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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

jModelTest • phylogenetic model selection and averaging

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

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

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

5.3 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

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

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

(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

(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

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

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

Figure 7. AIC confidence interval, parameter importances and model-averaged estimates.

jModelTest • phylogenetic model selection and averaging

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

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

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

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

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

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

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

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

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:

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:

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

e−BICi /2

e−BICi /2

j=1

where

B̂i − B̂ j

= (B̂il − B̂jl )

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

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

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:

wi IϕA−C (Mi ) ϕA−Cii=1

where

w+ (ϕA−C ) = wiIϕ A−C (Mi )i=1

and

1 if ϕA−C is in model Mi

0 otherwise

jModelTest • phylogenetic model selection and averaging

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,

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

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

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 36:182

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

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

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.

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