence sites evolve at variable rates. J. Comp. Biol. 1:1994;153-163.
26. Steel M. A. Recovering a tree from the leaf colourations it generates under a Markov model. Appl. Math. Lett. 7:1994;19-23.
27. Swofford D. L., Olsen G. J., Waddell P. J., Hillis D. M. Phylogenetic inference. Molecular Systematics. 1995;Sinauer, Sunderland. p. 407-514.
28. Uzzel T., Corbin K. W. Fitting discrete probability distributions to evolutionary events. Science. 172:1971;1089-1096.
29. Waddell P. J., Steel M. A. General time reversible distances with unequal rates across sites: Mixing Γ and inverse Gaussian distributions with invariant sites. Mol. Phyl. Evol. 8:1997;398-414.
30. Waterman M. S., Smith T. F., Singh M., Beyer W. A. Additive evolutionary trees. J. Theor. Biol. 64:1977;199-213.
31. Zharkikh A. Estimation of evolutionary distances between nucleotide sequences. J. Mol. Evol. 39:1994;315-329.