JModelTest 0.1.1 (April 2008) - Bioinformatics And Computational ...

Copy and paste this link to your website, so they can see this document directly without any plugins.



Keywords

model, selection, models, jModelTest, likelihood, phylogenetic, averaging, with, Figure, Model, (Figure, Evolution, Biology, will, that, parameter, Molecular, from, number, equal, this, tests, Bayesian, unequal, different, ratio, which, rate, weights, program

Transcript

INDEX 1
1. DISCLAIMER 3
2. PURPOSE 3
3. CITATION 3
4. HISTORY 3
5. USAGE 4
5.1 OPERATIVE SYSTEMS 4
5.2 STARTING THE PROGRAM 4
5.3 INPUT DATAFILES 5
5.4 LIKELIHOOD SETTINGS 5
5.5 MODEL SELECTION AND AVERAGING 8
5.5.1 AKAIKE INFORMATION CRITERION (AIC) 8
5.5.2 BAYESIAN INFORMATION CRITERION (BIC) 11
5.5.3 DECISION THEORY PERFORMANCE-BASED SELECTION (DT) 11
5.5.4 SEQUENTIAL LIKELIHOOD RATIO TESTS (SLRTS) 12
5.6 MODEL AVERAGED PHYLOGENY 13
6. MISCELLANEOUS OPTIONS 15
6.1 LRT CALCULATOR 15
6.2 RESULTS TABLE 15
7. THE PACKAGE 16
7.1 EXAMPLE FILE 17
8. THEORETICAL BACKGROUND 17
8.1 SEQUENTIAL LIKELIHOOD RATIO TESTS (SLRT) 17
8.1.1 HLRT 17
8.1.2 DLRT 18
8.2 AKAIKE INFORMATION CRITERION 19
8.3 BAYESIAN INFORMATION CRITERION 19
8.4 PERFORMANCE-BASED SELECTION 19
8.5 MODEL UNCERTAINTY 20
jModelTest 0.1.1 (April 2008)
© David Posada 2008 onwards
dposada@uvigo.es
http://darwin.uvigo.es/
See the jModeltest FORUM and FAQs at http://darwin.uvigo.es/
jModelTest • phylogenetic model selection and averaging
2
8.6 MODEL AVERAGING 20
8.6.1 MODEL AVERAGED PHYLOGENY 21
8.7 PARAMETER IMPORTANCE 21
9. ACKNOWLEDGEMENTS 21
10. CREDITS 21
11. REFERENCES 21
jModelTest • phylogenetic model selection and averaging
3
1. Disclaimer
This program is free software; you can redistribute it and/or modify it under the terms of the GNU
General Public License as published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version. This program is distributed in the hope that it will be
useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program; if not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
USA. The jModelTest distribution includes Phyml and Consense (Phylip package) executables.
These programs are protected by their own license and conditions, and using jModelTest implies
agreeing with those conditions as well.
2. Purpose
jModelTest is a tool to carry out statistical selection of best-fit models of nucleotide substitution. It
implements five different model selection strategies: hierarchical and dynamical likelihood ratio
tests (hLRT and dLRT), Akaike and Bayesian information criteria (AIC and BIC), and a decision
theory method (DT). It also provides estimates of model selection uncertainty, parameter
importances and model-averaged parameter estimates, including model-averaged phylogenies. The
theoretical background is described elsewhere (Posada and Buckley 2004b; Sullivan and Joyce
2005).
3. Citation
When using jModelTest you should cite all these:
Posada D. In press. jModelTest: Phylogenetic Model Averaging. Molecular Biology and Evolution.
Guindon S and Gascuel O (2003). A simple, fast and accurate method to estimate large phylogenies
by maximum-likelihood". Systematic Biology 52: 696-704.
And if you use jModelTest to build a model-averaged tree, you should also cite this:
Felsenstein, J. 2005. PHYLIP (Phylogeny Inference Package) version 3.6. Distributed by the author.
Department of Genome Sciences, University of Washington, Seattle (USA).
http://evolution.genetics.washington.edu/phylip.html
4. History
Version 0.0 (March 2005): started the program.
Version 0.1 (February 2008): the first version of jModelTest is released.
Version 0.1.1 (April 2008): minor changes.
jModelTest • phylogenetic model selection and averaging
4
5. Usage
jModelTest is a Java program developed in Xcode under MacOS X 10.5. It provides a GUI where
the user can select the input file (a DNA alignment) and specify the different options for the model
selection analysis. To accomplish most of its tasks, jModelTest builds up a pipeline with several
freely available programs:
 ReadSeq (Gilbert 2007): DNA alignment reading.
 Phyml (Guindon and Gascuel 2003): likelihood calculations. In Mac OS X and Linux the
program uses Phyml beta version 3.0, which is faster but can be unstable.
 Consense (Felsenstein 2005): consensus trees.
 Ted (D. Posada): euclidean distances between trees.
5.1 Operative Systems
Although jModelTest it is optimized for MacOS X, executables are provided to run the program
under Windows XP and Linux. In order to avoid potential problems during execution, the program
folder and folders therein should be located under a path without spaces.
5.2 Starting the program
jModelTest can be started in the OS systems described above if a recent Java environment is
