Re: [R-sig-phylo] units of sigsq
Aloha all, Well if all youʻre doing is plotting data, then sure, you can have a change of axes and something in g will still be in g with log-transformed axes. But does this apply to fitting models of BM or OU? The model is assuming that the "errors" or the small jumps in phenotype comes from a normal distribution. So by fitting a model on log-transformed data will assume that those changes come from a different distribution, on log(g). This has potentially deep implications, suggesting that the magnitude of the changes in the original scale would be larger for large values of g that for small values of g when on a log-scale. That would imply basically that itʻs easier to get a lot larger or a lot smaller in a single step if youʻre already big. This might make sense especially for genome size evolution, for example, where big changes in size arise by chromosomal duplication or transposable element activity, etc. Anyway, log-transformation is commonly applied to biological data. As for the units of time, yes I agree with Joe - it is the units that the depth of the tree is in. If it is time calibrated, then it is time. Otherwise it is generally mutations per branch length. Marguerite On Fri, Mar 19, 2021 at 2:20 PM Joe Felsenstein wrote: > Marguerite asked: > > > First - Joe - what do you mean by log(grams) has no units? The units of > grams is a unit, so log(mass) will have units of log-gm. As log is not the > same as 1/gm, log(gm) cannot be unit-free. > > I looked it up on Wikipedia, and was assured by it that Marguerite is > right, log(weight) has the same units as weight, except you're > supposed to call them log-gm. > > > I do think that unless there is a calibration with time, the tree > branch lengths are not in units of time but in units of base > substitutions per site. > > And I remain confused on what the units are, if you compute a linear > combination such as 2 log(wt) - 3 log(height). Which princip[al, le] > components machinery does. > > Joe > -- > Joe Felsenstein felse...@gmail.com, j...@gs.washington.edu > Department of Genome Sciences and Department of Biology, > University of Washington, Box 355065, Seattle, WA 98195-5065 USA > -- Marguerite A. Butler Professor Department of Biology 2538 McCarthy Mall, Edmondson Hall 216 Honolulu, HI 96822 Office: 808-956-4713 Dept: 808-956-8617 Lab: 808-956-5867 FAX: 808-956-4745 http://butlerlab.org http://manoa.hawaii.edu/biology/people/marguerite-butler http://www2.hawaii.edu/~mbutler [[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/
Re: [R-sig-phylo] units of sigsq
Marguerite asked: > First - Joe - what do you mean by log(grams) has no units? The units of grams > is a unit, so log(mass) will have units of log-gm. As log is not the same as > 1/gm, log(gm) cannot be unit-free. I looked it up on Wikipedia, and was assured by it that Marguerite is right, log(weight) has the same units as weight, except you're supposed to call them log-gm. I do think that unless there is a calibration with time, the tree branch lengths are not in units of time but in units of base substitutions per site. And I remain confused on what the units are, if you compute a linear combination such as 2 log(wt) - 3 log(height). Which princip[al, le] components machinery does. Joe -- Joe Felsenstein felse...@gmail.com, 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 at http://www.mail-archive.com/r-sig-phylo@r-project.org/
Re: [R-sig-phylo] units of sigsq
(log(g)^2)/MY: it�s about the accumulation of variance with time, and variance has units squared. And please don�t apologize for the question. You only have it because we as a field have been sloppy about not including units with our measurements in papers (I�m guilty of this, too). So it�s great that you�re doing the right thing and asking for help to do so. Best, Brian ___ Brian O'Meara Professor, Dept. of Ecology & Evolutionary Biology, UT Knoxville Acting Co-Head, Dept. of Ecology & Evolutionary Biology, UT Knoxville President-Elect, Society of Systematic Biologists He/Him/His From: R-sig-phylo on behalf of Karla Shikev Date: Friday, March 19, 2021 at 2:12 PM To: R Sig Phylo Listserv Subject: [R-sig-phylo] units of sigsq Dear all, Please indulge me in a simple (newbie) question. If I have a continuous trait (log(body size in g)) and a calibrated tree and use fitContinuous to estimate sigsq using a BM model, what is the unit of the siqsq estimate? log(g)/My? Thanks for your patience, Karla [[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/
Re: [R-sig-phylo] units of sigsq
Aloha all, Iʻm still reeling from the Atlanta murders and the rise of hate in general, so I may not be thinking straight, but if weʻre talking about Brownian motion, Iʻm not sure this is quite right. If the trait is log(grams) then the trait is unit-free. > First - Joe - what do you mean by log(grams) has no units? The units of grams is a unit, so log(mass) will have units of log-gm. As log is not the same as 1/gm, log(gm) cannot be unit-free. > The "time" > is probably branch length from a phylogeny. That in turn (from DNA > data) is usually DNA substitutions per site. > > So the units of the standard deviation aresites per substitution. > But this is not the standard deviation, it is its square. > > So (wait for it ...)square sites per square substitution > We worked out the units of BM and OU parameters in Cressler et al (2015). We parameterized it this way. If we have a trait X evolving under a Brownian motion, we can write the change in X per unit time as: dX(t) = sigma*dB(t) Where dX(t) (the change in X) will have the same units as X (in this case log-gm). and dB or a draw from the white noise distribution has units of time to the 1/2 power. Therefore sigma must have units of trait*time^(-1/2), and sigma^2 would have units of trait^2/time, or we will not obtain the correct units for X. Ted - yes, I agree with Joe - the matrix version of sigma and sigma^2 on a element-by-element basis will have the same units as the univariate case, except that you will have to substitute the units of each trait, as appropriate, if they are measured in different units. Marguerite > So (wait for it ...)square sites per square substitution > > Now that is pretty weird. But years ago people pointed out to me that > quantitative geneticists were accustomed to inferring variance > components of crop yield. The yield might be in bushels per acre. > So the units of its variance was: square bushels per square acre. > Don't even try to think about how you square a bushel, or how many > dimensions you have to go into to square an acre. Actually, you can > think about them: a bushel is three-dimensional volume, and an acre is > two dimensional area. So crop yield has units of meters, and > variance of crop yield should have units of square meters. > > That way lies madness ... > > Joe > - > Joe Felsenstein felse...