Hi Brian.
The issue isn't polytomies, per se, but phylogenetic uncertainty.
Actually, arbitrarily resolving polytomies with branches of zero length
will not affect your fitted regression model at all - so there is no
point in resolving polytomies randomly many times or any such thing.
With regard to phylogenetic uncertainty, the principle concern is that
variance on the estimated model coefficients will be too small (and thus
hypothesis tests too liberal) when the tree is known with error. One
solution that I have suggested before, and that I know will annoy some
readers by inelegantly merging Bayesianism & frequentism, is to fit our
regression model from a posterior sample of trees and then compute the
variance on parameter estimates as the mean variance for each fitted
model plus the variance among estimates across trees. Though a bit ugly,
to be sure, this has the effect of taking into account estimation error
& phylogenetic error. We can then proceed to use the total variance on
parameter estimates to conduct hypothesis tests or construct confidence
intervals about the parameters of our fitted model.
Reducing the number of degrees of freedom theoretically could achieve
the same effect because it would decrease the denominator of our
variance on parameter estimates - if we knew how by how much to reduce
that number. Unfortunately, there is not (and cannot be) a general rule
whereby we reduce the degrees of freedom by a set amount for each soft
polytomy in the tree. This is because all soft polytomies are not equal.
For instance, if a polytomy is present in our tree because there were a
series of closely-spaced branching events in the true phylogenetic
history, then the consensus tree is actually quite a good representation
of this history and using the consensus tree will have little ill
effect. Conversely, if a polytomy reflects substantive phylogenetic
disagreement among alternative topologies in the posterior sample, and
we have no way of knowing which is correct, then (presumably) a much
greater reduction in the degrees of freedom would be required to account
for this uncertainty.
I hope these comments are helpful.
All the best, Liam
Liam J. Revell, Assistant Professor of Biology
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: liam.rev...@umb.edu
blog: http://blog.phytools.org
On 7/9/2015 11:43 AM, Brian A. Gill wrote:
Hi Everyone.
I want to run PGLS on a Bayesian consensus tree that has multiple
polytomies.
What's current opinion on the best way to handle the polytomies?
There are several solutions I have come across looking at previous posts,
papers, ect.
1) Run PGLS with polytomies and manipulate degrees of freedom. Which
packages will run PGLS with polytomies? Most of the one's I've tried won't.
How can you adjust degrees of freedom?
2) Randonly resolve polytomies to make completely bifurcating tree. Use
zero or very small length internal branch lengths for resolution.
Potentially many alternative trees.
3) Run PGLS across 95% credible set of Bayesian trees. The problem here is
that MrBayes outputs only topologies for the credible set in the .trprobs
file. Does anyone know how to extract the 95% credible set from MrBayes
with branch length information?
Any suggestions would be greatly appreciated.
Brian
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