properly installed (see http://www.java.com/). After double-clicking on the jModelTest.jar file, the
program console, with several menus and a text panel, should open (Figure 1) (if this does not work,
open a console prompt, move to the jModelTest folder and type “java –jar jModeltest.1.0.jar”). The
text in this console can be edited (“Edit > …”) and saved to a file, (“Edit > Save console”) or printed
(“Edit > Print console”) at any time.
Figure 1. jModelTest console.
jModelTest • phylogenetic model selection and averaging
5
5.3 Input datafiles
The input file for jModelTest is a DNA sequence alignment in any of the formats allowed by
ReadSeq (Gilbert 2007) (see http://iubio.bio.indiana.edu/soft/molbio/readseq/java/), including fasta,
phylip, nexus, and other standards (note that ReadSeq does not read in long sequence names in
several formats). An input file can be specified by clicking on the menu “File > Load DNA
alignment”.
5.4 Likelihood settings
Likelihood calculations are carried out with Phyml (Guindon and Gascuel 2003). There are 88
models currently implemented in jModelTest, including 11 substitution schemes, equal or unequal
base frecuencies (+F), a proportion of invariable sites (+I) and rate variation among sites with a
number of rate categories (+G) (Table 1). The panel for the likelihood calculations is available from
the menu Analysis > “Compute likelihood scores” (Figure 2). Here it is possible to a large extent to
specify which models will be compared (a minimum of 3, and a maximum of 88). For example, the
user can select a diferent number of substitution schemes, whose exact names will depend on the
+F, +I and +G options.
3 schemes: JC, HKY and GTR.
5 schemes: JC, HKY, TN, TPM1, and GTR.
7 schemes: JC, HKY, TN, TPM1, TIM1, TVM and GTR.
11 schemes: JC, HKY, TN, TPM1, TPM2, TPM3, TIM1, TIM2, TIM3, TVM and GTR.
For each model, there is the option of fixing the topology or to optimize it. In all cases branch
lengths will be estimated and therefore counted as model paramenters. A fixed tree can be
estimated using the BIONJ algorithm (Gascuel 1997) with the JC model, or it can be specified by the
user from a file (in Newick format). Alternativel, potentially different BIONJ or a ML tree can be
estimated for each model, which will require more computation time, specially for the ML
optimization. Note that the LRTs methods will only be available when the likelihoods scores are
calculated upon a fixed topology.
Figure 2. Settings for the likelihood calculations.
jModelTest • phylogenetic model selection and averaging
6
The likelihood computations can take a very variable amount of time depending on the data,
number of candidate models and tree optimization. The console will print out the parameter
estimates and likelihood scores (Figure 3). In addition, a progress bar will show how these
calculations proceed (Figure 4).
Figure 3. Likelihood calculations.
Figure 4. Progress bar for the likelihood calculations.
jModelTest • phylogenetic model selection and averaging
7
Table 1. Substitution models available in jModelTest. Any of these models can include invariable
sites (+I), rate variation among sites (+G), or both (+I+G).
Model Reference
Free
parameters
Base
frequencies Substitution rates
Substitution
code
JC
(Jukes and Cantor
1969) 0 equal AC=AG=AT=CG=CT=GT 000000
F81 (Felsenstein 1981) 3 unequal AC=AG=AT=CG=CT=GT 000000
K80 (Kimura 1980) 1 equal AC=AT=CG=GT; AG=CT 010010
HKY
(Hasegawa, Kishino,
and Yano 1985) 4 unequal AC=AT=CG=GT; AG=CT 010010
TNef (Tamura and Nei 1993) 2 equal AC=AT=CG=GT; AG; CT 010020
TN (Tamura and Nei 1993) 5 unequal AC=AT=CG=GT; AG; CT 010020
TPM1 = K81 (Kimura 1981) 2 equal AC=GT; AT=CG; AG=CT 012210
TPM1uf (Kimura 1981) 5 unequal AC=GT; AT=CG; AG=CT 012210
TPM2 2 equal AC=AT; CG=GT; AG=CT 010212
TPM2uf 5 unequal AC=AT; CG=GT; AG=CT 010212
TPM3 2 equal AC=CG; AT=GT; AG=CT 012012
TPM3uf 5 unequal AC=CG; AT=GT; AG=CT 012012
TIM1ef (Posada 2003) 3 equal AC=GT; AT=CG; AG, CT 012230
TIM1 (Posada 2003) 6 unequal AC=GT; AT=CG; AG, CT 012230
TIM2ef 3 equal AC=AT; CG=GT; AG; CT 010232
TIM2 6 unequal AC=AT; CG=GT; AG; CT 010232
TIM3ef 3 equal AC=CG; AT=GT; AG; CT 012032
TIM3 6 unequal AC=CG; AT=GT; AG; CT 012032
TVMef (Posada 2003) 4 equal AC; AT, CG; GT; AG=CT 012314
TVM (Posada 2003) 7 unequal AC; AT; CG; GT; AG=CT 012314
SYM (Zharkikh 1994) 5 equal AC; AG; AT; CG; CT; GT 012345
GTR = REV (Tavaré 1986) 8 unequal AC; AG; AT; CG; CT; GT 012345
jModelTest • phylogenetic model selection and averaging
8
5.5 Model selection and averaging
Once all likelihood scores are in place, models can be selected according to different criteria from
the menu (“Analysis > …”).
5.5.1 Akaike information criterion (AIC)
Under the AIC framework, the user can select whether to use the AICc (corrected for small samples)
