Phylogenetic analysis of six mammal species for 15 trees and 105 trees.
data(mam15)mam15.mt is a matrix of size 3414 * 15. The (i,j) element is the site-wise log-likelihood value at site-i for tree-j for i=1,...,3414, and j=1,...,15. They are constrained trees with clade (cow, seal) being fixed.
mam15.ass is a list of length 25 for association vectors. The components are t1, t2, ..., t15 for trees, and e1, e2, ..., e10 for edges.
mam15.relltest is an object of class "relltest" of length 25.
mam15.aux is a list of tree topologies (tpl), clade patterns (cld), taxa names(tax).
mam105.mt, mam105.ass, mam105.relltst, mam105.aux are those for 105 unconstrained trees.
mam26.mt, mam26.ass, mam26.aux are those for 26 trees including the 15 constrained trees, 10 partially resolved trees corresponding to the 10 internal edges, and the star topology.
An example of phylogenetic analysis of six mammal species:
Homo sapiens (human), Phoca vitulina (harbor seal), Bos taurus (cow),
Oryctolagus cuniculus (rabbit), Mus musculus (mouse), Didelphis
virginiana (opossum). The data is stored in the file mam15.aa,
which contains amino acid sequences of length N=3414 for the six
species obtained from mtDNA (see Note below).
Here we fix (Phovi,Bosta) as a group of taxa.
With this constraint, we consider 15 tree topologies of the six mammals as stored in the
file mam15.tpl;
((Homsa,(Phovi,Bosta)),Orycu,(Musmu,Didvi)); t1 (Homsa,Orycu,((Phovi,Bosta),(Musmu,Didvi))); t2 (Homsa,((Phovi,Bosta),Orycu),(Musmu,Didvi)); t3 (Homsa,(Orycu,Musmu),((Phovi,Bosta),Didvi)); t4 ((Homsa,(Phovi,Bosta)),(Orycu,Musmu),Didvi); t5 (Homsa,((Phovi,Bosta),(Orycu,Musmu)),Didvi); t6 (Homsa,(((Phovi,Bosta),Orycu),Musmu),Didvi); t7 (((Homsa,(Phovi,Bosta)),Musmu),Orycu,Didvi); t8 (((Homsa,Musmu),(Phovi,Bosta)),Orycu,Didvi); t9 (Homsa,Orycu,(((Phovi,Bosta),Musmu),Didvi)); t10 (Homsa,(((Phovi,Bosta),Musmu),Orycu),Didvi); t11 ((Homsa,((Phovi,Bosta),Musmu)),Orycu,Didvi); t12 (Homsa,Orycu,(((Phovi,Bosta),Didvi),Musmu)); t13 ((Homsa,Musmu),Orycu,((Phovi,Bosta),Didvi)); t14 ((Homsa,Musmu),((Phovi,Bosta),Orycu),Didvi); t15
The log-likelihood values are calculated using the PAML software (Ziheng 1997)
for phylogenetic inference. The two files mam15.aa and
mam15.tpl are fed into PAML to generate the file
mam15.lnf of site-wise log-likelihood values.
Using the CONSEL software (Shimodaira and Hasegawa 2001), we convert
mam15.lnf and mam15.tpl to a format suitable for the scaleboot
package. We do not use CONSEL for calculating AU p-values, but
use it only for file conversion. We type
seqmt --paml mam15.lnf treeass --outgroup 6 mam15.tpl > mam15.log
The first line above generates mam15.mt, which is a simple text
file containing a matrix of site-wise log-likelihood values. The
second line above generates mam15.ass and mam15.log, which
contain information regarding which edges are included in a tree. A
part of mam15.log is as follows.
