This is the companion software for the paper A Balance Index for Phylogenetic Trees based on Quartets by Tomàs M. Coronado, Arnau Mir, Francesc Rosselló, and Gabriel Valiente.
You need to install the ETE Toolkit, a Python library to work with phylogenetic trees. See http://etetoolkit.org/ for more details.
sudo apt install python-numpy python-qt4 python-lxml python-six
pip install ete3
You also need to install SymPy, a Python library for symbolic mathematics. See http://www.sympy.org/ for more details.
pip install sympy
The Quartet Index companion software consists of a series of Python 2 scripts.
python qi_1_probabilities_shapes.py
This script will generate files P2.txt through P8.txt. These files have one line for each tree shape of the size in the file name, 2 through 8, with the tree shape and the symbolic formula (as a function of α and γ) for the variance of that tree shape under the α-γ model. For instance, there are 5 tree shapes with 4 leaves, and file P4.txt contains the following 5 lines:
((*,*),(*,*)); (a - 1)*(2*a - g - 2)/((a - 3)*(a - 2))
(*,(*,(*,*))); 2*(a - g - 1)*(2*a - g - 2)/((a - 3)*(a - 2))
(*,(*,*,*)); -2*(a - g)*(a - g - 1)/((a - 3)*(a - 2))
(*,*,(*,*)); -(a - g)*(5*a - g - 5)/((a - 3)*(a - 2))
(*,*,*,*); (a - g)*(2*a - g)/((a - 3)*(a - 2))
Grab some coffee. It can take a few hours to generate these files. Nevertheless, the files are included in this repository, for your convenience.
python qi_2_variance_table.py
This script will will generate file variance_table.txt. This file has one line for each value of i, j between 1 and 4 and for each value of k between 5 and 8, with the values of i, j, k, and the symbolic formula (as a function of α and γ) for the last sum in the formula for the variance of QIn under the α-γ model (Proposition 3 in the aforementioned paper). For instance, the first 4 lines of file variance_table.txt are:
1 1 5 q1**2*(-78*a**3 + 66*a**2*g + 306*a**2 + 18*a*g**2 - 324*a*g - 228*a - 6*g**3 + 18*g**2 + 228*g)/(a**3 - 9*a**2 + 26*a - 24)
1 1 6 q1**2*(2634*a**4 - 5592*a**3*g - 3876*a**3 + 3780*a**2*g**2 + 9396*a**2*g - 1914*a**2 - 888*a*g**3 - 6444*a*g**2 - 252*a*g + 3156*a + 66*g**4 + 924*g**3 + 2166*g**2 - 3156*g)/(a**4 - 14*a**3 + 71*a**2 - 154*a + 120)
1 1 7 q1**2*(3500*a**5 - 8400*a**4*g - 45840*a**4 + 6440*a**3*g**2 + 101320*a**3*g + 71100*a**3 - 1680*a**2*g**3 - 70600*a**2*g**2 - 159440*a**2*g - 8600*a**2 + 140*a*g**4 + 16280*a*g**3 + 102340*a*g**2 + 43840*a*g - 20160*a - 1160*g**4 - 14000*g**3 - 35240*g**2 + 20160*g)/(a**5 - 20*a**4 + 155*a**3 - 580*a**2 + 1044*a - 720)
1 1 8 q1**2*(1750*a**6 - 4200*a**5*g - 33250*a**5 + 3220*a**4*g**2 + 79100*a**4*g + 226770*a**4 - 840*a**3*g**3 - 59640*a**3*g**2 - 509760*a**3*g - 332710*a**3 + 70*a**2*g**4 + 14980*a**2*g**3 + 357610*a**2*g**2 + 734940*a**2*g + 85600*a**2 - 1190*a*g**4 - 80060*a*g**3 - 463830*a*g**2 - 241760*a*g + 51840*a + 5440*g**4 + 61600*g**3 + 156160*g**2 - 51840*g)/(a**6 - 27*a**5 + 295*a**4 - 1665*a**3 + 5104*a**2 - 8028*a + 5040)
Grab some more coffee. It can take a few more hours to generate this file. Nevertheless, the file is included in this repository, for your convenience.
