Apply a non-stationary nucleotide model to an alignment with 3 sequences

We load some sample data first and select just 3 sequences, all via apps.

[1]:

from cogent3.app import io, sample

reader = io.load_aligned(format="fasta", moltype="dna")
select_seqs = sample.take_named_seqs("Human", "Rhesus", "Galago")
process = reader + select_seqs
aln = process("../data/primate_brca1.fasta")
aln.names

[1]:

['Human', 'Rhesus', 'Galago']

We analyses these using the general Markov nucleotide, GN, model. Because we analyse just 3 sequences, there is only one possible unrooted tree. It’s not required to specify the tree in this instance.

[2]:

from cogent3.app import evo

gn = evo.model("GN")
gn

[2]:

model(type='model', sm='GN', tree=None, name=None, sm_args=None, lf_args=None, time_het=None, param_rules=None, opt_args=None, split_codons=False, show_progress=False, verbose=False)

We apply this to aln.

[3]:

fitted = gn(aln)
type(fitted)

[3]:

cogent3.app.result.model_result

model_result

As the output above indicates, fitted is a model_result object.

This object provides an interface for accessing attributes of a fitted model. The representation display (below), a styled table in a jupyter notebook, presents a summary view with the log-likelihood (lnL), number of free parameters (nfp) and whether all matrices satisfied the identifiability conditions diagonal largest in column (DLC) and a unique mapping of Q to P. (For description of these quantities and why they matter see Chang 1996 and Kaehler et al.)

model_result has dictionary behaviour, hence the key column. This will be demonstrated below.

[4]:

fitted

[4]:
GN
key lnL nfp DLC unique_Q
-5964.0129 17 True True

More detail on the fitted model are available via attributes. For instance, display the maximum likelihood estimates via the likelihood function attribute

[5]:

fitted.lf

[5]:

GN

log-likelihood = -5964.0129

number of free parameters = 17

Global params
A>C A>G A>T C>A C>G C>T G>A G>C G>T T>A
1.0628 3.1833 1.0207 1.7952 2.3276 5.6847 9.0910 1.1136 0.8313 1.4997
T>C
3.5575
Edge params
edge parent length
Human root 0.0214
Rhesus root 0.0208
Galago root 0.1781
Motif params
A C G T
0.3740 0.1755 0.2098 0.2408 
[6]:

fitted.lnL, fitted.nfp

[6]:

(-5964.012906757179, 17)

[7]:

fitted.source

[7]:

'../data/primate_brca1.fasta'

The model_result.tree attribute is an “annotated tree”. Maximum likelihood estimates from the model have been assigned to the tree. Of particular significance, the “length” attribute corresponds to the expected number of substitutions (or ENS). For a non-stationary model, like GN, this can be different to the conventional length (Kaehler et al).

[8]:

fitted.tree, fitted.alignment

[8]:

(Tree("(Human,Rhesus,Galago)root;"),
 3 x 2814 dna alignment: Human[TGTGGCACAAA...], Rhesus[TGTGGCACAAA...], Galago[TGTGGCAAAAA...])

We can access the sum of all branch lengths. Either as “ENS” or “paralinear” using the total_length() method.

[9]:

fitted.total_length(length_as="paralinear")

[9]:

0.9280297908804234

Fitting a separate nucleotide model to each codon position

Controlled by setting split_codons=True.

[10]:

gn = evo.model("GN", split_codons=True)

fitted = gn(aln)
fitted

[10]:
GN
key lnL nfp DLC unique_Q
-5866.9371 51 True True
1 -1955.5141 17
2 -1934.2598 17
3 -1977.1632 17

The model fit statistics, lnL and nfp are now sums of the corresponding values from the fits to the individual positions. The DLC and unique_Q are also a summary across all models. These only achieve the value True when all matrices, from all models, satisfy the condition.

We get access to the likelihood functions of the individual positions via the indicated dict keys.

[11]:

fitted[3]

[11]:

3

log-likelihood = -1977.1632

number of free parameters = 17

Global params
A>C A>G A>T C>A C>G C>T G>A G>C G>T T>A
1.7484 3.4215 2.4111 2.3729 3.4060 16.1603 16.9889 2.0343 1.7432 1.9241
T>C
5.2795
Edge params
edge parent length
Human root 0.0243
Rhesus root 0.0319
Galago root 0.1797
Motif params
A C G T
0.3375 0.1395 0.1647 0.3583