@gmail.com, 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 at > http://www.mail-archive.com/r-sig-phylo@r-project.org/ > -- Marguerite A. Butler Professor Department of Biology 2538 McCarthy Mall, Edmondson Hall 216 Honolulu, HI 96822 Office: 808-956-4713 Dept: 808-956-8617 Lab: 808-956-5867 FAX: 808-956-4745 http://butlerlab.org http://manoa.hawaii.edu/biology/people/marguerite-butler http://www2.hawaii.edu/~mbutler [[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/
Re: [R-sig-phylo] units of sigsq
Ted Garland asked: OK, Joe, that's for one trait at a time. > Would you please continue your discourse, but extend to multiple traits > and their covariances > OK, assuming that’s not a joke which it seems it was. If all characters are log of something, their variances all have units of sites squared per square substitution. But if you have different units in different characters each variance would have units. (CharXunit) squared times sites-squared per square substitution. A covariance would be (CharXunit times CharYunit) times sites squared per square substitution. If you had a principal component (usually misnamed a “principle” component) it is in terms of a linear combination of characters, and I am deeply puzzled how to give their units as they mix them. Joe -- Joe Felsenstein felse...@gmail.com, j...@gs.washington.edu Department of Genome Sciences and Department of Biology, University of Washington, Box 355065, Seattle, WA 98195-5065 USA [[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/
Re: [R-sig-phylo] units of sigsq
OK, Joe, that's for one trait at a time. Would you please continue your discourse, but extend to multiple traits and their covariances? Many thanks, Ted P.S - What's the emoji for tongue in cheek? I don't see a great one, but here's an emoticon: :-J On Fri, Mar 19, 2021 at 1:08 PM Joe Felsenstein wrote: > Folks -- > > If the trait is log(grams) then the trait is unit-free. The "time" > is probably branch length from a phylogeny. That in turn (from DNA > data) is usually DNA substitutions per site. > > So the units of the standard deviation aresites per substitution. > But this is not the standard deviation, it is its square. > > So (wait for it ...)square sites per square substitution > > Now that is pretty weird. But years ago people pointed out to me that > quantitative geneticists were accustomed to inferring variance > components of crop yield. The yield might be in bushels per acre. > So the units of its variance was: square bushels per square acre. > Don't even try to think about how you square a bushel, or how many > dimensions you have to go into to square an acre. Actually, you can > think about them: a bushel is three-dimensional volume, and an acre is > two dimensional area. So crop yield has units of meters, and > variance of crop yield should have units of square meters. > > That way lies madness ... > > Joe > - > Joe Felsenstein felse...@gmail.com, 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 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/
Re: [R-sig-phylo] units of sigsq
Folks -- If the trait is log(grams) then the trait is unit-free. The "time" is probably branch length from a phylogeny. That in turn (from DNA data) is usually DNA substitutions per site. So the units of the standard deviation aresites per substitution. But this is not the standard deviation, it is its square. So (wait for it ...)square sites per square substitution Now that is pretty weird. But years ago people pointed out to me that quantitative geneticists were accustomed to inferring variance components of crop yield. The yield might be in bushels per acre. So the units of its variance was: square bushels per square acre. Don't even try to think about how you square a bushel, or how many dimensions you have to go into to square an acre. Actually, you can think about them: a bushel is three-dimensional volume, and an acre is two dimensional area. So crop yield has units of meters, and variance of crop yield should have units of square meters. That way lies madness ... Joe - Joe Felsenstein felse...@gmail.com, 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 at http://www.mail-archive.com/r-sig-phylo@r-project.org/
Re: [R-sig-phylo] units of sigsq
Great! thanks, Florian! On Fri, Mar 19, 2021 at 4:45 PM Florian Boucher wrote: > Hi Karla, > > you're almost right, but since sigsq is the variance of the random walk > per unit time its unit is actually [unit of the trait]^2/[unit of time] > > Cheers, > Florian > > Le ven. 19 mars 2021 à 19:12, Karla Shikev a > écrit : > >> Dear all, >> >> Please indulge me in a simple (newbie) question. >> >> If I have a continuous trait (log(body size in g)) and a calibrated tree >> and use fitContinuous to estimate sigsq using a BM model, what is the unit >> of the siqsq estimate? log(g)/My? >> >> Thanks for your patience, >> >> Karla >> >> [[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/
Re: [R-sig-phylo] units of sigsq
Hi Karla, you're almost right, but since sigsq is the variance of the random walk per unit time its unit is actually [unit of the trait]^2/[unit of time] Cheers, Florian Le ven. 19 mars 2021 à 19:12, Karla Shikev a écrit : > Dear all, > > Please indulge me in a simple (newbie) question. > > If I have a continuous trait (log(body size in g)) and a calibrated tree > and use fitContinuous to estimate sigsq using a BM model, what is the unit > of the siqsq estimate? log(g)/My? > > Thanks for your patience, > > Karla > > [[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/
[R-sig-phylo] units of sigsq
Dear all, Please indulge me in a simple (newbie) question. If I have a continuous trait (log(body size in g)) and a calibrated tree and use fitContinuous to estimate sigsq using a BM model, what is the unit of the siqsq estimate? log(g)/My? Thanks for your patience, Karla [[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/
