[R-sig-phylo] Estimating marginal ancestral states under a non-reversible model of evolution.

[Jordan Gault]

Hello all,

I’m putting together a short lecture on ancestral state reconstruction and would like to include some worked examples of marginal ancestral state reconstruction on a small phylogeny. I’ve managed to do the calculations by hand for a binary, discrete character under an equal-rate model using the re-rooting method and have checked my values using the phytools function rerootingMethod. I would like to do a worked example for an unequal-rates model as well but my understanding is that the re-rooting method is inappropriate for non-reversible models of trait evolution. How are marginal ancestral states estimated for non-reversible models of trait evolution? Can anyone point me to a source that describes how this is done? Thanks for any help!

Cheers,
Jordan Gault
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[Joe Felsenstein]

Post by Jordan Gault
I would like to do a worked example for an unequal-rates model as well but my understanding is that the re-rooting method is inappropriate for non-reversible models of trait evolution. How are marginal ancestral states estimated for non-reversible models of trait evolution?

Why do "unequal rates" make the model nonreversible?

I assume that by unequal rates you mean not
rates different in different sites, but forward and
backward rates different at a single site.

If that is the case, the equilibrium frequencies
of the two states become correspondingly
different, and the model is still reversible. The
tree can be rerooted at any interior node
and the marginal ancestral states at that node
found by the usual likelihood "pruning"
algorithm.

J.F.
----
Joe Felsenstein ***@gs.washington.edu
Department of Genome Sciences and Department of Biology,
University of Washington, Box 355065, Seattle, WA 98195-5065 USA

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[Jordan Gault]

Hi Joe,

Yes, I meant forward and backward rates are different at a single site. I mistakenly thought that different forward and backward rates make the model nonreversible. Thanks for the correction.

-Jordan

Post by Joe Felsenstein

Post by Jordan Gault
I would like to do a worked example for an unequal-rates model as well but my understanding is that the re-rooting method is inappropriate for non-reversible models of trait evolution. How are marginal ancestral states estimated for non-reversible models of trait evolution?

Why do "unequal rates" make the model nonreversible?
I assume that by unequal rates you mean not
rates different in different sites, but forward and
backward rates different at a single site.
If that is the case, the equilibrium frequencies
of the two states become correspondingly
different, and the model is still reversible. The
tree can be rerooted at any interior node
and the marginal ancestral states at that node
found by the usual likelihood "pruning"
algorithm.
J.F.
----
Department of Genome Sciences and Department of Biology,
University of Washington, Box 355065, Seattle, WA 98195-5065 USA

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