RER: relative evolutionary rate

This analysis implements a relative evolutionary rate test inspired by RERConverge, also see walkthrough.

A key use-case is a study of how evolutionary rates associate with phenotypes, e.g. the subterranean phenotype, is here.

This analysis requires an alignment of protein sequences, a reference tree with given branch lengths, and a list of branches designated at the test set.

The reference tree is viewed as providing relative branch lengths, e.g. estimated from a genome-wide species tree alignment.

The RER analysis fits the following four models and compares them in a variety of ways. A companion visualization module can be found at https://observablehq.com/@spond/rer-viewer

Proportional

A single alignment-wide branch length scaling parameter R_shared is inferred. It simply scales all the branches relative to the input tree.

Proportional partitioned

Two alignment-wide branch length scaling parameters R_test, R_background are inferred: one for the test branches, and one for the background branches.

Unconstrained Test

All background branches are scaled with the same factor R_background. Every branch in the test set gets its own (independent) branch length.

Unconstrained

All branch lengths are inferred independently.

Summary of models

T the number of test branches B the number of background branches

Model	Test Branches	Background Branches	# Parameters
Proportional	Rshared x ref	Rshared x ref	1
Proportional Partitioned	Rtest x ref	Rbackground x ref	2
Unconstrained Test	Independent	Rbackground	T + 1
Unconstrained	Independent	Independent	T + B

These models form a nested chain:

Proportional ⊂ Proportional Partitioned ⊂ Unconstrained Test ⊂ Unconstrained

Example 1

An example invocation for a gene (LIM2) that was found to be accelerated in subterranean lineages in Partha et al.

hyphy RER.bf 
--alignment data/LIM2.fa 
--tree data/mam120master.tre 
--branches nanGal1 
--branches hetGla2 
--branches HLfukDam1 
--branches conCri1 
--branches chrAsi1 
--labeling-strategy none

Test branches are shown as thicker branches below (colors -- ratio to reference tree branch lengths; blue < 1, grey = 1, red > 1)

Reference	Proportional (Rshared = 0.17)
Proportional Partitoned (Rtest = 1.5, Rbackground = 0.17)	Unconstrained Test (Rbackground = 0.17)
Unconstrained

Example 2

An example invocation for a gene (LIM2) that was found to be decelerated in subterranean lineages in Partha et al.

hyphy RER.bf 
--alignment data/CHST8.fa 
--tree data/mam120master.tre 
--branches nanGal1 
--branches hetGla2 
--branches HLfukDam1 
--branches conCri1 
--branches chrAsi1 
--labeling-strategy none

Test branches are shown as thicker branches below (colors -- ratio to reference tree branch lengths; blue < 1, grey = 1, red > 1)

Reference	Proportional (Rshared = 0.47)
Proportional Partitoned (Rtest = 0.34, Rbackground = 0.47)	Unconstrained Test (Rbackground = 0.48)
Unconstrained

Hypothesis testing

The RER analysis will conduct all six nested model pairs likelihood ratio tests (LRT) and report the results as Holm-Bonferroni corrected p-values.

Example: LIM2

LRT test results between pairs of nested models

p-values corrected using the Holm-Bonferroni procedure (raw values in parentheses)

Null	Proportional Partitioned	Unconstrained Test	Unconstrained
Proportional	0.0000000 (0.00000)	0.0000000 (0.00000)	0.0000000 (0.00000)
Proportional Partitioned	N/A	0.0000285 (0.00003)	0.0000000 (0.00000)
Unconstrained Test	N/A	N/A	0.0000000 (0.00000)

Example: CHST8

LRT test results between pairs of nested models

p-values corrected using the Holm-Bonferroni procedure (raw values in parentheses)

Null	Proportional Partitioned	Unconstrained Test	Unconstrained
Proportional	0.0060750 (0.00202)	0.0138966 (0.00695)	0.0000000 (0.00000)
Proportional Partitioned	N/A	0.1688029 (0.16880)	0.0000000 (0.00000)
Unconstrained Test	N/A	N/A	0.0000000 (0.00000)

Test Interpretation for key pairs

Null	Alternative	Hypothesis
Proportional	Proportional Partitioned	Are average relative (to reference) evolutionary rates different between the two sets of branches? This is the test most directly comparable to the RERConverge test
Proportional Partitioned	Unconstrained Test	Is there evidence of relative rate (branch length) variation in the test clade, assuming that the background is proportional to the reference tree?
Unconstrained Test	Unconstrained	Is there evidence of relative rate (branch length) variation in the background branches?

Key analysis options

Substitution model

--model [one of LG, WAG, JTT, JC69, mtMet, mtVer, mtInv, gcpREV, HIVBm, HIVWm, GTR]

WAG is the default model.

Site-to-site rate variation

--rv [one None, Gamma, GDD]

None is the default

--rate-classes [2-10]

4 is the default

Labeling strategy

This option determines how RER approaches automatically internal nodes to the test set.

1. none : do not label any internal branches automatically
2. all-descendants : [default] label an internal node if and only if ALL of its descendants are labeled
3. some-descendants : label an internal node if and only if ANY of its descendants are labeled
4. parsimony : label internal nodes using parsimony