# leaves: 6 6 1 Homsa 2 Phovi 3 Bosta 4 Orycu 5 Musmu 6 Didvi# base edges: 10 10 6
123456 1 +++--- ; 2 ++++-- ; 3 +--+-- ; 4 -+++-- ; 5 ---++- ; 6 +--++- ; 7 -++++- ; 8 +++-+- ; 9 +---+- ; 10 -++-+- ;
The above defines edges named e1,...e10 (base edges) as clusters for six mammal species. For example, e1 = +++--- = (Homsa, Phovi, Bosta).
The converted files are read by the scaleboot package in R:
mam15.mt <- read.mt("mam15.mt")
mam15.ass <- read.ass("mam15.ass")
mam15.mt is a matrix of size 3414 * 6 for the site-wise
log-likelihood values. For testing trees, we need only mam15.mt.
mam15.ass is used for testing edges, and it is
a list of length 25 for association vectors for t1,t2,...,t15, and
e1,e2,...,e10. For example, mam15.ass$t1 = 1, indicating tree
"t1" is included in tree "t1", and mam15.ass$e1 = c(1, 5, 8),
indicating edge "e1" is included in trees "t1", "t5", and "t8".
Multiscale bootstrap resampling is performed by the function
relltest. The simplest way to get AU p-values for trees is:
mam15.trees <- relltest(mam15.mt) # resampling and fitting summary(mam15.trees) # calculates AU p-values
The relltest returns an object of class "relltest".
It calls the function scaleboot internally with
the number of bootstrap replicates nb=10000, and takes about 20
mins. Typically, nb=10000 is large enough, but it would be safe
to use larger value, say nb=100000 as in the examples below.
Note that the default value of scales in relltest has
a much wider range than that of CONSEL. It is
sa=9^seq(-1,1,length=13) for relltest, and
is sa=1/seq(from=0.5,to=1.4,by=0.1) for CONSEL.
The mam15.relltest object in data(mam15) is similar
to mam15.trees above, but is also calculated for
edges using mam15.ass. We can extract the result for trees by
mam15.trees <- mam15.relltest[1:15]
The results for trees stored in the mam15.trees object above are in
the order specified in the columns of mam15.mt. To sort it by
increasing order of the log-likelihood difference, we can type
stat <- attr(mam15.trees,"stat") # the log-likelihood differences o <- order(stat) # sort it in increasing order mam15.trees <- mam15.trees[o] # same as mam15.trees in Examples
Results of the fitting are shown by using the print method.
> mam15.treesTest Statistic, and Shimodaira-Hasegawa test: stat shtest t1 -2.66 94.51 (0.07) t3 2.66 80.25 (0.13) t2 7.40 57.85 (0.16) t5 17.57 17.30 (0.12) t6 18.93 14.32 (0.11) t7 20.11 11.49 (0.10) t4 20.60 10.98 (0.10) t15 22.22 7.34 (0.08) t8 25.38 3.31 (0.06) t14 26.32 3.29 (0.06) t13 28.86 1.71 (0.04) t9 31.64 0.61 (0.02) t11 31.75 0.57 (0.02) t10 34.74 0.20 (0.01) t12 36.25 0.12 (0.01)
