Allowing substitution model parameters to differ between branches¶
Section author: Gavin Huttley
A common task concerns assessing how substitution model exchangeability parameters differ between evolutionary lineages. This is most commonly of interest for the case of testing for natural selection. Here I’ll demonstrate the different ways of scoping parameters across trees for the codon model case and how these can be used for evolutionary modelling.
We start with the standard imports, plus using a canned codon substitution model and then load the sample data set.
from cogent3 import load_aligned_seqs, load_tree
from cogent3.evolve.models import MG94HKY
aln = load_aligned_seqs("data/long_testseqs.fasta")
tree = load_tree("data/test.tree")
We construct the substitution model and likelihood function and set the alignment.
sm = MG94HKY()
lf = sm.make_likelihood_function(tree, digits=2, space=3)
lf.set_alignment(aln)
At this point we have a likelihood function with two exchangeability parameters from the substitution model (kappa
the transition/transversion ratio; omega
the nonsynonymous/synonymous ratio) plus branch lengths for all tree edges. To facilitate subsequent discussion I now display the tree
print(tree.ascii_art())
/Human
/edge.0
/edge.1 \HowlerMon
 
 \Mouse
root
NineBande

\DogFaced
In order to scope a parameter on a tree (meaning specifying a subset of edges for which the parameter is to be treated differently to the remainder of the tree) requires uniquely identifying the edges. We do this using the following arguments to the likelihood function set_param_rule
method:
tip_names
: the name of two tipsoutgroup_name
: the name of a tip that is not part of the clade of interestclade
: ifTrue
, all lineages descended from the tree node identified by thetip_names
andoutgroup_name
argument are affected by the other arguments. IfFalse
, then thestem
argument must apply.stem
: Whether the edge leading to the node is included.
The next concepts include exactly what can be scoped and how. In the case of testing for distinctive periods of natural selection it is common to specify distinct values for omega
for an edge. I’ll first illustrate some possible uses for the arguments above by setting omega
to be distinctive for specific edges. I will set a value for omega so that printing the likelihood function illustrates what edges have been effected, but I won’t actually do any model fitting.
Specifying a clade¶
I’m going to cause omega
to attain a different value for all branches aside from the primate clade and stem (HowlerMon
, Human
, edge.0
).
lf.set_param_rule(
"omega",
tip_names=["DogFaced", "Mouse"],
outgroup_name="Human",
init=2.0,
clade=True,
)
lf
MG94HKY
loglikelihood = 9489.9506
number of free parameters = 10
kappa 

1.00 
edge  parent  length  omega 

Human  edge.0  0.03  1.00 
HowlerMon  edge.0  0.04  1.00 
edge.0  edge.1  0.04  1.00 
Mouse  edge.1  0.28  2.00 
edge.1  root  0.02  2.00 
NineBande  root  0.09  2.00 
DogFaced  root  0.11  2.00 
A  C  G  T 

0.37  0.19  0.21  0.23 
As you can see omega
for the primate edges I listed above have the default parameter value (1.0), while the others have what I’ve assigned. In fact, you could omit the clade
argument as this is the default, but I think for readability of scripts it’s best to be explicit.
Specifying a stem¶
This time I’ll specify the stem leading to the primates as the edge of interest.
Note
I need to reset the lf
so all edges have the default value again. I’ll show this only for this example, but rest assured I’m doing it for all others too.
lf.set_param_rule("omega", init=1.0)
lf.set_param_rule(
"omega",
tip_names=["Human", "HowlerMon"],
outgroup_name="Mouse",
init=2.0,
stem=True,
clade=False,
)
lf
MG94HKY
loglikelihood = 9424.8896
number of free parameters = 10
kappa 

1.00 
edge  parent  length  omega 

Human  edge.0  0.03  1.00 
HowlerMon  edge.0  0.04  1.00 
edge.0  edge.1  0.04  2.00 
Mouse  edge.1  0.28  1.00 
edge.1  root  0.02  1.00 
NineBande  root  0.09  1.00 
DogFaced  root  0.11  1.00 
A  C  G  T 

0.37  0.19  0.21  0.23 
Specifying clade and stem¶
I’ll specify that both the primates and their stem are to be considered.
lf.set_param_rule(
"omega",
tip_names=["Human", "HowlerMon"],
outgroup_name="Mouse",
init=2.0,
stem=True,
clade=True,
)
lf
MG94HKY
loglikelihood = 9442.4271
number of free parameters = 10
kappa 

1.00 
edge  parent  length  omega 

Human  edge.0  0.03  2.00 
HowlerMon  edge.0  0.04  2.00 
edge.0  edge.1  0.04  2.00 
Mouse  edge.1  0.28  1.00 
edge.1  root  0.02  1.00 
NineBande  root  0.09  1.00 
DogFaced  root  0.11  1.00 
A  C  G  T 

