Likelihood analysis of multiple lociΒΆ

Section author: Gavin Huttley

We want to know whether an exchangeability parameter is different between alignments. We will specify a null model, under which each alignment get’s it’s own motif probabilities and all alignments share branch lengths and the exchangeability parameter kappa (the transition / transversion ratio). We’ll split the example alignment into two-pieces.

>>> from cogent import LoadSeqs, LoadTree, LoadTable
>>> from cogent.evolve.models import HKY85
>>> from cogent.recalculation.scope import EACH, ALL
>>> from cogent.maths.stats import chisqprob
>>> aln = LoadSeqs("data/long_testseqs.fasta")
>>> half = len(aln)/2
>>> aln1 = aln[:half]
>>> aln2 = aln[half:]

We provide names for those alignments, then construct the tree, model instances.

>>> loci_names = ["1st-half", "2nd-half"]
>>> loci = [aln1, aln2]
>>> tree = LoadTree(tip_names=aln.getSeqNames())
>>> mod = HKY85()

To make a likelihood function with multiple alignments we provide the list of loci names. We can then specify a parameter (other than length) to be the same across the loci (using the imported ALL) or different for each locus (using EACH). We conduct a LR test as before.

>>> lf = mod.makeLikelihoodFunction(tree,loci=loci_names,digits=2,space=3)
>>> lf.setParamRule("length", is_independent=False)
>>> lf.setParamRule('kappa', loci = ALL)
>>> lf.setAlignment(loci)
>>> lf.optimise(local=True)
>>> print lf
Likelihood Function Table
=========================
   locus   motif   mprobs
-------------------------
1st-half       T     0.22
1st-half       C     0.18
1st-half       A     0.38
1st-half       G     0.21
2nd-half       T     0.24
2nd-half       C     0.19
2nd-half       A     0.35
2nd-half       G     0.22
-------------------------
==============
kappa   length
--------------
 3.98     0.13
--------------
>>> all_lnL = lf.getLogLikelihood()
>>> all_nfp = lf.getNumFreeParams()
>>> lf.setParamRule('kappa', loci = EACH)
>>> lf.optimise(local=True)
>>> print lf
Likelihood Function Table
================
   locus   kappa
----------------
1st-half    4.33
2nd-half    3.74
----------------
=========================
   locus   motif   mprobs
-------------------------
1st-half       T     0.22
1st-half       C     0.18
1st-half       A     0.38
1st-half       G     0.21
2nd-half       T     0.24
2nd-half       C     0.19
2nd-half       A     0.35
2nd-half       G     0.22
-------------------------
======
length
------
  0.13
------
>>> each_lnL = lf.getLogLikelihood()
>>> each_nfp = lf.getNumFreeParams()
>>> LR = 2 * (each_lnL - all_lnL)
>>> df = each_nfp - all_nfp

Just to pretty up the result display, I’ll print a table consisting of the test statistics created on the fly.

>>> print LoadTable(header=['LR', 'df', 'p'],
...             rows=[[LR, df, chisqprob(LR, df)]], digits=2, space=3)
================
  LR   df      p
----------------
1.59    1   0.21
----------------