Starless bias and parameter-estimation bias in the likelihood-based phylogenetic method

Xuhua Xia

doi:10.3934/genet.2018.4.212

AIMS Genetics, 2018, 5(4): 212-223. doi: 10.3934/genet.2018.4.212. Research article

Export file:

Format

RIS(for EndNote,Reference Manager,ProCite)
BibTex
Text

Content

Citation Only
Citation and Abstract

Starless bias and parameter-estimation bias in the likelihood-based phylogenetic method

Xuhua Xia

1 Department of Biology, University of Ottawa, Ottawa, Canada, K1N 6N5
2 Ottawa Institute of Systems Biology, Ottawa, Canada, K1H 8M5

Received: , Accepted: , Published:

Abstract Full Text(HTML) Figure/Table Supplementary Related pages

I analyzed various site pattern combinations in a 4-OTU case to identify sources of starless bias and parameter-estimation bias in likelihood-based phylogenetic methods, and reported three significant contributions. First, the likelihood method is counterintuitive in that it may not generate a star tree with sequences that are equidistant from each other. This behaviour, dubbed starless bias, happens in a 4-OTU tree when there is an excess (i.e., more than expected from a star tree and a substitution model) of conflicting phylogenetic signals supporting the three resolved topologies equally. Special site pattern combinations leading to rejection of a star tree, when sequences are equidistant from each other, were identified. Second, fitting gamma distribution to model rate heterogeneity over sites is strongly confounded with tree topology, especially in conjunction with the starless bias. I present examples to show dramatic differences in the estimated shape parameter α between a star tree and a resolved tree. There may be no rate heterogeneity over sites (with the estimated α > 10000) when a star tree is imposed, but α < 1 (suggesting strong rate heterogeneity over sites) when an (incorrect) resolved tree is imposed. Thus, the dependence of “rate heterogeneity’’ on tree topology implies that “rate heterogeneity’’ is not a sequence-specific feature, cautioning against interpreting a small α to mean that some sites are under strong purifying selection and others not. Thirdly, because there is no existing (and working) likelihood method for evaluating a star tree with continuous gamma-distributed rate, I have implemented the method for JC69 in a self-contained R script for a four-OTU tree (star or resolved), in addition to another R script assuming a constant rate over sites. These R scripts should be useful for teaching and exploring likelihood methods in phylogenetics.

Figure/Table

Supplementary

Article Metrics

Keywords: maximum likelihood; molecular phylogenetics; rate heterogeneity; starless; star-tree paradox

Citation: Xuhua Xia. Starless bias and parameter-estimation bias in the likelihood-based phylogenetic method. AIMS Genetics, 2018, 5(4): 212-223. doi: 10.3934/genet.2018.4.212

References:

1. Saitou N, Nei M (1987) The neighbor-joining method: A new method for reconstructing phylogenetic trees. Mol Biol Evol 4: 406–425.
2. Desper R, Gascuel O (2004) Theoretical foundation of the balanced minimum evolution method of phylogenetic inference and its relationship to weighted least-squares tree fitting. Mol Biol Evol 21: 587–598.
3. Xia X (2014) Phylogenetic bias in the likelihood method caused by missing data coupled with Among-Site rate variation: An analytical approach. In: Basu M, Pan Y, Wang J, editors. Bioinformatics Research and Applications: Springer, 12–23.
4. Jukes TH, Cantor CR (1969) Evolution of protein molecules. In: Munro HN, editor. Mammalian Protein Metabolism. New York: Academic Press, 21–123.
5. Hasegawa M, Kishino H (1989) Heterogeneity of tempo and mode of mitochondrial DNA evolution among mammalian orders. Jpn J Genet 64: 243–258.
6. Kishino H, Hasegawa M (1989) Evaluation of the maximum likelihood estimate of the evolutionary tree topologies from DNA sequence data, and the branching order in Hominoidea. J Mol Evol 29: 170–179.
7. Hasegawa M, Kishino H, Yano T (1985) Dating of the human-ape splitting by a molecular clock of mitochondrial DNA. J Mol Evol 22: 160–174.
8. Tamura K, Nei M (1993) Estimation of the number of nucleotide substitutions in the control region of mitochondrial DNA in humans and chimpanzees. Mol Biol Evol 10: 512–526.
9. Lanave C, Preparata G, Saccone C, et al. (1984) A new method for calculating evolutionary substitution rates. J Mol Evol 20: 86–93.
10. Tavaré S (1986) Some probabilistic and statistical problems in the analysis of DNA sequences. In: Miura RM, editor. Lectures on Mathematics in the Life Sciences. Providence, RI: Amer Math Soc: 57–86.
11. Xia X (2017) Deriving transition probabilities and evolutionary distances from substitution rate matrix by probability reasoning. J Genet Genome Res 3: 031.
12. Xia X (2018) Nucleotide substitution models and evolutionary distances. Bioinf Cell: 269–314.
13. Yang Z (2007) PAML 4: Phylogenetic analysis by maximum likelihood. Mol Biol Evol 24: 1586–1591.
14. Xia X (2018) Maximum likelihood in molecular phylogenetics. Bioinf Cell: 381–395.
15. Guindon S, Dufayard JF, Lefort V, et al. (2010) New algorithms and methods to estimate maximum-likelihood phylogenies: Assessing the performance of PhyML 3.0. Syst Biol 59: 307–321.
16. Xia X (2018) DAMBE7: New and improved tools for data analysis in molecular biology and evolution. Mol Biol Evol 35: 1550–1552.

show all references

This article has been cited by:

1. Katherine E Noah, Jiasheng Hao, Luyan Li, Xiaoyan Sun, Brian Foley, Qun Yang, Xuhua Xia, Major Revisions in Arthropod Phylogeny Through Improved Supermatrix, With Support for Two Possible Waves of Land Invasion by Chelicerates, Evolutionary Bioinformatics, 2020, 16, 117693432090373, 10.1177/1176934320903735

Reader Comments

your name: * your email: *

Download full text in PDF

Associated material

Metrics