For a reduced dataset (~2500 species) comparing
M1<-mvOU(tree, data, model="OU1", param=list(alpha="constraint",
sigma="constraint"))
M2<-mvOU(tree, data, model="OU1", param=list(decomp="symmetricPositive"))
I got the following parameters (both successfully converged)
M1$AIC
33842.8
M1$alpha
fem mal
fem 4.976388 0.0000000
mal 0.000000 0.1350497
M1$sigma
fem mal
fem 506.1483 0.00000
mal 0.0000 20.20244
####
$AIC
33008.37
M2$alpha
fem mal
fem 0.24784677 0.02521073
mal 0.02521073 0.13524606
M2$sigma
fem mal
fem 30.49145 16.77868
mal 16.77868 21.96677
So I haven't been getting negative values for the alpha matrix (although
they are not allowed in M2 correct?)
The huge value in the M1$sigma is a bit strange to me. Maybe Julien's
suggestion of only constraining the alpha matrix would be helpful and give
more reasonable parameters?
One of the reasons I was thinking about negative off-diagonal alpha values
is that there is a theoretical expectation that selection on male
ornamentation will drag female values higher than their optima, and
selection for drabness in females will drag male values lower than their
optima. I thought this might come out as a negative value in the alpha
matrix, but it seems like it is more correct to think about the offdiagonal
values as dragging the one trait toward's the other trait's optima, so that
a positive value would be expected in both cases (females getting dragged
up, males getting dragged down).
Cody
__________________________________________________________________
Cody Dey
codyj...@gmail.com
On Wed, May 6, 2015 at 1:27 PM, Aaron King <kin...@umich.edu> wrote:
> and even more strange are the complex eigenvalues. I imagine
> significantly negative eigenvalues of the alpha matrix must be interpreted
> as evidence for disruptive selection, but I see the potential for issues of
> identifiability that have the potential to complicate the interpretation....
>
> What eigenvalues are you getting in your estimations so far? Or have none
> of them yet succeeded?
>
> A.
>
> On Wed, May 6, 2015 at 10:36 AM, Julien Clavel <julien.cla...@hotmail.fr>
> wrote:
>
>> Hi Cody,
>>
>> I remember a similar discussion with Aaron some time ago. It seems
>> difficult to interpret negative eigenvalues in the multivariate
>> Ornstein-Uhlenbeck process, excepted maybe in some particular situations.
>> Adaptation should result in positive values. Krzysztof Bartoszek writes a
>> bit on it and possible interpretations in terms of character displacement
>> or repulsion between traits (Bartoszek et al. 2012 - J. Theor. Biol.).
>>
>> Maybe Aaron have more idea on it?
>>
>> Julien
>>
>> ------------------------------
>> Date: Wed, 6 May 2015 10:10:10 -0400
>> Subject: Re: [R-sig-phylo] Off-diagonal elements in multivariate OU
>> evolution
>> From: codyj...@gmail.com
>> To: julien.cla...@hotmail.fr
>> CC: kin...@umich.edu; r-sig-phylo@r-project.org
>>
>>
>> Hi Julien and Aaron,
>>
>> Thank to you both for your suggestions.
>>
>> Julien, yes I think that is more what I am interested in, but I was
>> (probably incorrectly) worried that an unconstrained sigma matrix might
>> scoop up some of the signal that is actually due to an interaction in
>> 'selection', and would therefore appear to be a good model.
>>
>> Do decomp="diagonal" and decomp="diagonalPositive" have different
>> biological interpretations? What do negative values in the alpha matrix
>> mean?
>>
>>
>>
>> __________________________________________________________________
>>
>> Cody Dey
>> codyj...@gmail.com
>>
>> On Wed, May 6, 2015 at 9:51 AM, Julien Clavel <julien.cla...@hotmail.fr>
>> wrote:
>>
>> Hi Cody,
>>
>> Maybe in your case you are rather interested in testing whether there is
>> significant interaction in the "selection" strength (i.e. you constrain the
>> alpha matrix but not the sigma matrix) than testing for significant
>> correlations between traits?
>>
>> e.g.
>>
>> mvOU(tree, data, model="OU1", param=list(decomp="diagonal"))
>>
>> vs.
>>
>> mvOU(tree, data, model="OU1", param=list(decomp="symmetricPositive"))
>>
>> Best,
>>
>> Julien
>>
>> > Date: Wed, 6 May 2015 08:41:04 -0400
>> > From: codyj...@gmail.com
>> > To: kin...@umich.edu
>> > CC: r-sig-phylo@r-project.org
>> > Subject: Re: [R-sig-phylo] Off-diagonal elements in multivariate OU
>> evolution
>> >
>> > Hi Aaron and Julien,
>> >
>> > Thanks for the responses. I will try different methods for computing the
>> > log-likelihood and will report back on the list (they take a while to
>> > run...).
>> >
>> > The traits are a continuous plumage ornamentation score for male and
>> female
>> > passerines. They way they are calculated is a bit complicated, but they
>> > have approximately the same mean and variances, and both have a maximum
>> > value of 100.
