Simone, others,

Perhaps I misunderstand, but I believe Slater (2014) shows that there is no
correct branch length transformation for a non-ultrametric tree under an OU
process. The correct transformation that Slater applies is Hansen's, yes,
but to the VCV matrix. Slater does point out there is one VCV-free approach
that does work for non-ultrametric trees, and that is the pruning-algorithm
that was at the time implemented in diversitree.

Some quotes from Slater (2014):

"The time-dependent decay in covariance that accrues after divergence under
OU results in the rather unique phenomenon that non-ultrametric trees
cannot be rescaled according to an OU process as ultrametric trees can."

"This is a necessary error, because a treelike structure cannot be
represented with different shared path lengths for pairs of descendents
that branch from the same ancestor. However, using Hansen’s (1997) formula
to directly transform V results in the correct pattern (Fig. 1d); Vt4,t1 is
higher than Vt4,t2 because the phylogenetic distance between t1 and t4, and
thus the time available for covariance decay, is lower as a result of t1
going extinct before the present. It is additionally worth noting that
branch length scaling results in underestimated variances for fossil taxa
(upper left diagonal of 1b, c, and d); branch length transformation reduces
the variance of t1 compared with that of the other species, while direct
matrix scaling increases the variance of the fossil taxon to a similar
value as in the extant species."

"For example, although problems with branch length rescaling render
Freckleton’s (2012) approach inappropriate, it is still possible to use
VCV-free approaches to rapidly compute likelihoods with non-ultrametric
data. The pruning algorithm used by FitzJohn (2012) in his DIVERSITREE
package, which is based on Felsenstein (1973, 1981), can be used to fit OU
models to non-ultrametric trees because it works on per branch basis,
rather than by scaling all branch lengths simultaneously."

Again, this is (I think) common knowledge that OU
branch-length-transformations cannot be safely applied to non-ultrametric
trees, in our post-Slater-2014 world. However, following Lucas's comment, I
wanted to make sure the record is correct for those who stumble on this
thread later. As Slater (2014) points out, us paleontologists are ever
increasingly users of phylogenetic comparative methods, and so as
methods-developers, we should always take into account the possibility that
a user's dataset may include fossil tips.


PS: I've cc'd Graham so he can rebuke me if I'm way off-the-mark here.

On Tue, Jun 12, 2018 at 12:33 AM, Simone Blomberg <>

> This sounded wrong to me, as the OU process should be agnostic to the
> dataset: There are no restrictions inherent in the OU process that apply
> particularly to phylogenetic data, whether the tree is ultrametric or not.
> I re-read Slater 2014 and it is clear that you can use branch length
> transformations with OU, so long as you use the (correct) Hansen formula,
> not the Butler-king formula, which does indeed require an ultrametric tree.
> Cheers,
> Simone.
> Sent from my iPhone
> > On 12 Jun 2018, at 8:01 am, David Bapst <> wrote:
> >
> > Just to follow off what Lucas said, but please note you cannot rescale
> > branches of a phylogeny using an OU model when the tree is
> > non-ultrametric (such as when it contains extinct, fossil taxa as
> > tips). Slater (2014, MEE) discusses this more in a brief correction to
> > Slater (2013).
> >
> > I don't know if anyone in this conversation has a non-ultrametric
> > tree, but I wanted to make that clear for anyone who stumbles on this
> > thread n the future using a google search.
> > -Dave
> >
> >
> >
> >> On Sun, Jun 10, 2018 at 12:25 PM, Lucas Jardim <
>> wrote:
> >> Hi Bruno,
> >>
> >> You can transform the branches of your phylogeny using the estimated
> >> parameters of OU models. Then, if those models describe the observed
> data
> >> adequatly, the transformed tree should model the observed data as a
> >> Brownian motion model. So you can use an ancestral state reconstruction
> >> based on Brownian motion model. However, I do not know if that is the
> best
> >> approach as optimum values would not be included into the reconstruction
> >> process.
> >>
> >> Best,
> >> --
> >> Lucas Jardim
> >> Doutor em Ecologia e Evolução
> >> Bolsista do INCT-EECBio (Ecologia, Evolução e Conservação da
> >> Biodiversidade)
> >> Instituto de Ciências Biológicas
> >> Laboratório de Ecologia Teórica e Síntese
> >> Universidade Federal de Goiás
> >>
> >>
> >>        [[alternative HTML version deleted]]
> >>
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> >
> >
> > --
> > David W. Bapst, PhD
> > Asst Research Professor, Geology & Geophysics, Texas A & M University
> >
> > Google Calendar:
> >
> > _______________________________________________
> > R-sig-phylo mailing list -
> >
> > Searchable archive at

David W. Bapst, PhD
Asst Research Professor, Geology & Geophysics, Texas A & M University
Postdoc, Ecology & Evolutionary Biology, Univ of Tenn Knoxville
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