instead of the standard AIC, which is the default (Figure 5). If the AICc is specified, the user needs to
specify the sample size, which by default is the number of sites in the alignment. A confidence
interval (CI) of models including a specified fraction of the models (by default 100%) will also be
built according to the cumulative weight. When model does not fit completely within the CI (the
previous model in the sorted table has a cumulative weight below the CI and this model has a
cumulative weight above the CI and) it will be included in the CI with a probability equal to the
portion of its cumulative weight that is inside the CI. For example, in the table displayed in the
Figure 5, the model F81+G has a probability of (0.9500 – 0.9412) / 0.0220 = 0.4 of being include
within the 95% CI.
Parameter importances are rescaled by the total weight of the models included in the confidence
interval. In order to obtain and model averaged estimates, weights are rescaled by the parameter
importance. If the user wish to do so, a block of PAUP* commands specifying the likelihood settings
of the AIC model can be written to the console.
Figure 5. Options for the AIC selection.
Once the calculations have been carried out, the program reports the model selected, which is the
one with the smallest AIC. Model selection uncertainty is displayed in a table in which models are
sorted in increasing order according to their AIC score. This table also includes the AIC differences
and the relative and cumulative AIC weights (Figure 6). These results are also available at the
"Model > Show model table" menu, in which the selected model is displayed in red. After this, the
confidence interval, parameter importances and model-averaged estimates are displayed (Figure 7).
jModelTest • phylogenetic model selection and averaging
9
Figure 6. Results of the AIC selection. -lnL: negative log likelihood; K: number of estimated
parameters; AIC: Akaike Information Criterion; delta: AIC difference; weight: AIC weight;
cumWeight: cumulative AIC weight.
jModelTest • phylogenetic model selection and averaging
10
Figure 7. AIC confidence interval, parameter importances and model-averaged estimates.
jModelTest • phylogenetic model selection and averaging
11
5.5.2 Bayesian information criterion (BIC)
The options (Figure 8) and results for the BIC selection are analogous to those described above for
the AIC, expect for the lack of a correction for small samples.
Figure 8. Options for the BIC selection.
5.5.3 Decision theory performance-based selection (DT)
The options for the DT selection (Figure 9) are analogous to those described above for the BIC.
However, the calculation of weights here is different. This because DT statistic is of a different
nature, and the standard theory does not apply anymore. Right now, the DT weights are simply the
rescaled reciprocal DT scores ((1/DTi)/sum). The weights reported here are very gross and should be
used with caution. Remember also that parameter importances and model averaged estimates use
these weights.
Figure 9. Options for the DT performance-based selection.
jModelTest • phylogenetic model selection and averaging
12
5.5.4 Sequential likelihood ratio tests (sLRTs)
Sequential likelihood ratio tests for model selection can be implemented under a particular
hierarchy of likelihood ratio tests (sLRTs), in which the user can specify the order of the LRTs and
whether parameters are added (forward selection) or removed (backward selection) (Figure 10).
Alternatively, the order of the LRTs can be set automatically or dynamically (dLRTs) by comparing
the current model with the one that is one hypothesis away and provides the largest increase (under
forward selection) or smallest decrease (under backward selection) in likelihood (Figure 11). The
sLRTs will be available only if the likelihoods scores were calculated upon a fixed topology, due to
the nesting requirement of the chi-square approximation.
Figure 10. Options for the sequential LRTs.
The number and type of hypotheses tested (i.e., of LRTs performed) will depend on the particular
models included in the candidate set. The possible tests are:
 Base frequencies
• freq = unequal base frequencies (option +F, Figure 2).
 Substitution constraints (nss = number of substitution schemes in Figures 2 and 11)
• titv = transition/transversion ratio (nss = 3 , 5, 7, 11).
• 2ti4tv = 2 different transition rates and 4 different transversion rates (nss = 3).
• 2ti = 2 different transition rates (nss = 5, 7, 11).
• 2tv = 2 different transversion rates (AC=GT and AT=CG when nss = 3 and 5; all
options for nss = 11).
• 4tv = 4 different transversion rates (nss = 5, 7, 11).
 Rate variation among sites
• gamma = gamma-distributed rate heterogeneity (option +G, Figure 2).
• pinv = proportion of invariable sites (option +I, Figure 2).