0.37  0.19  0.21  0.23 
Alternate arguments for specifying edges¶
The likelihood function set_param_rule
method also has the arguments of edge
and edges
. These allow specific naming of the tree edge(s) to be affected by a rule. In general, however, the tip_names
+ outgroup_name
combo is more robust.
Applications of scoped parameters¶
The general usecases for which a tree scope can be applied are:
constraining all edges identified by a rule to have a specific value which is constant and not modifiable
lf.set_param_rule(
"omega",
tip_names=["Human", "HowlerMon"],
outgroup_name="Mouse",
clade=True,
is_constant=True,
)
all edges identified by a rule have the same but different value to the rest of the tree
lf.set_param_rule(
"omega", tip_names=["Human", "HowlerMon"], outgroup_name="Mouse", clade=True
)
allowing all edges identified by a rule to have different values of the parameter with the remaining tree edges having the same value
lf.set_param_rule(
"omega",
tip_names=["Human", "HowlerMon"],
outgroup_name="Mouse",
clade=True,
is_independent=True,
)
allowing all edges to have a different value
lf.set_param_rule("omega", is_independent=True)
I’ll demonstrate these cases sequentially as they involve gradually increasing the degrees of freedom in the model. First we’ll constrain omega
to equal 1 on the primate edges. I’ll then optimise the model.
Note
here I’m specifying a constant value for the parameter and so I must use the argument value
to set it. This not to be confused with the argument init
that is used for providing initial (starting) values for fitting.
lf.set_param_rule(
"omega",
tip_names=["Human", "HowlerMon"],
outgroup_name="Mouse",
clade=True,
value=1.0,
is_constant=True,
)
lf.optimise(local=True, show_progress=False)
lf
MG94HKY
loglikelihood = 8640.9290
number of free parameters = 9
kappa 

3.87 
edge  parent  length  omega 

Human  edge.0  0.09  1.0 
HowlerMon  edge.0  0.12  1.0 
edge.0  edge.1  0.12  0.921816033174961 
Mouse  edge.1  0.84  0.921816033174961 
edge.1  root  0.06  0.921816033174961 
NineBande  root  0.28  0.921816033174961 
DogFaced  root  0.34  0.921816033174961 
A  C  G  T 

0.37  0.19  0.21  0.23 
I’ll now free up omega
on the primate clade, but making it a single value shared by all primate lineages.
lf.set_param_rule(
"omega",
tip_names=["Human", "HowlerMon"],
outgroup_name="Mouse",
clade=True,
is_constant=False,
)
lf.optimise(local=True, show_progress=False)
lf
MG94HKY
loglikelihood = 8639.7171
number of free parameters = 10
kappa 

3.85 
edge  parent  length  omega 

Human  edge.0  0.09  0.77 
HowlerMon  edge.0  0.12  0.77 
edge.0  edge.1  0.12  0.92 
Mouse  edge.1  0.84  0.92 
edge.1  root  0.06  0.92 
NineBande  root  0.28  0.92 
DogFaced  root  0.34  0.92 
A  C  G  T 

0.37  0.19  0.21  0.23 
Finally I’ll allow all primate edges to have different values of omega
.
lf.set_param_rule(
"omega",
tip_names=["Human", "HowlerMon"],
outgroup_name="Mouse",
clade=True,
is_independent=True,
)
lf.optimise(local=True, show_progress=False)
lf
MG94HKY
loglikelihood = 8638.9572
number of free parameters = 11
kappa 

3.85 
edge  parent  length  omega 

Human  edge.0  0.09  0.59 
HowlerMon  edge.0  0.12  0.95 
edge.0  edge.1  0.12  0.92 
Mouse  edge.1  0.84  0.92 
edge.1  root  0.06  0.92 
NineBande  root  0.28  0.92 
DogFaced  root  0.34  0.92 
A  C  G  T 

0.37  0.19  0.21  0.23 
We now allow omega
to be different on all edges.
lf.set_param_rule("omega", is_independent=True)
lf.optimise(local=True, show_progress=False)
lf
MG94HKY
loglikelihood = 8636.1383
number of free parameters = 15
kappa 

3.85 
edge  parent  length  omega 

Human  edge.0  0.09  0.59 
HowlerMon  edge.0  0.12  0.95 
edge.0  edge.1  0.12  1.13 
Mouse  edge.1  0.84  0.92 
edge.1  root  0.06  0.38 
NineBande  root  0.28  1.27 
DogFaced  root  0.34  0.84 
A  C  G  T 

0.37  0.19  0.21  0.23 