python qi_3_variance_alpha_gamma.py
This script will generate file Var_2_64.txt. This file has one line for each value of n between 2 and 64, with the value of n and the symbolic formula for the variance of QIn under the α-γ model as a function of α and γ. For instance, the first 4 lines of file Var_2_64.txt are:
2 0
3 0
4 ((a - 3)*(a - 2)*(q1**2*(a - g)*(-5*a + g + 5) + 2*q2**2*(a - g)*(-a + g + 1) - q3**2*(a - 1)*(-2*a + g + 2) + q4**2*(a - g)*(2*a - g)) - (q1*(a - g)*(-5*a + g + 5) + 2*q2*(a - g)*(-a + g + 1) - q3*(a - 1)*(-2*a + g + 2) + q4*(a - g)*(2*a - g))**2)/((a - 3)**2*(a - 2)**2)
5 (5*(a - 4)*(a - 3)*(a - 2)*(a**3 - 9*a**2 + 26*a - 24)*(q1**2*(a - g)*(-5*a + g + 5) + 2*q2**2*(a - g)*(-a + g + 1) - q3**2*(a - 1)*(-2*a + g + 2) + q4**2*(a - g)*(2*a - g)) - 25*(a - 4)*(a**3 - 9*a**2 + 26*a - 24)*(q1*(a - g)*(-5*a + g + 5) + 2*q2*(a - g)*(-a + g + 1) - q3*(a - 1)*(-2*a + g + 2) + q4*(a - g)*(2*a - g))**2 + 2*(a - 3)*(a - 2)*(-6*q3**4*(a - 2)*(a - 1)*(-3*a + 2*g + 3)*(a**3 - 9*a**2 + 26*a - 24) + (a - 4)*(a - 3)*(a - 2)*(3*q1**4*(-13*a**3 + 11*a**2*g + 51*a**2 + 3*a*g**2 - 54*a*g - 38*a - g**3 + 3*g**2 + 38*g) + q2**4*(11*a**3 - 38*a**2*g + 9*a**2 + 39*a*g**2 - 21*a*g - 20*a - 12*g**3 + 12*g**2 + 20*g)) - (a - g)*(a**3 - 9*a**2 + 26*a - 24)*(2*q1**2*q2**2*(3*(a - g)*(-7*a + 3*g + 7) + (-5*a + g + 5)*(-2*a + 3*g + 2)) - 12*q1**2*q3**2*(a - 1)*(-4*a + g + 4) + 6*q1**2*q4**2*(2*a - g)*(-9*a + g + 9) - 12*q2**2*q3**2*(a - 1)*(-3*a + 2*g + 3) + 4*q2**2*q4**2*(2*a - g)*(-2*a + 3*g + 2) + 3*q4**4*(2*a - g)*(7*a - 3*g + 3))))/((a - 4)*(a - 3)**2*(a - 2)**2*(a**3 - 9*a**2 + 26*a - 24))
Grab still some more coffee. It can take half an hour to generate this file. Nevertheless, the file is included in this repository, for your convenience.
python qi_4_variance_alpha_gamma_n.py
This script will generate file Var_n.txt. This file has only one line, with the symbolic formula for the variance of QIn under the α-γ model as a function of α, γ and n.
It shall only take a few minutes to generate this file. Nevertheless, the file is included in this repository, for your convenience.
python qi_5_variance.py alpha gamma n
This script will take values for α, γ and n, and print the value of the variance of QIn under the α-γ model. For instance:
$ python qi_5_variance.py 0.5 0.5 4
0.16*q3**2
$ python qi_5_variance.py 0 0.5 4
-0.458333333333333*q1**2 - 0.25*q2**2 + 0.416666666666667*q3**2 + 0.0416666666666667*q4**2 - (-2.75*q1 - 1.5*q2 + 2.5*q3 + 0.25*q4)**2/36
python qi_6_value_fast.py tree.nw
This script will take a phylogenetic tree in Newick format and print the value of QI for the tree. For instance, if file figure_4.nw contains the Newick string ((1,2,3),4,(5,(6,7)));:
$ python qi_6_value_fast.py figure_4.nw
53