It is possible to transform the branch lengths of a non-ultrametric tree to make the OU process equivalent to a BM process (on the transformed branch lengths), but there’s an extra correction needed at the tips (i.e. need to transform the data too via a diagonal matrix). It makes likelihood calculations a lot faster, but I have not seen this used for ancestral state estimation. This approach is described in Ho & Ané (2014) https://doi.org/10.1093/sysbio/syu005. It’s implemented in the R packages phylolm<https://cran.r-project.org/package=phylolm>, Rphylopars<https://cran.r-project.org/package=Rphylopars>, or l1ou<https://github.com/khabbazian/l1ou>. Cécile
On Jun 14, 2018, at 8:25 AM, David Bapst <dwba...@tamu.edu<mailto:dwba...@tamu.edu>> wrote: 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. Cheers, -Dave 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 <s.blombe...@uq.edu.au<mailto: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<mailto: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<mailto: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 [[alternative HTML version deleted]] _______________________________________________ R-sig-phylo mailing list - R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo Searchable archive at http://www.mail-archive.com/r- sig-ph...@r-project.org<mailto:sig-ph...@r-project.org>/ -- David W. Bapst, PhD Asst Research Professor, Geology & Geophysics, Texas A & M University https://github.com/dwbapst/paleotree Google Calendar: https://goo.gl/EpiM4J _______________________________________________ R-sig-phylo mailing list - R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo Searchable archive at http://www.mail-archive.com/r- sig-ph...@r-project.org<mailto:sig-ph...@r-project.org>/ -- David W. Bapst, PhD Asst Research Professor, Geology & Geophysics, Texas A & M University Postdoc, Ecology & Evolutionary Biology, Univ of Tenn Knoxville https://github.com/dwbapst/paleotree Google Calendar: https://goo.gl/EpiM4J [[alternative HTML version deleted]] _______________________________________________ R-sig-phylo mailing list - R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/ [[alternative HTML version deleted]] _______________________________________________ R-sig-phylo mailing list - R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/
