My goal, it seems to me, is to get a bunch of replications of data in which one trait shows a phylogenetic signal, but the other one does not, but also that both share some predefined correlation with each other (over time). I can then test different kinds of methods to see which would be most appropriate statistical method for this kind of problem.
I can see how I could simulate traits evolving with a given correlation value over a given tree, using sim.char() in R. However, won't this leave me with traits in which both have the same phylogenetic signal? Is my only option to simulate huge numbers of traits, half of which are evolving consistent with some tree, and the other half are independent of the tree (i.e., random numbers?), and then correlate pairs (one from each of these groups), retaining just those that have the level of correlation I'm interested in exploring? Thanks for any suggestions, -Tom On Jul 26, 2013, at 6:42 PM, Theodore Garland Jr <theodore.garl...@ucr.edu> wrote: > Hi Tom, > > So far I have resisted jumping in here, but maybe this will help. > Come up with a model for how you think your traits of interest might evolve > together in a correlated fashion along a phylogenetic tree. > Now implement it in a computer simulation along a phylogenetic tree. > Also implement the model with no correlation between the traits. > Analyze the data with whatever methods you choose. > Check the Type I error rate and then the power of each method. Also check > the bias and means squared error for the parameter you are trying to estimate. > See what method works best. > Use that method for your data if you have some confidence that the model you > used to simulate trait evolution is reasonable, based on your understanding > (and intuition) about the biology involved. > > Lots of us have done this sort of thing, e.g., check this: > > Martins, E. P., and T. Garland, Jr. 1991. Phylogenetic analyses of the > correlated evolution of continuous characters: a simulation study. Evolution > 45:534-557. > > > > Cheers, > Ted > > Theodore Garland, Jr., Professor > Department of Biology > University of California, Riverside > Riverside, CA 92521 > Office Phone: (951) 827-3524 > Wet Lab Phone: (951) 827-5724 > Dry Lab Phone: (951) 827-4026 > Home Phone: (951) 328-0820 > Skype: theodoregarland > Facsimile: (951) 827-4286 = Dept. office (not confidential) > Email: tgarl...@ucr.edu > http://www.biology.ucr.edu/people/faculty/Garland.html > http://scholar.google.com/citations?hl=en&user=iSSbrhwAAAAJ > > Inquiry-based Middle School Lesson Plan: > "Born to Run: Artificial Selection Lab" > http://www.indiana.edu/~ensiweb/lessons/BornToRun.html > > From: r-sig-phylo-boun...@r-project.org [r-sig-phylo-boun...@r-project.org] > on behalf of Tom Schoenemann [t...@indiana.edu] > Sent: Friday, July 26, 2013 3:21 PM > To: Tom Schoenemann > Cc: r-sig-phylo@r-project.org > Subject: Re: [R-sig-phylo] PGLS vs lm > > OK, so I haven't gotten any responses that convince me that PGLS isn't > biologically suspect. At the risk of thinking out loud to myself here, I > wonder if my finding might have to do with the method detecting phylogenetic > signal in the error (residuals?): > > From: > Revell, L. J. (2010). Phylogenetic signal and linear regression on species > data. Methods in Ecology and Evolution, 1(4), 319-329. > > I note the following: "...the suitability of a phylogenetic regression should > actually be diagnosed by estimating phylogenetic signal in the residual > deviations of Y given our predictors (X1, X2, etc.)." > > Let's say one variable, "A", has a strong evolutionary signal, but the other, > variable "B", does not. Would we expect this to affect a PGLS differently if > we use A to predict B, vs. using B to predict A? > > If so, it would explain my findings. However, given the difference, I can > have no confidence that there is, or is not, a significant covariance between > A and B independent of phylogeny. Doesn't this finding call into question the > method itself? > > More directly, how is one to interpret such a finding? Is there, or is there > not, a significant biological association? > > -Tom > > > On Jul 21, 2013, at 11:47 PM, Tom Schoenemann <t...