Multiscale Bootstrap Probabilities (percent): 1 2 3 4 5 6 7 8 9 10 11 12 13 t1 86 81 77 73 68 63 58 52 46 41 36 31 28 t3 14 19 23 27 30 32 32 31 30 27 25 22 20 t2 0 0 0 0 1 2 4 5 7 9 10 11 11 t5 0 0 0 0 0 1 1 2 3 5 6 6 7 t6 0 0 0 0 1 2 3 5 6 7 8 9 9 t7 0 0 0 0 0 0 0 1 2 3 4 5 5 t4 0 0 0 0 0 1 2 3 4 4 5 6 6 t15 0 0 0 0 0 0 0 0 1 1 2 2 3 t8 0 0 0 0 0 0 0 0 0 0 1 1 1 t14 0 0 0 0 0 0 0 1 1 2 3 4 4 t13 0 0 0 0 0 0 0 0 0 0 1 1 2 t9 0 0 0 0 0 0 0 0 0 0 0 1 1 t11 0 0 0 0 0 0 0 0 0 0 0 1 1 t10 0 0 0 0 0 0 0 0 0 0 0 0 0 t12 0 0 0 0 0 0 0 0 0 0 0 0 0
Numbers of Bootstrap Replicates: 1 2 3 4 5 6 7 8 9 10 11 12 13 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05
Scales (Sigma Squared): 1 2 3 4 5 6 7 8 9 10 11 12 13 0.1111 0.1603 0.2311 0.3333 0.4808 0.6933 1 1.442 2.080 3 4.327 6.241 9.008
AIC values of Model Fitting: poly.1 poly.2 poly.3 sing.3 t1 89483.40 964.33 964.75 966.33 t3 75434.97 1750.22 1306.50 1752.22 t2 29361.29 403.41 36.33 -6.21 t5 23893.19 260.44 -0.22 -14.11 t6 35791.26 330.50 4.31 -2.49 t7 15221.10 93.59 -10.33 -12.04 t4 29790.60 453.95 5.22 -7.57 t15 6874.98 46.16 -10.48 -17.08 t8 1747.13 -6.88 -12.39 -13.68 t14 10905.94 131.48 2.65 -10.79 t13 3411.26 27.66 -8.30 -15.14 t9 1494.58 19.46 -13.78 -15.86 t11 914.42 -19.65 -19.71 -19.61 t10 259.68 -14.79 -17.27 -16.76 t12 178.79 -19.19 -19.61 -19.30
The AU p-values are shown by the summary method.
> summary(mam15.trees)Corrected P-values (percent): raw k.1 k.2 k.3 model aic t1 57.58 (0.16) 56.16 (0.04) 74.55 (0.05) 74.55 (0.05) poly.2 964.33 t3 31.86 (0.15) 30.26 (0.05) 46.41 (0.09) 45.33 (0.13) poly.3 1306.50 t2 3.68 (0.06) 3.68 (0.03) 12.97 (0.20) 16.12 (0.45) sing.3 -6.21 t5 1.34 (0.04) 1.33 (0.02) 7.92 (0.25) 10.56 (0.56) sing.3 -14.11 t6 3.18 (0.06) 3.15 (0.02) 13.15 (0.21) 15.86 (0.44) sing.3 -2.49 t7 0.49 (0.02) 0.52 (0.01) 3.66 (0.21) 4.75 (0.42) sing.3 -12.04 t4 1.55 (0.04) 1.53 (0.02) 10.54 (0.27) 14.84 (0.66) sing.3 -7.57 t15 0.08 (0.01) 0.07 (0.00) 1.11 (0.19) 1.85 (0.48) sing.3 -17.08 t8 0.00 (0.00) 0.00 (0.00) 0.04 (0.03) 0.07 (0.07) sing.3 -13.68 t14 0.22 (0.01) 0.23 (0.01) 2.76 (0.26) 4.59 (0.71) sing.3 -10.79 t13 0.02 (0.00) 0.01 (0.00) 0.50 (0.20) 1.30 (0.83) sing.3 -15.14 t9 0.00 (0.00) 0.00 (0.00) 0.23 (0.05) 1.41 (0.29) sing.3 -15.86 t11 0.00 (0.00) 0.00 (0.00) 0.00 (0.00) 0.00 (0.00) poly.3 -19.71 t10 0.00 (0.00) 0.00 (0.00) 0.00 (0.00) 0.00 (0.00) poly.3 -17.27 t12 0.00 (0.00) 0.00 (0.00) 0.00 (0.00) 0.00 (0.00) poly.3 -19.61
The p-values for 15 trees are shown above. "raw" is the ordinary bootstrap probability, "k.1" is equivalent to "raw" but calculated from the multiscale bootstrap, "k.2" is equivalent to the third-order AU p-value of CONSEL, and finally "k.3" is an improved version of AU p-value.
