Skip to contents

pml computes the likelihood of a phylogenetic tree given a sequence alignment and a model. optim.pml optimizes the different model parameters. For a more user-friendly interface see pml_bb.


as.pml(x, ...)

pml(tree, data, bf = NULL, Q = NULL, inv = 0, k = 1, shape = 1,
  rate = 1, model = NULL, site.rate = "gamma", ASC = FALSE, ...)

optim.pml(object, optNni = FALSE, optBf = FALSE, optQ = FALSE,
  optInv = FALSE, optGamma = FALSE, optEdge = TRUE, optRate = FALSE,
  optRooted = FALSE, control = pml.control(), model = NULL,
  rearrangement = ifelse(optNni, "NNI", "none"), subs = NULL,
  ratchet.par = ratchet.control(), ...)

# S3 method for pml
vcov(object, ...)



So far only an object of class modelTest.


Further arguments passed to or from other methods.


A phylogenetic tree, object of class phylo.


An alignment, object of class phyDat.


Base frequencies (see details).


A vector containing the lower triangular part of the rate matrix.


Proportion of invariable sites.


Number of intervals of the discrete gamma distribution.


Shape parameter of the gamma distribution.




allows to choose an amino acid models or nucleotide model, see details.


Indicates what type of gamma distribution to use. Options are "gamma" approach of Yang 1994 (default), ""gamma_quadrature"" after the Laguerre quadrature approach of Felsenstein 2001 or "freerate".


ascertainment bias correction (ASC), allows to estimate models like Lewis' Mkv.


An object of class pml.


Logical value indicating whether topology gets optimized (NNI).


Logical value indicating whether base frequencies gets optimized.


Logical value indicating whether rate matrix gets optimized.


Logical value indicating whether proportion of variable size gets optimized.


Logical value indicating whether gamma rate parameter gets optimized.


Logical value indicating the edge lengths gets optimized.


Logical value indicating the overall rate gets optimized.


Logical value indicating if the edge lengths of a rooted tree get optimized.


A list of parameters for controlling the fitting process.


type of tree tree rearrangements to perform, one of "none", "NNI", "stochastic" or "ratchet"


A (integer) vector same length as Q to specify the optimization of Q


search parameter for stochastic search


pml or optim.pml return a list of class pml, some are useful for further computations like


the phylogenetic tree.


the alignment.


Log-likelihood of the tree.


Site log-likelihoods.


Weight of the site patterns.


Base frequencies in pml can be supplied in different ways. For amino acid they are usually defined through specifying a model, so the argument bf does not need to be specified. Otherwise if bf=NULL, each state is given equal probability. It can be a numeric vector given the frequencies. Last but not least bf can be string "equal", "empirical" and for codon models additionally "F3x4".

The topology search uses a nearest neighbor interchange (NNI) and the implementation is similar to phyML. The option model in pml is only used for amino acid models. The option model defines the nucleotide model which is getting optimized, all models which are included in modeltest can be chosen. Setting this option (e.g. "K81" or "GTR") overrules options optBf and optQ. Here is a overview how to estimate different phylogenetic models with pml:


Via model in optim.pml the following nucleotide models can be specified: JC, F81, K80, HKY, TrNe, TrN, TPM1, K81, TPM1u, TPM2, TPM2u, TPM3, TPM3u, TIM1e, TIM1, TIM2e, TIM2, TIM3e, TIM3, TVMe, TVM, SYM and GTR. These models are specified as in Posada (2008).

So far 17 amino acid models are supported ("WAG", "JTT", "LG", "Dayhoff", "cpREV", "mtmam", "mtArt", "MtZoa", "mtREV24", "VT","RtREV", "HIVw", "HIVb", "FLU", "Blosum62", "Dayhoff_DCMut" and "JTT_DCMut") and additionally rate matrices and amino acid frequencies can be supplied.

It is also possible to estimate codon models (e.g. YN98), for details see also the chapter in vignette("phangorn-specials").

If the option 'optRooted' is set to TRUE than the edge lengths of rooted tree are optimized. The tree has to be rooted and by now ultrametric! Optimising rooted trees is generally much slower.

If rearrangement is set to stochastic a stochastic search algorithm similar to Nguyen et al. (2015). and for ratchet the likelihood ratchet as in Vos (2003). This should helps often to find better tree topologies, especially for larger trees.


Felsenstein, J. (1981) Evolutionary trees from DNA sequences: a maximum likelihood approach. Journal of Molecular Evolution, 17, 368--376.

Felsenstein, J. (2004). Inferring Phylogenies. Sinauer Associates, Sunderland.

Yang, Z. (2006). Computational Molecular evolution. Oxford University Press, Oxford.

