Aloha all,

There is no requirement for an ultra metric tree in the formulae reported in 
Butler-King 2004. Interested investigators should in particular read the 
supplementary materials where the mathematical details are worked out. 

We do generally use ultrametric trees because as comparative biologists, it is 
more straightforward to think about evolution in units of time rather than in 
terms of mutational units, etc. However this is by choice, not any 
methodological limitation. 

Once the model parameters are found, the phylogenetic variance-covariance 
matrix defined by the alpha, thetas, and sigmas can be used to compute 
ancestral states using a weighted least squares reconstruction method (instead 
of the typical BM var-cov matrix). The mapping of the alphas, thetas, and 
sigmas onto the tree are incorporated into this V-COV matrix, so that accounts 
for the OU model. 

NOTES: 
1) without knowing why you are doing this, I do feel compelled to warn you that 
it is unclear why one would want to estimate ancestral states for 
poorly-fitting models. Be careful!

2) I hope you realize that ancestral states are in general poorly estimated, 
even assuming the “correct” model. This is because there is less and less 
information to anchor the values as you get farther from the tips, similar to 
the root estimation problem described below.  This issue was clearly exposed in 
Schluter et al 1997 (and less famously so in Butler and Losos 1997). These 
depressing results were among the motivations for developing model-fit 
approaches in the first place. 

3) In 2008/2009 the algorithms in OUCH, SLOUCH, and possibly other methods have 
changed in the estimation of the value of the root state (X0) which is an 
internal calculation in fitting the model.  Ho and Ane 2013, and Hansen et al 
2008 both reported that the root state X0 is ill-defined (unless there are 
fossil data to anchor the value). This makes sense intuitively, as all of the 
information is from the tips, and the root is very far down the tree. A 
reasonable assumption is that it is distributed according to the stationary 
distribution of the OU process (X0 ~ N(theta(0), sigma^2/2*alpha) and this 
assumption is what these methods now employ. 

4) Whatever you end up doing, do check for the robustness of your results with 
parametric bootstrap on your fitted models (a la Boettinger et al 2012). As 
many investigators have reported, these parameters can have large confidence 
intervals, and can covary with one another (being on a likelihood ridge, etc.). 
But do note that even when parameters may not be uniquely identifiable, it may 
still be possible to have robust model selection (see Cressler et al 2015).  So 
perhaps you want to fit ancestral states to see if the different models give 
you the same states? IDK?

So in short, yes, you can do it, with any number of methods. But why? If you 
can answer your biological question with methods that do not involve estimation 
of a parameter that is inherently fraught with error, it might be better to go 
another way. Bottom line - use caution and be thoughtful!

I am sure if I have made any errors Aaron, Clay, or Thomas will help.

Hope this helps

Marguerite

Schluter, D., T. Price, A. O. Mooers, and D. Ludwig. 1997. Likelihood of 
ancestor states in adaptive radiation. Evolution 51:1699–1711.

Butler, M. A., and J. B. Losos. 1997. Testing for unequal amounts of evolution 
in a continuous character on dif- ferent branches of a phylogenetic tree using 
linear and squared-change parsimony: an example using Lesser Antillean Anolis 
lizards. Evolution 51:1623–1635. 

Hansen T.F., Pienaar J., Orzack S.H. 2008. A comparative method for studying 
adaptation to a randomly evolving environment. Evolution 62:1965–1977.

Ho L.S.T., Ané C.. 2014. Intrinsic inference difficulties for trait evolution 
with Ornstein-Uhlenbeck models. Methods Ecol. Evol. 2:1133–1146.

Cressler C., Butler M.A., and King A. A. (2015) Detecting adaptive evolution in 
phylogenetic comparative analysis using the Ornstein-Uhlenbeck model.  Sys. 
Bio. 64(6):953-968. DOI: 10.1093/sysbio/syv043

Boettiger C., Coop G., Ralph P. 2012. Is your phylogeny informative? Measuring 
the power of comparative methods. Evolution 66: 2240–2251. 

____________________________________________
Marguerite A. Butler
Professor

Department of Biology 
2538 McCarthy Mall, Edmondson Hall 216 
Honolulu, HI 96822

Office: 808-956-4713
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http://www2.hawaii.edu/~mbutler


> On Jun 11, 2018, at 7:33 PM, Simone Blomberg <s.blombe...@uq.edu.au> wrote:
> 
> 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 <dwba...@tamu.edu> 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 <lucas.ljard...@gmail.com> 
>>> 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
>>> http://dinizfilho.wix.com/dinizfilholab
>>> 
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>>> 
>>> _______________________________________________
>>> R-sig-phylo mailing list - R-sig-phylo@r-project.org
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>> 
>> 
>> 
>> -- 
>> David W. Bapst, PhD
>> Asst Research Professor, Geology & Geophysics, Texas A & M University
>> https://github.com/dwbapst/paleotree
>> Google Calendar: https://goo.gl/EpiM4J
>> 
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