@indiana.edu> wrote: > > > Thanks Liam, > > > > A couple of questions: > > > > How does one do a hypothesis test on a regression, controlling for > > phylogeny, if not using PGLS as I am doing? I realize one could use > > independent contrasts, though I was led to believe that is equivalent to a > > PGLS with lambda = 1. > > > > I take it from what you wrote that the PGLS in caper does a ML of lambda > > only on y, when doing the regression? Isn't this patently wrong, > > biologically speaking? Phylogenetic effects could have been operating on > > both x and y - we can't assume that it would only be relevant to y. > > Shouldn't phylogenetic methods account for both? > > > > You say you aren't sure it is a good idea to jointly optimize lambda for x > > & y. Can you expand on this? What would be a better solution (if there is > > one)? > > > > Am I wrong that it makes no evolutionary biological sense to use a method > > that gives different estimates of the probability of a relationship based > > on the direction in which one looks at the relationship? Doesn't the fact > > that the method gives different answers in this way invalidate the method > > for taking phylogeny into account when assessing relationships among > > biological taxa? How could it be biologically meaningful for phylogeny to > > have a greater influence when x is predicting y, than when y is predicting > > x? Maybe I'm missing something here. > > > > -Tom > > > > > > On Jul 21, 2013, at 8:59 PM, Liam J. Revell <liam.rev...@umb.edu> wrote: > > > >> Hi Tom. > >> > >> Joe pointed out that if we assume that our variables are multivariate > >> normal, then a hypothesis test on the regression is the same as a test > >> that cov(x,y) is different from zero. > >> > >> If you insist on using lambda, one logical extension to this might be to > >> jointly optimize lambda for x & y (following Freckleton et al. 2002) and > >> then fix the value of lambda at its joint MLE during GLS. This would at > >> least have the property of guaranteeing that the P-values for y~x and x~y > >> are the same.... > >> > >> I previously posted code for joint estimation of lambda on my blog here: > >> http://blog.phytools.org/2012/09/joint-estimation-of-pagels-for-multiple.html. > >> > >> With this code to fit joint lambda, our analysis would then look something > >> like this: > >> > >> require(phytools) > >> require(nlme) > >> lambda<-joint.lambda(tree,cbind(x,y))$lambda > >> fit1<-gls(y~x,data=data.frame(x,y),correlation=corPagel(lambda,tree,fixed=TRUE)) > >> fit2<-gls(x~y,data=data.frame(x,y),correlation=corPagel(lambda,tree,fixed=TRUE)) > >> > >> I'm not sure that this is a good idea - but it is possible.... > >> > >> - Liam > >> > >> Liam J. Revell, Assistant Professor of Biology > >> University of Massachusetts Boston > >> web: http://faculty.umb.edu/liam.revell/ > >> email: liam.rev...@umb.edu > >> blog: http://blog.phytools.org > >> > >> On 7/21/2013 6:15 PM, Tom Schoenemann wrote: > >>> Hi all, > >>> > >>> I'm still unsure of how I should interpret results given that using PGLS > >>> to predict group size from brain size gives different significance > >>> levels and lambda estimates than when I do the reverse (i.e., predict > >>> brain size from group size). Biologically, I don't think this makes any > >>> sense. If lambda is an estimate of the phylogenetic signal, what > >>> possible evolutionary and biological sense are we to make if the > >>> estimates of lambda are significantly different depending on which way > >>> the association is assessed? I understand the mathematics may allow > >>> this, but if I can't make sense of this biologically, then doesn't it > >>> call into question the use of this method for these kinds of questions > >>> in the first place? What am I missing here? > >>> > >>> Here is some results from data I have that illustrate this (notice that > >>> the lambda values are significantly different from each other): > >>> > >>> Group size predicted by brain size: > >>> > >>>> model.group.by.brain<-pgls(log(GroupSize) ~ log(AvgBrainWt), data = > >>>> primate_tom, lambda='ML') > >>>> summary(model.group.by.brain) > >>> > >>> Call: > >>> pgls(formula = log(GroupSize) ~ log(AvgBrainWt), data = primate_tom, > >>> lambda = "ML") > >>> > >>> Residuals: > >>> Min 1Q Median 3Q Max > >>> -0.27196 -0.07638 