In the case of the TIM and TPM family for nss = 11, the model with highest likelihood (TIM1 or
TIM2 or TIM3; TPM1 or TPM2 or TPM3) will be used in the LRT. The level of significance for each
individual LRT can be specified. By default this is value 0.01. The standard chi-square
approximation is used in all tests, except for those involving gamma distributed rate variation among
sites or a proportion of invariable sites, where a mixed chi-square is used instead. The default
hierarchy for 24 models (nss=3, +F, +I, +G), in which the order of tests is titv-2titv-pinv-gamma is
displayed in Figure 13.
jModelTest • phylogenetic model selection and averaging
13
Figure 11. Possible LRTs for different substitution types according to the number of substitution
schemes specified (Figure 2). The exact names of the models compared will change according to the
+F, +I and +G options and the outcome of their LRTs.
5.6 Model averaged phylogeny
Like any other model parameter, the program can compute a model averaged estimate of the tree
topology (Figure 12). This estimate is obtained by calculating a weighted (using will be AIC, BIC or
DT weights) consensus (majority rule) from all the trees corresponding to the models in the
candidate set (or within a given confidence interval) (Figure 13). This option is only available when
the tree topology has been optimized for every model. A strict consensus can also be computed,
although in this case the weights have no meaning.
jModelTest • phylogenetic model selection and averaging
14
Figure 12. Options for the sequential LRTs.
Figure 13. Console output showing a model-averaged phylogeny for 24 models with the AIC.
jModelTest • phylogenetic model selection and averaging
15
6. Miscellaneous options
6.1 LRT calculator
The program includes a very simple calculator to perform likelihood ratios tests using the standard
or a mixed chi-square approximation (Figure 14). The models tested should be nested (the null
hypothesis is a special case of the alternative hypothesis).
Figure 14. LTR calculator.
6.2 Results table
The likelihood scores (Figure 15) and the results from the different analyses (Figure 16) are stored in
a table that can be displayed at any time from the menu “Results > Show results table”.
Figure 15. Model table showing the likelihood scores and parameter estimates for each value.
jModelTest • phylogenetic model selection and averaging
16
Figure 16. Model table showing the AIC scores and related measures. The AIC model is indicated in
red.
7. The package
The jModelTest package includes several files in different subdirectories. These files should not be
moved around. It is best to put the jModelTest folder in a path without spaces.
jModelTest
+ -------- doc
+ -------- examples
+ -------- exe
+ ---- phyml
+ ---- consense
+ ---- ted
+ jModelTest.x.x.jar
+ -------- license
+ README.html
README.html: quick instructions and comments for users.
/doc/jModelTest.x.x.pdf: Documentation in PDF format
/examples/example.nex: an example data file in NEXUS format
/exe/phyml/*: phyml executables for mac OS X, windows and linux.
/exe/consense/*: consense executables for mac OS X, windows and linux.
/exe/ted/*: ted executables for mac OS X, windows and linux.
/license/gpl.html: GNU general public license in HTML format
jModelTest • phylogenetic model selection and averaging
17
7.1 Example file
The example file (example.nex) included is an alignment of 10 DNA sequences 1000 bp long. This
alignment was simulated on a tree obtained from the coalescent process and under the HKY+I
model, with these parameter values:
Effective population size = 10000
Mutation rate per nucleotide per site = 5e-5
Base frequencies (A, C, G, T) = 0.4, 0.2, 0.1, 0.3
Transition/transversion rate = 4
Alpha parameter of the gamma distribution = 0.4
8. Theoretical background
All phylogenetic methods make assumptions, whether explicit or implicit, about the process of DNA
substitution (Felsenstein 1988). Consequently, all the methods of phylogenetic inference depend on
their underlying substitution models. To have confidence in inferences it is necessary to have
confidence in the models (Goldman 1993b). Because of this, it makes sense to justify the use of a
particular model. Statistical model selection is one way of doing this. For a review of model
selection in phylogenetics see Sullivan and Joyce (2005) and Johnson and Omland (2003). The
strategies includes in jModelTest include sequential likelihood ratio tests (LRTs), Akaike Information
Criterion (AIC), Bayesian Information Criterion (BIC) and performance-based decision theory (DT).
8.1 Sequential Likelihood Ratio Tests (sLRT)
In traditional statistical theory, a widely accepted statistic for testing the goodness of fit of models is
the likelihood ratio test statistic (LRT):

