I would say no: standard errors of theta values do not have a biological interpretation, in my opinion. Going back to a sample from a single population and its mean: the standard deviation of the sample has a biological interpretation (e.g within-population variation), but the standard error does not. It has a statistical interpretation: about estimate uncertainty. Similarly with the OU model: the standard errors of theta estimates are also about uncertainty in these estimates. Even in the best case scenario when the model that you are using is correct, these standard errors would be affected by your sample size (i.e. go down with the number of tips in your tree), whereas a biological interpretation like plasticity should not be affected by the sample size.
On top of all this, a mismatch between the evolution process and the assumed OU model would affect the theta estimates and their standard errors. The new version of phylolm (on github, not on CRAN) has bootstrap-based standard errors, if you wanted to follow-up on Brian’s idea. It also has the possibility to add measurement error in the model when analyzing data Cécile > On Sep 15, 2016, at 9:11 PM, Brian O'Meara <omeara.br...@gmail.com> wrote: > > That's a really cool question. I don't know. I'm pretty sure that > practically, the answer is no (esp when you consider all the issues -- any > feasible OU is too simple a model to match reality, tree errors, data > errors, etc. -- that also come into an analysis). However, I could imagine > that in a perfect world you could look at expected standard errors created > using parametric bootstrapping from the MLE of the parameters and see if > the actual standard errors are different -- maybe it could reflect > plasticity or some other factor. But I really don't know. You might look at > some of the methods that can deal with intraspecific and interspecific > processes to get at this sort of biological question (the Felsenstein 2008 > Contrasts revisited paper might be interesting as a start, though it's not > OU and comes at this from a different direction), but it's fun to think > about ways to go from what is treated as annoying noise to a meaningful > signal. > > Best, > Brian > > _______________________________________________________________________ > Brian O'Meara, http://www.brianomeara.info, especially Calendar > <http://brianomeara.info/calendars/omeara/>, CV > <http://brianomeara.info/cv/>, and Feedback > <http://brianomeara.info/teaching/feedback/> > > Associate Professor, Dept. of Ecology & Evolutionary Biology, UT Knoxville > Associate Head, Dept. of Ecology & Evolutionary Biology, UT Knoxville > Associate Director for Postdoctoral Activities, National Institute for > Mathematical & Biological Synthesis <http://www.nimbios.org> (NIMBioS) > Communication Director, Society of Systematic Biologists > > On Thu, Sep 15, 2016 at 5:37 PM, Xiaojing Wei <weixx...@umn.edu> wrote: > >> Dear R-sig-phylo users, >> >> I wonder if the standard errors of the theta estimates in OU models have >> any biologically meaningful interpretations. For instance, could it give >> some indication of plasticity in traits, or the optimal level of plasticity >> in traits? Or does it simply reflect estimation uncertainty of the >> phylogeny or the OU model? >> >> Thanks a lot! >> >> -- >> Xiaojing Wei >> PhD student >> Dept. of Ecology, Evolution, and Behavior >> University of Minnesota >> Rm. 211 Ecology Bld., 1987 Upper Buford Cir. >> St. Paul, 55108 >> >> [[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/ >> > > [[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/ _______________________________________________ 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/