The details for each tree are shown by extracting the corresponding element. For example, details for the seventh largest tree in the log-likelihood value ("t4") is obtained by
> mam15.trees[[7]] # same as mam15.trees$t4Multiscale Bootstrap Probabilities (percent): 1 2 3 4 5 6 7 8 9 10 11 12 13 0.00 0.00 0.01 0.08 0.27 0.80 1.55 2.55 3.58 4.42 5.22 6.00 6.38
Numbers of Bootstrap Replicates: 1 2 3 4 5 6 7 8 9 10 11 12 13 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05 1e+05
Scales (Sigma Squared): 1 2 3 4 5 6 7 8 9 10 11 12 13 0.1111 0.1603 0.2311 0.3333 0.4808 0.6933 1 1.442 2.080 3 4.327 6.241 9.008
Coefficients: beta0 beta1 beta2 poly.1 2.8388 (0.0048) poly.2 1.8556 (0.0061) 0.3259 (0.0019) poly.3 1.7157 (0.0085) 0.4508 (0.0061) -0.0152 (0.0007) sing.3 1.6178 (0.0153) 0.5435 (0.0143) 0.3261 (0.0201)
Model Fitting: rss df pfit aic poly.1 29814.60 12 0.0000 29790.60 poly.2 475.95 11 0.0000 453.95 poly.3 25.22 10 0.0050 5.22 sing.3 12.43 10 0.2571 -7.57
Best Model: sing.3 > summary(mam15.trees[[7]])
Raw Bootstrap Probability: 1.55 (0.04)
Corrected P-values (percent): k.1 k.2 k.3 aic poly.1 0.23 (0.00) 0.23 (0.00) 0.23 (0.00) 29790.60 poly.2 1.46 (0.02) 6.30 (0.09) 6.30 (0.09) 453.95 poly.3 1.57 (0.02) 9.50 (0.21) 10.57 (0.27) 5.22 sing.3 1.53 (0.02) 10.54 (0.27) 14.84 (0.66) -7.57
Best Model: sing.3
> plot(mam15.trees[[7]],legend="topleft")
The plot diagnostics found in the bottom line are especially useful for confirming which model is fitting best.
See other examples below.
Yang, Z. (1997). PAML: a program package for phylogenetic analysis by maximum likelihood, Computer Applications in BioSciences, 13:555-556 (software is available from http://abacus.gene.ucl.ac.uk/software/paml.html).
Shimodaira, H. and Hasegawa, M. (2001). CONSEL: for assessing the confidence of phylogenetic tree selection, Bioinformatics, 17, 1246-1247 (software is available from http://stat.sys.i.kyoto-u.ac.jp/prog/consel/).
# NOT RUN {
data(mam15)
## show the results for trees and edges
mam15.relltest # print stat, shtest, bootstrap probabilities, and AIC
summary(mam15.relltest) # print AU p-values
# }
# NOT RUN {
## simpler script to create mam15.trees
mam15.mt <- read.mt("mam15.mt")
mam15.ass <- read.ass("mam15.ass")
mam15.trees <- relltest(mam15.mt,nb=100000)
# }
# NOT RUN {
# }
# NOT RUN {
## script to create mam15.relltest
mam15.mt <- read.mt("mam15.mt")
mam15.ass <- read.ass("mam15.ass")
mam15.relltest <- relltest(mam15.mt,nb=100000,ass=mam15.ass)
# }
# NOT RUN {
# }
# NOT RUN {
## Parallel version of the above script (but different in random seed)
## It took 13 mins (40 cpu's of Athlon MP 2000+)
mam15.mt <- read.mt("mam15.mt")
mam15.ass <- read.ass("mam15.ass")
library(parallel)
cl <- makeCluster(40)
mam15.relltest <- relltest(mam15.mt,nb=100000,ass=mam15.ass,cluster=cl)
# }
# NOT RUN {
# }
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