LRT = 2 (l1 − l 0 )
where l1 is the maximum likelihood under the more parameter-rich, complex model (alternative
hypothesis) and l0 is the maximum likelihood under the less parameter-rich simple model (null
hypothesis). When the models compared are nested (the null hypothesis is a special case of the
alternative hypothesis) and the null hypothesis is correct, the LRT statistic is asymptotically
distributed as a χ2 with q degrees of freedom, where q is the difference in number of free parameters
between the two models (Kendall and Stuart 1979; Goldman 1993b). Note that, to preserve the
nesting of the models, the likelihood scores need to be estimated upon the same tree. When some
parameter is fixed at its boundary (p-inv, α), a mixed χ2 is used instead (Ohta 1992; Goldman and
Whelan 2000). The behavior of the χ2 approximation for the LRT has been investigated with quite a
bit of detail (Goldman 1993a; Goldman 1993b; Yang, Goldman, and Friday 1995; Whelan and
Goldman 1999; Goldman and Whelan 2000).
8.1.1 hLRT
Likelihood ratio tests can be carried out sequentially by adding parameters (forward selection) to a
simple model (JC), or by removing parameters (backward selection) from a complex model
(GTR+I+G) in a specific order or hierarchy (hLRT; see Figure 17). The performance of hierarchical
LRTs for phylogenetic model selection has been discussed by Posada and Buckley (2004a) .
jModelTest • phylogenetic model selection and averaging
18
Figure 17. Example of a particular forward hierarchy of likelihood ratio tests for 24 models. At any
level the null hypothesis (model on top) is either accepted (A) or rejected (R). In this example the
model selected is GTR+I.
8.1.2 dLRT
Alternatively, the order in which parameters are added or removed can be selected automatically
(Figure 18). One option to accomplish this is to add the parameter that maximizes a significant gain
in likelihood during forward selection, or to add the parameter that minimizes a non-significant loss
in likelihood during backward selection (Posada and Crandall 2001a). In this case, the order of the
tests is not specified a priori, but it will depend on the particular data.
Figure 18. Dynamical likelihood ratio tests for 24 models. At any level a hypothesis is either
accepted (A) or rejected (R). In this example the model selected is GTR+I. Hypotheses tested are: F =
base frequencies; S = substitution type; I = proportion of invariable sites; G = gamma rates.
jModelTest • phylogenetic model selection and averaging
19
8.2 Akaike Information Criterion
The Akaike information criterion (AIC, (Akaike 1974) is an asymptotically unbiased estimator of the
Kullback-Leibler information quantity (Kullback and Leibler 1951). We can think of the AIC as the
amount of information lost when we use a specific model to approximate the real process of
molecular evolution. Therefore, the model with the smallest AIC is preferred. The AIC is computed
as:

