Hi All,
Just a follow up on this. I was thinking about what Liam suggested, and
I think it's a different test to what I suggested, but maybe I'm wrong.
In particular, Liam's using squared contrasts in y, so that's asking
whether the absolute size of changes in y depends on x at the ancestral
node. I might have missed something here, but that sounds very similar
in principle to Freckleton's test of whether the variance of trait
differences is unrelated to their absolute values [1], except that the
latter looks for correlations between the absolute value of differences
in x versus x at the ancestral node. It might be useful to consult that
paper [1] to get some more ideas for how to interpret those kinds of
results.
However, I think that this test is not quite the same as asking whether
the rate of evolution of y depends on x. For example, it's possible you
could (correctly) see a relationship with Liam's test even if there was
no relationship between the rate of evolution of y and x - as long as
larger ancestral x's produce higher variance in y, then Liam's test will
reveal a relationship. But the direction of the effect of x on the rate
of y could still be completely randomly assigned among datapoints (that
information disappears when squaring the y's).
Not sure if I'm just confused here. Any thoughts?
Rob
On 16 March 2013 09:30, john d <[email protected]
<mailto:[email protected]>> wrote:
Thank you all for your ideas. I'll probably explore further Liam's
method.
sincerely,
john
On Tue, Mar 12, 2013 at 5:33 PM, Liam J. Revell <[email protected]
<mailto:[email protected]>> wrote:
> I did a little further exploration of this proposed "method" -
the results &
> discussion are here:
>
http://blog.phytools.org/2013/03/investigating-whether-rate-of-one.html
>
> Maybe this will be of some help in deciding the best approach to
go forward
> with.
>
>
> All the best, Liam
>
> Liam J. Revell, Assistant Professor of Biology
> University of Massachusetts Boston
> web: http://faculty.umb.edu/liam.revell/
> email: [email protected] <mailto:[email protected]>
> blog: http://blog.phytools.org
>
> On 3/11/2013 6:03 PM, Liam J. Revell wrote:
>>
>> Hi John & Matt.
>>
>> What about the admittedly ad hoc approach of computing the
correlation
>> between the states at ancestral nodes for x & the squared
contrasts for
>> corresponding nodes for y? Then you can generate a null
distribution for
>> the test statistic (say, a Pearson or Spearman rank correlation) by
>> simulation. This seems to give reasonable type I error when the
null is
>> correct, and when I simulate under the alternative (i.e., the
rate of
>> Brownian evolution along a branch depends on the state at the
>> originating node) it sometimes is significant.
>>
>> Here's a function that does what I've described (I think -
please check
>> it carefully!). It needs phytools and all dependencies.
>>
>>
ratebystate<-function(tree,x,y,nsim=100,method=c("pearson","spearman")){
>> method<-method[1]
>> if(!is.binary.tree(tree)) tree<-multi2di(tree)
>> V<-phyl.vcv(cbind(x,y),vcv(tree),lambda=1)$R
>> a<-fastAnc(tree,x)
>> b<-pic(y,tree)[names(a)]^2
>> r<-cor(a,b,method=method)
>> beta<-setNames(lm(b~a)$coefficients[2],NULL)
>> foo<-function(tree,V){
>> XY<-sim.corrs(tree,V)
>> a<-fastAnc(tree,XY[,1])
>> b<-pic(XY[,2],tree)[names(a)]^2
>> r<-cor(a,b,method=method)
>> return(r)
>> }
>> r.null<-c(r,replicate(nsim-1,foo(tree,V)))
>> P<-mean(abs(r.null)>=abs(r))
>> return(list(beta=beta,r=r,P=P,method=method))
>> }
>>
>> Perhaps this is a good idea. I don't know. All the best, Liam
>>
>> Liam J. Revell, Assistant Professor of Biology
>> University of Massachusetts Boston
>> web: http://faculty.umb.edu/liam.revell/
>> email: [email protected] <mailto:[email protected]>
>> blog: http://blog.phytools.org
>>
>> On 3/11/2013 4:03 PM, Matt Pennell wrote:
>>>
>>> John,
>>>
>>> This is a tricky question. If your independent variables were
>>> discrete, you
>>> could use a stochastic character mapping approach to map "state
regimes"
>>> onto your tree and ask whether the regimes had different rates
using a
>>> model selection approach. (This could be done with the R packages
>>> phytools
>>> or ouwie, depending on what models of trait evolution you are
>>> interested in
>>> investigating).
>>>
>>> However, since your independent variables are continuous, there
is no
>>> equivalent of the stochastic mapping approach to answer this
question. As
>>> far as I am aware, no model-based framework exists to address your
>>> question
>>> (sorry that to be a downer). One could conceivably derive such
a model
>>> following Rich Fitzjohn's approach in QuaSSE (Sys Bio 2010) but
>>> instead of
>>> the rate of speciation/extinction depending on the state of the
>>> continuous
>>> variable, let the rate of a second variable be a function of
the state of
>>> the first. But this would certainly be a lot of effort to
accomplish.
>>>
>>> I agree with you as I do not think getting rates from standardized
>>> independent contrasts (sensu Garland 1992) will really allow you to
>>> get at
>>> your question.
>>>
>>> the TL;DR version is that no such method exists (at least to my
>>> knowledge)
>>> but this would definitely be a useful innovation.
>>>
>>> hope this was at least somewhat helpful.
>>>
>>> cheers,
>>> matt
>>>
>>>
>>>
>>>
>>> On Mon, Mar 11, 2013 at 12:50 PM, john d <[email protected]
<mailto:[email protected]>> wrote:
>>>
>>>> Dear colleagues,
>>>>
>>>> I got a philosophical/methodological/practical question.
>>>>
>>>> I have a continuous dependent variable (e.g. range size) and a few
>>>> "independent" variables (e.g. body mass, encephalization
ratio), and I
>>>> want to test how the rate of evolution of the dependent
variable is
>>>> affected by the independent variables. The PCMs that I'm
familiar with
>>>> cannot be used to answer this question, because they usually
try to
>>>> predict the dependent variable based on the independent variables
>>>> (e.g. PGLM) instead of looking at the rates of evolution. The
whole
>>>> thing gets tricky if one decides to deal with the rates of
evolution
>>>> of the indepentent variables as well (or not).
>>>>
>>>> I guess one possibility would be to use standardized independent
>>>> contrasts (as in Garland 1992) for the estimation of rates.
But I'm
>>>> not sure how to try to predict the *rate* of evolution of
range size
>>>> from the values of the "independent" variables (and not their own
>>>> rates, which is what I guess I'd get if I transformed all
variables
>>>> into standardized contrasts).
>>>>
>>>> Any thoughts?
>>>>
>>>> John
>>>>
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>>>
>>> [[alternative HTML version deleted]]
>>>
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>>
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Research Fellow,
Ecology, Evolution, and Genetics,
Research School of Biology,
Australian National University
phone: +61 (0)2 6125 3611
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