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.
ˇ´ Wang, H. (2011). Confidence Intervals for the Substitution Number in the
ˇ» Download the R-codes
Nucleotide Substitution Models. Molecular Phylogenetics Evolution, 60,
ˇ´ 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.
ˇ´ Chen, W. and Wang, H. (2015). Variance Estimation for Nucleotide
Substitution Models. Molecular Phylogenetics and Evolution, to appear
ˇ´ F81 model (Felsenstein 1981) (F81)
ˇ´ F84 model (Felsenstein 1984) (F84)
ˇ´ HKY85 model (Hasegawa, Kishino and Yano 1985) (HKY85)
ˇ´ TN93 model (Tamura and Nei 1993) (TN93)
The R project web for free download is
Please ensure you already have installed R to run the codes.
ˇ» Run the code.
ˇ» R code user manual.
ˇ» A data Example
ˇ´ 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.
ˇ´ 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.
If you have any questions on the codes, please feel free to contact us at
email@example.com (Primary) ; firstname.lastname@example.org (Secondary).
We welcome your feedback and comments.