AIC = −2l + 2K ,
where l is the maximum log-likelihood value of the data under this model and Ki is the number of
free parameters in the model, including branch lengths if they were estimated de novo. When
sample size (n) is small compared to the number of parameters (say, n/K < 40) the use of a secondorder AIC, AICc (Sugiura 1978; Hurvich and Tsai 1989), is recommended:

AICc = AIC +
2K(K +1)
n − K −1
,
The AIC compares several candidate models simultaneously, it can be used to compare both nested
and non-nested models, and model-selection uncertainty can be easily quantified using the AIC
differences and Akaike weights (see Model uncertainty below). Burnham and Anderson (2003)
provide an excellent introduction to the AIC and model selection in general.
8.3 Bayesian Information Criterion
An alternative to the use of the AIC is the Bayesian Information Criterion (BIC) (Schwarz 1978):

BIC = −2l+K logn
Given equal priors for all competing models, choosing the model with the smallest BIC is equivalent
to selecting the model with the maximum posterior probability. Alternatively, Bayes factors for
models of molecular evolution can be calculated using reversible jump MCMC (Huelsenbeck,
Larget, and Alfaro 2004). We can easily use the BIC instead of the AIC to calculate BIC differences
or BIC weights.
8.4 Performance-based selection
Minin et al. (2003) developed a novel approach that selects models on the basis of their
phylogenetic performance, measured as the expected error on branch lengths estimates weighted by
their BIC. Under this decision theoretic framework (DT) the best model is the one with that
minimizes the risk function:
Ci ≈ B̂i − B̂ j
j=1
R
∑  
e−BICi /2
e−BICi /2
j=1
R

,
where
B̂i − B̂ j
2
= (B̂il − B̂jl )
2
l=1
2t−3

and where t is the number of taxa. Indeed, simulations suggested that models selected with this
criterion result in slightly more accurate branch length estimates than those obtained under models
selected by the hLRTs (Minin et al. 2003; Abdo et al. 2005).
jModelTest • phylogenetic model selection and averaging
20
8.5 Model Uncertainty
The AIC, Bayesian and DT methods can rank the models, allowing us to assess how confident we
are in the model selected. For these measures we could present their differences (Δ). For example,
for the ith model, the AIC (BIC, DT) difference is:
Δi = AICi −min(AIC) ,
where min AIC is the smallest AIC value among all candidate models. The AIC differences are easy
to interpret and allow a quick comparison and ranking of candidate models. As a rough rule of
thumb, models having Δi within 1-2 of the best model have substantial support and should receive
consideration. Models having Δi within 3-7 of the best model have considerably less support, while
models with Δi > 10 have essentially no support. Very conveniently, we can use these differences to
obtain the relative AIC (BIC) weight (wi) of each model:

wi =
exp(−1/2Δ i )
exp(−1/2Δr )r=1
R

which can be interpreted, from a Bayesian perspective, as the probability that a model is the best
approximation to the truth given the data. The weights for every model add to 1, so we can establish
an approximate 95% confidence set of models for the best models by summing the weights from
largest to smallest from largest to smallest until the sum is 0.95 (Burnham and Anderson 1998, pp.
169-171; Burnham and Anderson 2003). This interval can also be set up stochastically (see above
“Model selection and averaging”). Note that this equation will not work for the DT (see the DT
explanation on “Model selection and averaging”).
8.6 Model Averaging
Often there is some uncertainty in selecting the best candidate model. In such cases, or just one
when does not want to rely on a single model, inferences can be drawn from all models (or an
optimal subset) simultaneously. This is known as model averaging or multimodel inference. See
Posada and Buckley (2004a) and references therein for an explanation of application of these
techniques in the context of phylogenetics.
Within the AIC or Bayesian frameworks, it is straightforward to obtain a model-averaged estimate of
any parameter (Madigan and Raftery 1994; Raftery 1996; Hoeting, Madigan, and Raftery 1999;
Wasserman 2000; Burnham and Anderson 2003; Posada 2003). For example, a model-averaged
estimate of the substitution rate between adenine and cytosine (ϕA-C) using the Akaike weights (wi)
for R candidate models would be:
ϕ̂A−C =
wi  IϕA−C (Mi )  ϕA−Cii=1
R

w+ (ϕA−C ) ,
where

w+ (ϕA−C ) = wiIϕ A−C (Mi )i=1
R
∑ ,
and

Iϕ A−C (Mi ) =
1 if ϕA−C is in model Mi
0 otherwise


 ,
jModelTest • phylogenetic model selection and averaging
21
Note that need to be careful when interpreting the relative importance of parameters. When the
number of candidate models is less than the number of possible combinations of parameters, the
presence-absence of some pairs of parameters can be correlated, and so their relative importances.
8.6.1 Model averaged phylogeny
Indeed, the averaged parameter could be the topology itself, so we could construct a model–
averaged estimate of phylogeny. For example, one could estimate a ML tree for all models (or a best
subset) and with those one could build a weighted consensus tree using the corresponding Akaike
weights. See Posada and Buckley (2004a) for a practical example.
8.7 Parameter importance
It is possible to estimate the relative importance of any parameter by summing the weights across
all models that include the parameters we are interested in. For example, the relative importance of
the substitution rate between adenine and cytosine across all candidate models is simply the
denominator above,

