Yeah, that is definitely a mistake in the documentation! I have
fixed it on the master branch. If I make a 3.7.0 release before I
do a 4.0, then I will include it.
All the site models have `posP` as the fraction of sites that are
positively selected with dN/dS = `posW`.
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OK, so actually my original response here wasn't quite right. I've updated the command-line documentation so that we have:
m2a posP: The fraction of positively selected sites. m2a_test posP: The fraction of positively selected sites. m8a posP: The fraction of *neutral* sites. m8 posP: The fraction of positively selected sites. m8a_test posP: The fraction of positively-selected or neutral sites.
On the master branch, I've updated the command-line documentation for the m8a and m8 models, and added new documentation for the m8a_test model
It is still the case that all the site models have `posP` as the fraction of sites with dN/dS=`posW`. But m8a (which is the same as m8[posW=1]) does not have an explicit posW parameter. Since posW=1 for m8a, posP is the fraction of NEUTRAL sites.
The relationship between all the m<number> models from PAML
is a bit weird and complicated. You may have to read the
references in the m7, m8a, and m2a models to get the full picture.
P.S. The command line documentation comes from JSON files, like
P.P.S. Here is the new description for m8a_test -- it is somewhat long:
This is a Bayesian version of the M8a test for positive selection. The
original M8a test is a likelihood-ratio test. The Bayesian version of the
test chooses a prior with 50% mass on the null hypothesis H0 and 50% on
the alternative hypothesis H1:
H0: no positive selection
H1: some positive selection.
When posSelection = 0, the value of posW is ignored and dN/dS=1. When
posSelection = 1, the value of posW is used and dN/dS=posW. The posterior
probability of posSelection gives the posterior probability of H1. The
Bayes Factor is given by Pr(posSelection=1)/Pr(posSelection=0).
The M8a test (Swanson et al, 2003) has null and alternative hypotheses
H0: m8[posW=1] = m8a
This is an improvement over the test originally proposed by Yang (2000):
H0: m8[posP=1] = m7
In the originally proposed likelihood-ratio test, a mixture of conserved
and neutral sites would not fit the null hypothesis (m7), leading to the
erroneous inference of positive selection. In the M8a test, the null
hypothesis (m8a) has been improved to handle both neutral and conserved
sites, so that positive selection is not incorrectly inferred.
Just to confirm,
In a hypothetical scenario where m8a_test is used. Assuming the resulting estimate of the parameter posSelection is zero (or very close to zero). The estimate of posW should always be one (or close to one). Is that correct?
1. When posSelection=0, the value of posW is never used. We just use 1.0 instead. So when posSelection=0, posW is actually drawn from the prior of posW.
When I have used these models, I reported Pr(posSelection=1) and E(posW|posSelection=1) instead of E(posW), so this did not come up.
2. To get expectations conditional on posSeletion=1, I used a command like this:
stats-select -sm8a_test:posSelection=1 < C1.log | statreport --mean -Note that Pr(posSelection=1) = E(posSelection).
3. It is certainly possible IN THEORY to log `if posSelection == 1 then posW else 1.0` instead of `posW`. That is a Haskell expression that would do what you want. However, until version 4 is ready, this might be difficult.
Hmm... do you think E(if posSelection == 1 then posW else 1.0) makes sense mathematically? I guess it would correspond to estimating posW under a prior with a point mass on 1.0....
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