Hi,

>> Note that vcv(nonultrametric_tree, cor=TRUE) is different from
>> vcv(chronoMPL(nonultrametric_tree), cor = TRUE), which is relates to my
>> previous question (which one is preferred?)
> 
> It (mainly) depends whether you want to assume a "clock-like" evolution for 
> the traits you are studying.

Assuming that Sinichi is working with contemporaneous species, the assumption 
of comparative analyses is that the time available for phenotypic evolution 
(the off diagonal element of the VCV matrix) is the same for all species. The 
rate of phenotypic evolution may of course differ among species, but I think 
that this is not the same as allowing the expected change in the traits to 
depend on the branch lengths of a non-ultrametric tree, as would be the case in 
vcv(nonultrametric_tree, cor=TRUE). In such a case, a model allowing for 
variation in rate of trait evolution in conjunction with an ultrametric tree 
would be more appropriate. Of course, as pointed out by Brian, estimating 
divergence times is no piece of cake and there may be uncertainty associated 
with that step of phylogeny estimation as well.

Cheers

Alejandro

_______________________________________________
Dr Alejandro Gonzalez Voyer
Newton Advanced Fellow
Investigador Asociado C

Laboratorio de Conducta Animal
Instituto de Ecología
Circuito Exterior S/N
Ciudad Universitaria
Universidad Nacional Autónoma de México
México, D.F.
04510
México

Tel: +52 55 5622 9044
E-mail: alejandro.gonza...@iecologia.unam.mx

Lab website: www.alejandrogonzalezvoyer.com

> El 31/10/2016, a las 1:30 p.m., Emmanuel Paradis <emmanuel.para...@ird.fr> 
> escribió:
> 
> Le 30/10/2016 à 03:09, Shinichi Nakagawa a écrit :
>> Dear Emmanuel and Alejandro
>> 
>> Many thanks for your replies.
>> 
>> Emmanuel, I understand what you said if I use vcv(nonultrametric_tree,
>> cor=FALSE) in a phylogenetic comparative method (PCM). But if I use
>> vcv(nonultrametric_tree, cor=TRUE), isn't this the same as assuming a
>> ultrametric tree? I may be missing something here?
> 
> No, this is not necessarily the same thing since the off-diagonal elements of 
> the matrices may be different depending on how branch lenghts are changed by 
> chronoMPL (or other procedures you might use to make the tree ultrametric).
> 
>> Note that vcv(nonultrametric_tree, cor=TRUE) is different from
>> vcv(chronoMPL(nonultrametric_tree), cor = TRUE), which is relates to my
>> previous question (which one is preferred?)
> 
> It (mainly) depends whether you want to assume a "clock-like" evolution for 
> the traits you are studying.
> 
> Cheers,
> 
> Emmanuel
> 
>> Many thanks
>> 
>> Shinichi
>> 
>> On Sun, Oct 30, 2016 at 9:53 AM, Alejandro Gonzlaez Voyer
>> <alejandro.gonza...@iecologia.unam.mx
>> <mailto:alejandro.gonza...@iecologia.unam.mx>> wrote:
>> 
>>    Hi,
>> 
>>    I would venture in adding that with an additive tree the differences
>>    in evol rates among species are determined by the genes used to
>>    estimate the tree, given differences in substitution rates among
>>    genes. I do think its important to bear in mind.
>> 
>>    Cheers
>> 
>>    Alejandro
>> 
>>    Alejandro Gonzalez Voyer
>>    Instituto de Ecologia
>>    UNAM
>> 
>> 
>> 
>> 
>>    > On Oct 29, 2016, at 2:45 PM, Emmanuel Paradis
>>    <emmanuel.para...@ird.fr <mailto:emmanuel.para...@ird.fr>> wrote:
>>    >
>>    > Sure they are different. I forgot to mention that.
>>    >
>>    > In comparative analyses, the expected quantity of trait change (=
>>    the variance in the VCV matrix) is given by the product of the rate
>>    of evolution of the trait with branch length. So using a
>>    non-ultrametric tree is a way to assume different rates of evolution
>>    for each branch. With an ultrametric tree, you somehow assume a
>>    "clock-like" trait evolution (i.e., the quantity of change from the
>>    root of the tree to the tips is the same).
>>    >
>>    > BTW, the first command you give below should be (misplaced right
>>    parenthesis):
>>    >
>>    > vcv(chronoMPL(nonultrametric_tree), cor = TRUE)
>>    >
>>    > Best,
>>    >
>>    > Emmanuel
>>    >
>>    >> Le 29/10/2016 à 13:12, Shinichi Nakagawa a écrit :
>>    >> Dear  Emmanuel
>>    >>
>>    >> Many thanks for your swift reply.
>>    >>
>>    >> If we get a correlation matrix, via chronoMPL [i.e.
>>    >> vcv(chronoMPL(nonultrametric_tree,cor=T))], this correlation
>>    matrix is
>>    >> different from a correlation matrix obtained directly from vcv [i.e.
>>    >> vcv(nonultrametric_tree, cor=T)].
>>    >>
>>    >> Could you enlighten me about differences and why chronoMPL method
>>    might
>>    >> be preferred?
>>    >>
>>    >> Best wishes and thanks in advance.
>>    >>
>>    >> Shinichi
>>    >>
>>    >> On Sat, Oct 29, 2016 at 8:50 PM, Emmanuel Paradis
>>    >> <emmanuel.para...@ird.fr <mailto:emmanuel.para...@ird.fr>
>>    <mailto:emmanuel.para...@ird.fr <mailto:emmanuel.para...@ird.fr>>>
>>    wrote:
>>    >>
>>    >>    Dear Shinichi,
>>    >>
>>    >>    A fast solution is provided by the function chronoMPL in ape;
>>    it does
>>    >>    not require calibration points (see the references in the help
>>    page of
>>    >>    this function for the assumptions). The function chronos (also
>>    in ape)
>>    >>    is another possibility but it needs at least one calibration point
>>    >>    (though this can be fixed to unity at the root).
>>    >>
>>    >>    Note that a correlation matrix can be calculated from a
>>    non-ultrametric
>>    >>    tree: see the function vcv.
>>    >>
>>    >>    Best,
>>    >>
>>    >>    Emmanuel
>>    >>
>>    >>    Le 29/10/2016 à 05:26, Shinichi Nakagawa a écrit :
>>    >>    > Dear List
>>    >>    >
>>    >>    > We would like make several non-ultrametic trees (based on
>>    >>    molecular data;
>>    >>    > downloaded from treeBASE) into ultrametric trees using R. Could
>>    >>    you advice
>>    >>    > us what is the best and the most general way of doing this
>>    please?
>>    >>    >
>>    >>    > We would like to use resultant ultrametric trees in
>>    phyologenetic
>>    >>    > comparative analysis (by turning into correlation matrices).
>>    >>    >
>>    >>    > Best wishes,
>>    >>    >
>>    >>    > Shinichi Nakagawa
>>    >>    >
>>    >>    >       [[alternative HTML version deleted]]
>>    >>    >
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