w+ (ϕA−C ).
9. Acknowledgements
Thanks to Stephane Guindon for his generous help with Phyml, and to John Huelsenbeck for
suggesting the stochastic calculation of confidence intervals.
10. Credits
 Phyml by Guindon and Gascuel
 ReadSeq by Don Gilbert (http://iubio.bio.indiana.edu/soft/molbio/readseq/java/).
 Consense by Joe Felnsenstein
 Table utilities by Philip Milne.;
 BrowserLauncher by Eric Albert.
11. References
Abdo, Z., V. N. Minin, P. Joyce, and J. Sullivan. 2005. Accounting for uncertainty in the tree topology has little
effect on the decision-theoretic approach to model selection in phylogeny estimation. Molecular
Biology and Evolution 22:691-703.
Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control
19:716-723.
Alfaro, M. E., and J. P. Huelsenbeck. 2006. Comparative performance of Bayesian and AIC-based measures of
phylogenetic model uncertainty. Systematic Biology 55:89-96.
Burnham, K. P., and D. R. Anderson. 2003. Model selection and multimodel inference: a practical informationtheoretic approach. Springer-Verlag, New York, NY.
Burnham, K. P., and D. R. Anderson. 1998. Model selection and inference: a practical information-theoretic
approach. Springer-Verlag, New York, NY.
Felsenstein, J. 1988. Phylogenies from molecular sequences: inference and reliability. Annual Review of
Genetics 22:521-565.
Felsenstein, J. 1981. Evolutionary trees from DNA sequences: A maximum likelihood approach. Journal of
Molecular Evolution 17:368-376.
Felsenstein, J. 2005. PHYLIP (Phylogeny Inference Package). Department of Genome Sciences, University of
Washington, Seattle.
jModelTest • phylogenetic model selection and averaging
22
Gascuel, O. 1997. BIONJ: an improved version of the NJ algorithm based on a simple model of sequence data.
Molecular Biology and Evolution 14:685-695.
Gilbert, D. 2007. ReadSeq. Indiana University, Bloomington.
Goldman, N. 1993a. Simple diagnostic statistical test of models of DNA substitution. Journal of Molecular
Evolution 37:650-661.
Goldman, N. 1993b. Statistical tests of models of DNA substitution. Journal of Molecular Evolution 36:182198.
Goldman, N., and S. Whelan. 2000. Statistical tests of gamma-distributed rate heterogeneity in models of
sequence evolution in phylogenetics. Molecular Biology and Evolution 17:975-978.
Guindon, S., and O. Gascuel. 2003. A simple, fast, and accurate algorithm to estimate large phylogenies by
maximum likelihood. Systematic Biology 52:696-704.
Hasegawa, M., K. Kishino, and T. Yano. 1985. Dating the human-ape splitting by a molecular clock of
mitochondrial DNA. Journal of Molecular Evolution 22:160-174.
Hoeting, J. A., D. Madigan, and A. E. Raftery. 1999. Bayesian model averaging: A tutorial. Statistical Science
14:382-417.
Huelsenbeck, J. P., B. Larget, and M. E. Alfaro. 2004. Bayesian Phylogenetic Model Selection Using Reversible
Jump Markov Chain Monte Carlo. Molecular Biology and Evolution 21:1123-1133.
Hurvich, C. M., and C.-L. Tsai. 1989. Regression and time series model selection in small samples. Biometrika
76:297-307.
Johnson, J. B., and K. S. Omland. 2003. Model selection in ecology and evolution. Trends in Ecology &
Evolution 19:101-108.
Jukes, T. H., and C. R. Cantor. 1969. Evolution of protein molecules. Pp. 21-132 in H. M. Munro, ed.
Mammalian Protein Metabolism. Academic Press, New York, NY.
Kendall, M., and A. Stuart. 1979. The Advanced Theory of Statistics. Charles Griffin, London.
Kimura, M. 1981. Estimation of evolutionary distances between homologous nucleotide sequences.
Proceedings of the National Academy of Sciences, U.S.A. 78:454-458.
Kimura, M. 1980. A simple method for estimating evolutionary rate of base substitutions through comparative
studies of nucleotide sequences. Journal of Molecular Evolution 16:111-120.
Kullback, S., and R. A. Leibler. 1951. On information and sufficiency. Annals of Mathematical Statistics 22:7986.
Madigan, D. M., and A. E. Raftery. 1994. Model selection and accounting for model uncertainty in graphical
models using Occam's Window. Journal of the American Statistical Association 89:1335-1346.
Minin, V., Z. Abdo, P. Joyce, and J. Sullivan. 2003. Performance-based selection of likelihood models for