>> >
>> > A scatterplot fills in most of the space above the 1:1 line (i.e. males
>> are
>> > almost always more ornamented than females, but all other combinations
>> are
>> > possible albeit with different densities) and there is a correlation in
>> the
>> > raw data of R2 ~ 0.28
>> >
>> > My goal is to test whether there are cross-sex genetic constraints that
>> > limit the independent evolution of male and female ornamentation, and
>> then
>> > in other analyses look at sex-specific responses to different ecological
>> > factors. It seems obvious to me that there is co-evolution of male and
>> > female ornamentation given the correlation between the sexes (in the raw
>> > data) and my knowledge of the system, but it would be nice to show this
>> > statistically.
>> >
>> > Cody
>> >
>> >
>> >
>> > __________________________________________________________________
>> >
>> > Cody Dey
>> > codyj...@gmail.com
>> >
>> > On Wed, May 6, 2015 at 7:00 AM, Aaron King <kin...@umich.edu> wrote:
>> >
>> > > Cody,
>> > >
>> > > Have you taken care to scale your data so that they have
>> approximately the
>> > > same means and variances? Sometimes numerical issues arise due to a
>> > > mismatch of scales? What are your variables? If you plot one against
>> the
>> > > other, what do you see?
>> > >
>> > > Regarding the interpretations: a good deal depends on just what the
>> > > variables are. The conclusion: significant off-diagonal elements ->
>> > > coevolution is overly simplistic, but that is the general idea, yes.
>> > >
>> > > Aaron
>> > >
>> > > On Tue, May 5, 2015 at 5:17 PM, Cody Dey <codyj...@gmail.com> wrote:
>> > >
>> > >> Hi all,
>> > >>
>> > >> I have a large dataset (~6000 species) including two traits of
>> interest. I
>> > >> am hoping to test whether the extant patterns are more consistent
>> with
>> > >> each
>> > >> trait evolving independently under OU processes (with 1 regime per
>> trait)
>> > >> or if the traits have co-evolved in some manner (i.e. the traits
>> influence
>> > >> one another's optima).
>> > >>
>> > >> I have been trying to use mvMORPH and mvSLOUCH to fit two models
>> (one of
>> > >> independent evolution, and one of dependent evolution) using the code
>> > >> below. My plan was then to compare AIC values from the two models.
>> From
>> > >> what I gather, the off-diagonal elements of the alpha and sigma
>> matrix
>> > >> determine whether there is co-evolution of the trait optima, and the
>> > >> stochastic element of the OU processes, respectively.
>> > >>
>> > >> ##in mvMORPH
>> > >>
>> > >> independ.evolv<-mvOU(tree, data, model="OU1",
>> > >> param=list(alpha="constraint", sigma="constraint"))
>> > >> depend.evolv<-mvOU(tree, data, model="OU1", param=list(alpha=NULL,
>> > >> sigma=NULL))
>> > >>
>> > >> ##and a similar thing in mvSLOUCH
>> > >> independ.evolv<-ouchModel(tree, data, regimes=NULL, Atype="Diagonal",
>> > >> Syytype="Diagonal")
>> > >> depend.evolv<-ouchModel(tree, data, regimes=NULL,
>> > >> Atype="DecomposableReal",
>> > >> Syytype="UpperTri")
>> > >>
>> > >> My questions are:
>> > >>
>> > >> 1. Is my interpretation of these models correct? Specifically I am
>> > >> concerned about the interpretation of the alpha matrix. I am somewhat
>> > >> confused as to how the off-diagonal alpha elements influence the OU
>> > >> process
>> > >> when I have specified 1 regime per trait.
>> > >>
>> > >> 2. I am frequently encountering errors during model fitting in
>> mvMORPH of
>> > >> the type"Error in loglik_mvmorph(dat, matEstim$V, matEstim$W, n, p,
>> error
>> > >> =
>> > >> error, : the leading minor of order 5833 is not positive definite". I
>> > >> gather this has to do with a problem in the matrix decomposition,
>> but is
>> > >> there a practical solution? I have tried some of the other 'decomp'
>> > >> options but this does not seem to help.
>> > >>
>> > >> 3. I had a few emails with Krzysztof Bartoszek (author of mvSLOUCH)
>> and he
>> > >> suggested that such a large dataset would be problematic. Would this
>> be an
>> > >> issue for mvMORPH as well? If so, is there a generally acceptable
>> > >> work-around for reducing the size of comparative data sets to
>> accommodate
>> > >> models like this?
>> > >>
>> > >> Many thanks in advance
>> > >>
>> > >>
>> > >>
>> ____________________________________________________________________________
>> > >>
>> > >> Cody Dey
>> > >> codyj...@gmail.com
>> > >> McMaster University
>> > >> Department of Biology
>> > >>
>> > >> [[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/
>> > >>
>> > >
>> > >
>> > >
>> > > --
>> > > Aaron A. King, Ph.D.
>> > > Ecology & Evolutionary Biology
>> > > Mathematics
>> > > Center for the Study of Complex Systems
>> > > University of Michigan
>> > > GPG Public Key: 0x15780975
>> > >
>> >
>> > [[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/
>>
>>
>>
>
>
> --
> Aaron A. King, Ph.D.
> Ecology & Evolutionary Biology
> Mathematics
> Center for the Study of Complex Systems
> University of Michigan
> GPG Public Key: 0x15780975
>
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