Molecular Biology and Evolution, Vol 9, 1119-1147, Copyright © 1992 by Society for Molecular Biology and Evolution
A Zharkikh and WH Li
The statistical properties of sample estimation and bootstrap estimation of
phylogenetic variability from a sample of nucleotide sequences are studied
by using model trees of three taxa with an outgroup and by assuming a
constant rate of nucleotide substitution. The maximum-parsimony method of
tree reconstruction is used. An analytic formula is derived for estimating
the sequence length that is required if P, the probability of obtaining the
true tree from the sampled sequences, is to be equal to or higher than a
given value. Bootstrap estimation is formulated as a two-step sampling
procedure: (1) sampling of sequences from the evolutionary process and (2)
resampling of the original sequence sample. The probability that a
bootstrap resampling of an original sequence sample will support the true
tree is found to depend on the model tree, the sequence length, and the
probability that a randomly chosen nucleotide site is an informative site.
When a trifurcating tree is used as the model tree, the probability that
one of the three bifurcating trees will appear in > or = 95% of the
bootstrap replicates is < 5%, even if the number of bootstrap replicates
is only 50; therefore, the probability of accepting an erroneous tree as
the true tree is < 5% if that tree appears in > or = 95% of the
bootstrap replicates and if more than 50 bootstrap replications are
conducted. However, if a particular bifurcating tree is observed in, say,
< 75% of the bootstrap replicates, then it cannot be claimed to be
better than the trifurcating tree even if > or = 1,000 bootstrap
replications are conducted. When a bifurcating tree is used as the model
tree, the bootstrap approach tends to overestimate P when the sequences are
very short, but it tends to underestimate that probability when the
sequences are long. Moreover, simulation results show that, if a tree is
accepted as the true tree only if it has appeared in > or = 95% of the
bootstrap replicates, then the probability of failing to accept any
bifurcating tree can be as large as 58% even when P = 95%, i.e., even when
95% of the samples from the evolutionary process will support the true
tree. Thus, if the rate-constancy assumption holds, bootstrapping is a
conservative approach for estimating the reliability of an inferred
phylogeny for four taxa.
ORIGINAL ARTICLE
Statistical properties of bootstrap estimation of phylogenetic variability from nucleotide sequences. I. Four taxa with a molecular clock
Center for Demographic and Population Genetics, University of Texas, Houston 77225.
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