phylogeny estimation. Systematic Biology 52:674-683.
Ohta, T. 1992. Theoretical study of near neutrality. II. Effect of subdivided population structure with local
extinction and recolonization. Genetics:917-923.
Pol, D. 2004. Empirical problems of the hierarchical likelihood ratio test for model selection. Systematic
Biology 53:949-962.
Posada, D. 2001. The effect of branch length variation on the selection of models of molecular evolution.
Journal of Molecular Evolution 52:434-444.
Posada, D. 2003. Using Modeltest and PAUP* to select a model of nucleotide substitution. Pp. 6.5.1-6.5.14 in
A. D. Baxevanis, D. B. Davison, R. D. M. Page, G. A. Petsko, L. D. Stein, and G. D. Stormo, eds.
Current Protocols in Bioinformatics. John Wiley & Sons, Inc.
Posada, D., and T. R. Buckley. 2004a. Model selection and model averaging in phylogenetics: advantages of
the AIC and Bayesian approaches over likelihood ratio tests. Systematic Biology 53:793-808.
Posada, D., and T. R. Buckley. 2004b. Model selection and model averaging in phylogenetics: advantages of
Akaike Information Criterion and Bayesian approaches over likelihood ratio tests. Systematic Biology
53:793-808.
Posada, D., and K. A. Crandall. 2001a. Selecting the best-fit model of nucleotide substitution. Systematic
Biology 50:580-601.
Posada, D., and K. A. Crandall. 2001b. Selecting models of nucleotide substitution: an application to human
immunodeficiency virus 1 (HIV-1). Molecular Biology and Evolution 18:897-906.
Raftery, A. E. 1996. Hypothesis testing and model selection. Pp. 163-187 in W. R. Gilks, S. Richardson, and D.
J. Spiegelhalter, eds. Markov chain Monte Carlo in practice. Chapman & Hall, London ; New York.
Schwarz, G. 1978. Estimating the dimension of a model. The Annals of Statistics 6:461-464.
Sugiura, N. 1978. Further analysis of the data by Akaike's information criterion and the finite corrections.
Communications in Statistics–Theory and Methods A7:13-26.
Sullivan, J., and P. Joyce. 2005. Model selection in phylogenetics. Annual Review of Ecology, Evolution and
Systematics 36:445-466.
jModelTest • phylogenetic model selection and averaging
23
Tamura, K., and M. Nei. 1993. Estimation of the number of nucleotide substitutions in the control region of
mitochondrial DNA in humans and chimpanzees. Molecular Biology and Evolution 10:512-526.
Tavaré, S. 1986. Some probabilistic and statistical problems in the analysis of DNA sequences. Pp. 57-86 in R.
M. Miura, ed. Some mathematical questions in biology - DNA sequence analysis. Amer. Math. Soc.,
Providence, RI.
Wasserman, L. 2000. Bayesian Model Selection and Model Averaging. Journal of Mathematical Psychology
44:92-107.
Whelan, S., and N. Goldman. 1999. Distributions of statistics used for the comparison of models of sequence
evolution in phylogenetics. Molecular Biology and Evolution 16:1292-1299.
Yang, Z., N. Goldman, and A. Friday. 1995. Maximum likelihood trees from DNA sequences: a peculiar
statistical estimation problem. Systematic Biology 44:384-399.
Zharkikh, A. 1994. Estimation of evolutionary distances between nucleotide sequences. Journal of Molecular
Evolution 39:315-329.

PDF Document reader online

This website is focused on providing document in readable format, online without need to install any type of software on your computer. If you are using thin client, or are not allowed to install document reader of particular type, this application may come in hand for you. Simply upload your document, and Docureader.top will transform it into readable format in a few seconds. Why choose Docureader.top?

  1. Unlimited sharing - you can upload document of any size. If we are able to convert it into readable format, you have it here - saved for later or immediate reading
  2. Cross-platform - no compromised when reading your document. We support most of modern browers without the need of installing any of external plugins. If your device can oper a browser - then you can read any document on it
  3. Simple uploading - no need to register. Just enter your email, title of document and select the file, we do the rest. Once the document is ready for you, you will receive automatic email from us.

Previous 10

Next 10