Adachi, J., P. J. Waddell, W. Martin, and M. Hasegawa (2000) Plastid genome phylogeny and a model of amino acid substitution for proteins encoded by chloroplast DNA. Journal of Molecular Evolution, 50, 348--358

Rota-Stabelli, O., Z. Yang, and M. Telford. (2009) MtZoa: a general mitochondrial amino acid substitutions model for animal evolutionary studies. Mol. Phyl. Evol, 52(1), 268--72

Whelan, S. and Goldman, N. (2001) A general empirical model of protein evolution derived from multiple protein families using a maximum-likelihood approach. Molecular Biology and Evolution, 18, 691--699

Le, S.Q. and Gascuel, O. (2008) LG: An Improved, General Amino-Acid Replacement Matrix Molecular Biology and Evolution, 25(7), 1307--1320

Yang, Z., R. Nielsen, and M. Hasegawa (1998) Models of amino acid substitution and applications to Mitochondrial protein evolution. Molecular Biology and Evolution, 15, 1600--1611

Abascal, F., D. Posada, and R. Zardoya (2007) MtArt: A new Model of amino acid replacement for Arthropoda. Molecular Biology and Evolution, 24, 1--5

Kosiol, C, and Goldman, N (2005) Different versions of the Dayhoff rate matrix - Molecular Biology and Evolution, 22, 193--199

L.-T. Nguyen, H.A. Schmidt, A. von Haeseler, and B.Q. Minh (2015) IQ-TREE: A fast and effective stochastic algorithm for estimating maximum likelihood phylogenies. Molecular Biology and Evolution, 32, 268--274.

Vos, R. A. (2003) Accelerated Likelihood Surface Exploration: The Likelihood Ratchet. Systematic Biology, 52(3), 368--373

Yang, Z., and R. Nielsen (1998) Synonymous and nonsynonymous rate variation in nuclear genes of mammals. Journal of Molecular Evolution, 46, 409-418.

Lewis, P.O. (2001) A likelihood approach to estimating phylogeny from discrete morphological character data. Systematic Biology 50, 913--925.


Klaus Schliep


#> NJ> data(Laurasiatherian)
#> NJ> dm <-
#> NJ> tree <- NJ(dm)
#> NJ> plot(tree)

# Jukes-Cantor (starting tree from NJ)
  fitJC <- pml(tree, Laurasiatherian)
# optimize edge length parameter
  fitJC <- optim.pml(fitJC)
#> optimize edge weights:  -54808.83 --> -54230.41 
#> optimize edge weights:  -54230.41 --> -54230.41 
#> optimize edge weights:  -54230.41 --> -54230.41 
#> model: JC 
#> loglikelihood: -54230.41 
#> unconstrained loglikelihood: -17300.92 
#> Rate matrix:
#>   a c g t
#> a 0 1 1 1
#> c 1 0 1 1
#> g 1 1 0 1
#> t 1 1 1 0
#> Base frequencies:  
#>    a    c    g    t 
#> 0.25 0.25 0.25 0.25 

if (FALSE) {
# search for a better tree using NNI rearrangements
  fitJC <- optim.pml(fitJC, optNni=TRUE)

# JC + Gamma + I - model
  fitJC_GI <- update(fitJC, k=4, inv=.2)
# optimize shape parameter + proportion of invariant sites
  fitJC_GI <- optim.pml(fitJC_GI, optGamma=TRUE, optInv=TRUE)
# GTR + Gamma + I - model
  fitGTR <- optim.pml(fitJC_GI, rearrangement = "stochastic",
      optGamma=TRUE, optInv=TRUE, model="GTR")

# 2-state data (RY-coded)
  dat <- acgt2ry(Laurasiatherian)
  fit2ST <- pml(tree, dat)
  fit2ST <- optim.pml(fit2ST,optNni=TRUE)
#> optimize edge weights:  -19749.4 --> -17092.17 
#> optimize edge weights:  -17092.17 --> -17092.17 
#> optimize topology:  -17092.17 --> -17024.81  NNI moves:  10 
#> optimize edge weights:  -17024.81 --> -17024.81 
#> optimize topology:  -17024.81 --> -17024.81  NNI moves:  0 
#> model: Mk 
#> loglikelihood: -17024.81 
#> unconstrained loglikelihood: -8702.769 
#> Rate matrix:
#>   r y
#> r 0 1
#> y 1 0
#> Base frequencies:  
#>   r   y 
#> 0.5 0.5 
# show some of the methods available for class pml
#>  [1] AICc   BIC    anova  glance logLik plot   print  simSeq update vcov  
#> see '?methods' for accessing help and source code