#Overview Empar is an implementation of the EM algorithm for effective parameter estimation of the (discrete-time) Markov evolutionary models.

Current version uses Boost 1_61_0 (see the license). http://www.boost.org/doc/libs/1_61_0/more/getting_started/unix-variants.html#get-boost

make

./main <tree file> <fasta file> <model>,

where

• tree file —- Newick tree (not necessarily bifurcated)
• fasta file —- input alignment in a fasta format
• model —- phylogenetic model: jc, k80, k81, ssm,

e.g.

./main data/test.tree data/data.fa ssm,

The nodes in the tree are labeled starting with the leaves as listed in the Newick input tree, followed by the internal nodes starting from the root and going top down from left to right. For example, given a tree:

((human:0.01,ape:0.2,hamster:0.3):0.5,bird:0.4,amoeba:0.8)

the leaves take the labels 0-4: human, ape, hamster, burred, amoeba. There are two internal nodes: the 'right' one is labeled as the root (6), the 'left' one with three leaves is labeled as (5). Subsequently, the edges are listed top-down, starting from the root, from left to right: (5, 6) 0.5; (5, 3) 0.4; (5, 4) 0.8; (6, 0) 0.01; (6, 1) 0.2; (6, 2) 0.3.

This is also the order in which the estimated matrices are listed in the output file.

WARNING is generated when a node of valency 2 is present. This is due to the fact that the parameters associated with the outgoing edges are non-identifiable. Neither are the branches stemming from such edges. In fact, one can identify only the product of such matrices and the sum of the branches.

The estimated parameters are saved in the files with the same basename as the fasta file and ".dat/.cov“ suffix

1. name_of_the_fasta_file.dat, which contains the list of all the estimated matrices in the order of the branches (and the root if in the case of the SSM)

2. name_of_the_fasta_file.cov, which is the variance-covariance matrix for the free parameters (#num_edges * #free_param)X(#num_edges*#free_param). Parameter variance is calculated from the observed Fisher information. The order follows the order of the edges and lists the free off-diagonal parameters of the model, e.g. JC69 lists only 1 parameter of moving to another state per matrix.

Model: Strand Symmetric
Tree:
nodes:   7
nleaves: 5
nedges:  6
Edges:
  (5, 6)  0.5
  (5, 3)  0.4
  (5, 4)  0.8
  (6, 0)  0.01
  (6, 1)  0.2
  (6, 2)  0.3
Node names: human ape hamster bird amoeba

Reading fasta file:
Mulitple sequence alignment of length 10000bp on 5 taxa.

Reading species 1 >human

Reading species 2 >ape

Reading species 3 >hamster

Reading species 4 >bird

Reading species 5 >amoeba

Elapsed time: 17.70391 s

Likelihood: -52403.9605116558

Branch lengths:
0.521413645823845  0.383754440749502  0.781680154271902  0.0104890363458518 …
 0.200244346606503  0.304842430545834  

Newick Tree:
((human:0.0104890363458518,ape:0.200244346606503,hamster:0.304842430545834):0.521413645823845,…
bird:0.383754440749502,amoeba:0.781680154271902)

If is replaced by :test, it uses transition parameters simulated internally for which it calculates theoretical values of the joint distribution, p. The counts are taken to be pN, where N is the length of the alignment. This option was created for the purpose of testing.

./main test2.tree :test k81

If one of the output branch lengths is given as nan it is due to a negative determinant of a transition matrix. This may happen for a number of reasons: the estimated matrix has a small determinant (e.g. short data) and for numerical reasons, at times it takes a negative value. Secondly, the parameters may not be identifiable (non-identifiable up to the permutation of rows in all but JC69, for which this problem does not occur): e.g. matrices whose diagonal entries are smaller or comparable to the off-diagonal ones. The algorithm attempts to recover many of this cases, however, it may happen that not all cases can be dealt with (see the reference paper for more details on the method).

Kedzierska A.M. and Casanellas M.: “ EM for parameter estimation of Markov models on trees ” (revision).

For generating data under non-homogeneous models:

Kedzierska A.M. and Casanellas M.: “ GenNon-h: Simulating multiple sequence alignments under the non-homogeneous DNA models”, BMC Bioinformatics 2012, 13:216.