Welcome to the website for  
Variance Estimation of the  
Nucleotide Substitution Models  

The current variance estimators for most evolutionary models were derived when a nucleotide substitution number estimator was approximated with a simple first order Taylor expansion. In this study, we derive three variance estimators for the F81, F84, HKY85 and TN93 nucleotide substitution models, respectively. They are obtained using the second order Taylor expansion of the substitution number estimator, the first order Taylor expansion of a squared deviation and the second order Taylor expansion of a squared deviation, respectively. These variance estimators are compared with the existing variance estimator in terms of a simulation study. It shows that the variance estimator, which is derived using the second order Taylor expansion of a squared deviation, is more accurate than the other three estimators. In addition, we also compare these estimators with an estimator derived by the bootstrap method. The simulation shows that the performance of this bootstrap estimator is similar to the estimator derived by the second order Taylor expansion of a squared deviation. Since the latter one has an explicit form, it is more efficient than the bootstrap estimator.

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¡»   Reference

    ¡´    Wang, H. (2011). Confidence Intervals for the Substitution Number in the
           Nucleotide Substitution Models. Molecular Phylogenetics Evolution, 60,
           472-479.
    ¡´    Wang, H., Tzeng, Y.H. and Li, W.H. (2008). Improved variance estimators
           for one- and two-parameter models of nucleotide substitution. Journal of
           Theoretical Biology, 254, 164-167.

    ¡´    Chen, W. and Wang, H. (2015). Variance Estimation for Nucleotide
           Substitution Models. Molecular Phylogenetics and Evolution, to appear

¡»   Download the R-codes
¡´    F81 model (Felsenstein 1981) (F81)
¡´    F84 model (Felsenstein 1984) (F84)
¡´    HKY85 model (Hasegawa, Kishino and Yano 1985) (HKY85)
¡´    TN93 model (Tamura and Nei 1993) (TN93)

The R project web for free download is http://www.r-project.org.

Please ensure you already have installed R to run the codes.

¡»   Run the code.

¡»   R code user manual.

¡»   A data Example

Data source:
¡´    J.P. Dumbacher, T.K. Pratt, and R.C. Fleischer, (2003). Phylogeny of the
      owlet-nightjars (Aves: Aegothelidae) based on mitochondrial DNA
      sequence. Molecular Phylogenetics Evolution, 29, 540-549.
¡´    Wang, H. and Hung, S.L. (2012). Phylogenetic tree selection by the adjusted
       K-means approach. Journal of Applied Statistics, 39, 643-655.


The data set for the genome of the 11 owlet-nightjars.
¡@ Download link¡@ File type¡@ File size¡@ Update¡@
Data file DATA¡@ rar 4.26KB¡@ 2014.07.30¡@

¡»   Contact

If you have any questions on the codes, please feel free to contact us at
hsiuyingwang@nctu.edu.tw (Primary) ; wang@stat.nctu.edu.tw  (Secondary).
We welcome your feedback and comments. ¡@