0.00399 0.10107 0.43852 > >>> > >>> Branch length transformations: > >>> > >>> kappa [Fix] : 1.000 > >>> lambda [ ML] : 0.759 > >>> lower bound : 0.000, p = 4.6524e-08 > >>> upper bound : 1.000, p = 2.5566e-10 > >>> 95.0% CI : (0.485, 0.904) > >>> delta [Fix] : 1.000 > >>> > >>> Coefficients: > >>> Estimate Std. Error t value Pr(>|t|) > >>> (Intercept) -0.080099 0.610151 -0.1313 0.895825 > >>> log(AvgBrainWt) 0.483366 0.136694 3.5361 0.000622 *** > >>> --- > >>> Signif. codes: 0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 > >>> � � 1 > >>> > >>> Residual standard error: 0.1433 on 98 degrees of freedom > >>> Multiple R-squared: 0.1132, Adjusted R-squared: 0.1041 > >>> F-statistic: 12.5 on 2 and 98 DF, p-value: 1.457e-05 > >>> > >>> > >>> Brain size predicted by group size: > >>> > >>>> model.brain.by.group<-pgls(log(AvgBrainWt) ~ log(GroupSize), data = > >>>> primate_tom, lambda='ML') > >>>> summary(model.brain.by.group) > >>> > >>> Call: > >>> pgls(formula = log(AvgBrainWt) ~ log(GroupSize), data = primate_tom, > >>> lambda = "ML") > >>> > >>> Residuals: > >>> Min 1Q Median 3Q Max > >>> -0.38359 -0.08216 0.00902 0.05609 0.27443 > >>> > >>> Branch length transformations: > >>> > >>> kappa [Fix] : 1.000 > >>> lambda [ ML] : 1.000 > >>> lower bound : 0.000, p = < 2.22e-16 > >>> upper bound : 1.000, p = 1 > >>> 95.0% CI : (0.992, NA) > >>> delta [Fix] : 1.000 > >>> > >>> Coefficients: > >>> Estimate Std. Error t value Pr(>|t|) > >>> (Intercept) 2.740932 0.446943 6.1326 1.824e-08 *** > >>> log(GroupSize) 0.050780 0.043363 1.1710 0.2444 > >>> --- > >>> Signif. codes: 0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 > >>> � � 1 > >>> > >>> Residual standard error: 0.122 on 98 degrees of freedom > >>> Multiple R-squared: 0.0138, Adjusted R-squared: 0.003737 > >>> F-statistic: 1.371 on 2 and 98 DF, p-value: 0.2586 > >>> > >>> > >>> On Jul 14, 2013, at 6:18 AM, Emmanuel Paradis <emmanuel.para...@ird.fr> > >>> wrote: > >>> > >>>> Hi all, > >>>> > >>>> I would like to react a bit on this issue. > >>>> > >>>> Probably one problem is that the distinction "correlation vs. > >>>> regression" is not the same for independent data and for phylogenetic > >>>> data. > >>>> > >>>> Consider the case of independent observations first. Suppose we are > >>>> interested in the relationship y = b x + a, where x is an environmental > >>>> variable, say latitude. We can get estimates of b and a by moving to 10 > >>>> well-chosen locations, sampling 10 observations of y (they are > >>>> independent) and analyse the 100 data points with OLS. > >>> Here we cannot say anything about the correlation between x and y > >>> because we controlled the distribution of x. In practice, even if x is > >>> not controlled, this approach is still valid as long as the observations > >>> are independent. > >>>> > >>>> With phylogenetic data, x is not controlled if it is measured "on the > >>>> species" -- in other words it's an evolving trait (or intrinsic > >>>> variable). x may be controlled if it is measured "outside the species" > >>>> (extrinsic variable) such as latitude. So the case of using regression > >>>> or correlation is not the same than above. > >>> Combining intrinsic and extinsic variables has generated a lot of debate > >>> in the literature. > >>>> > >>>> I don't think it's a problem of using a method and not another, but > >>>> rather to use a method keeping in mind what it does (and its > >>>> assumptions). Apparently, Hansen and Bartoszek consider a range of > >>>> models including regression models where, by contrast to GLS, the > >>>> evolution of the predictors is modelled explicitly. > >>>> > >>>> If we want to progress in our knowledge on how evolution works, I think > >>>> we have to not limit ourselves to assess whether there is a > >>>> relationship, but to test more complex models. The case presented by Tom > >>>> is particularly relevant here (at least to me): testing whether group > >>>> size affects brain size or the opposite (or both) is an > >>> important question. There's been also a lot of debate whether > >>> comparative data can answer this question. Maybe what we need here is an > >>> approach based on simultaneous equations (aka structural equation > >>> models), but I'm not aware whether this exists in a phylogenetic > >>> framework. The approach by Hansen and Bartoszek could be a step in this > >>> direction. > >>>> > >>>> Best, > >>>> > >>>> Emmanuel > >>>> > >>>> Le 13/07/2013 02:59, Joe Felsenstein a �crit : > >>>>> > >>>>> Tom Schoenemann asked me: > >>>>> > >>>>>> With respect to your crankiness, is this the paper by Hansen that you > >>>>>> are referring to?: > >>>>>> > >>>>>> Bartoszek, K., Pienaar, J., Mostad, P., Andersson, S., & Hansen, T. F. > >>>>>> (2012). A phylogenetic comparative method for studying multivariate > >>>>>> adaptation. Journal of Theoretical Biology, 314(0), 204-215. > >>>>>> > >>>>>> I wrote Bartoszek to see if I could get his R code to try the method > >>>>>> mentioned in there. If I can figure out how to apply it to my data, > >>>>>> that will be great. I agree that it is clearly a mistake to assume one > >>>>>> variable is responding evolutionarily only to the current value of > >>>>>> the other (predictor variables). > >>>>> > >>>>> I'm glad to hear that *somebody* here thinks it is a mistake (because > >>>>> it really is). I keep mentioning it here, and Hansen has published > >>>>> extensively on it, but everyone keeps saying "Well, my friend used it, > >>>>> and he got tenure, so it must be OK". > >>>>> > >>>>> The paper I saw was this one: > >>>>> > >>>>> Hansen, Thomas F & Bartoszek, Krzysztof (2012). Interpreting the > >>>>> evolutionary regression: The interplay between observational and > >>>>> biological errors in phylogenetic comparative studies. Systematic > >>>>> Biology 61 (3): 413-425. ISSN 1063-5157. > >>>>> > >>>>> J.F. > >>>>> ---- > >>>>> Joe Felsenstein j...@gs.washington.edu > >>>>> Department of Genome Sciences and Department of Biology, > >>>>> University of Washington, Box 355065, Seattle, WA 98195-5065 USA > >>>>> > >>>>> _______________________________________________ > >>>>> R-sig-phylo mailing list - R-sig-phylo@r-project.org > >>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > >>>>> Searchable archive > >>>>> athttp://www.mail-archive.com/r-sig-phylo@r-project.org/ > >>>>> > >>> > >>> _________________________________________________ > >>> P. Thomas Schoenemann > >>> > >>> Associate Professor > >>> Department of Anthropology > >>> Cognitive Science Program > >>> Indiana University > >>> Bloomington, IN 47405 > >>> Phone: 812-855-8800 > >>> E-mail: t...@indiana.edu > >>> > >>> Open Research Scan Archive (ORSA) Co-Director > >>> Consulting Scholar > >>> Museum of Archaeology and Anthropology > >>> University of Pennsylvania > >>> > >>> http://www.indiana.edu/~brainevo > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> [[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/ > >> > > > > _________________________________________________ > > P. Thomas Schoenemann > > > > Associate Professor > > Department of Anthropology > > Cognitive Science Program > > Indiana University > > Bloomington, IN 47405 > > Phone: 812-855-8800 > > E-mail: t...@indiana.edu > > > > Open Research Scan Archive (ORSA) Co-Director > > Consulting Scholar > > Museum of Archaeology and Anthropology > > University of Pennsylvania > > > > http://www.indiana.edu/~brainevo > > > > > > > > > > > > > > > > > > > > > > > > [[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/ > > _________________________________________________ > P. Thomas Schoenemann > > Associate Professor > Department of Anthropology > Cognitive Science Program > Indiana University > Bloomington, IN 47405 > Phone: 812-855-8800 > E-mail: t...@indiana.edu > > Open Research Scan Archive (ORSA) Co-Director > Consulting Scholar > Museum of Archaeology and Anthropology > University of Pennsylvania > > http://www.indiana.edu/~brainevo > > > > > > > > > > > > [[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/ _________________________________________________ P. Thomas Schoenemann Associate Professor Department of Anthropology Cognitive Science Program Indiana University Bloomington, IN 47405 Phone: 812-855-8800 E-mail: t...@indiana.edu Open Research Scan Archive (ORSA) Co-Director Consulting Scholar Museum of Archaeology and Anthropology University of Pennsylvania http://www.indiana.edu/~brainevo [[alternative HTML version deleted]]
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