So I tried a 12-taxon fully pectinate tree with Blomberg's K as calculated
by picante::Kcalc()

library(picante)
library(ape)
aa<-"(A,(B,(C,(D,(E,(F,(G,(H,(I,(J,(K,L)))))))))));"
t1<-read.tree(text=aa)
t4 <- compute.brlen(t1,method="Grafen",1)
tipvals <- c(0,1,0,1,0,1,0,1,0,1,0,1)
Kcalc(tipvals,t4)

K = 0.3487135


There are possible 924 permutations of 6 'painted' tips from 000000111111
to 111111000000 (each of those two extreme distributions gives the maximum
value of K for this particular tree & number [6] of painted tips: 2.37703)

There are 336 discrete integer value results of K for this tree, and
painting 6 tips:

Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
 0.3438  0.3676  0.4489  0.5332  0.5945  2.3770


A histogram of all 924 possible values of K (for 6 painted tips) shows that
Blomberg's K in terms of value distribution is extremely positively skewed
(it has a skewness of 2.671139), which is great if you're looking to test
phylogenetic signal without false positives, but not so great if you're
trying to assess "evenness" at the other tail of the distribution. In the
case of this exact tree, because I've enumerated all possible permutations
of 6 painted tips, I can calculate the 5% significance threshold as values
of K that are 0.3480158 or less.  It seems some normalisation procedure
might be needed before safely using Blomberg's K to assess the significance
of evenness, if one is not going to exhaustively examine/enumerate all
possible values (which I can't do for a 1000+ tip tree).

Does that make sense?

Certainly interesting...


Ross








On 14 March 2017 at 14:53, Ross Mounce <ross.mou...@gmail.com> wrote:

> Thanks Dave,
>
> I'll try Blomberg's K with small simulated fully-bifurcating trees of
> simple shape (e.g. fully pectinate), where I can easily paint the tips
> myself in what I believe to be a "maximally stratified manner" e.g.
> 010101010 to see if Blomberg's K does actually reach minimum (i.e. 0.00000
> ?) for such a distribution. If it does, great! This is the measure I need.
>
> I still wonder though, for a complex tree structure in terms of
> balance/shape somewhere intermediate between fully balanced and fully
> pectinate; how does one arrive empirically at _the_ most optimal
> stratified/even sampling ('painting') of tips if say only 25% of tips
> are/can be 'painted'. I guess a lot depends on how one defines what 'even
> sampling' on a phylogeny actually is, does it include branch lengths et
> cetera...
>
> I'll give it a try anyway,
>
> Thanks again,
>
> Ross
>
>
> On 14 March 2017 at 14:33, David Bapst <dwba...@gmail.com> wrote:
>
>> Ross,
>>
>> An interesting question. I understand it as that you want to test if
>> the trait is overdispersed relative to phylogeny, which still makes me
>> think that measures of 'phylogenetic signal' might be still be useful,
>> even though the typical interpretation is 'signal' as 'heritability'.
>> I would try some toy examples with smallish trees and artificial data
>> and play with different signal measures; particularly your idea
>> regarding that the variance is high at the level of closest
>> relatedness suggests that you perhaps should investigate Blomberg's K
>> as a measure, rather than Pagel's lambda:
>>
>> Blomberg, S. P., T. Garland, and A. R. Ives. 2003. Testing for
>> phylogenetic signal in comparative data: behavioral traits are more
>> labile. Evolution 57.
>>
>> However, your soft polytomies are worrisome; I suggest using the MPT
>> or posterior tree sample, if such exists, or considering resolving
>> those polytomies somehow.
>>
>> Cheers,
>> -Dave
>>
>> On Tue, Mar 14, 2017 at 5:45 AM, Ross Mounce <ross.mou...@gmail.com>
>> wrote:
>> > Hi all,
>> >
>> > I'm interested in the distribution of a non-heritable binary
>> > trait/observation across a large tree 1000+ tip tree. The tree is
>> > non-distinct in shape and balance, it is neither fully pectinate nor
>> fully
>> > balanced. It has many soft polytomies too.
>> >
>> > I believe the distribution of this trait to be significantly stratified
>> > such that just for the sake of explanation, every other tip is "present"
>> > for the trait. So essentially I'm interested in testing the evenness of
>> > distribution of "present" tips across the tree.
>> >
>> > In this instance it doesn't seem to me that I should be testing for
>> > "phylogenetic signal" or using models that do that, nor am I testing the
>> > randomicity of distribution of the trait.
>> > Specifically, I want to test if the observed distribution is
>> significantly
>> > close to "perfect" stratification for the given number of "presences"
>> > (which is ~33% of the tips of the tree), on the given fixed tree shape.
>> >
>> > TL;DR
>> >
>> > How can I meaningfully test the evenness of the distribution of a binary
>> > trait across a tree, with R?
>> >
>> >
>> > Any ideas?
>> >
>> > Thanks,
>> >
>> > Ross
>> >
>> >
>> > --
>> > --
>> > -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/
>> -/-/-/-/-/-/-/-
>> > Ross Mounce, PhD
>> > Software Sustainability Institute Fellow
>> > Dept. of Plant Sciences, University of Cambridge
>> > www.rossmounce.co.uk <http://rossmounce.co.uk/>
>> > -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/
>> -/-/-/-/-/-/-/-
>> >
>> >         [[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-ph...@r-project.org/
>>
>>
>>
>> --
>> David W. Bapst, PhD
>> Adjunct Asst. Professor, Geology and Geol. Eng.
>> South Dakota School of Mines and Technology
>> 501 E. St. Joseph
>> Rapid City, SD 57701
>>
>> http://webpages.sdsmt.edu/~dbapst/
>> http://cran.r-project.org/web/packages/paleotree/index.html
>>
>
>
>
> --
> --
> -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-
> /-/-
> Ross Mounce, PhD
> Software Sustainability Institute Fellow 2016
> Dept. of Plant Sciences, University of Cambridge
> www.rossmounce.co.uk <http://rossmounce.co.uk/>
> -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-
> /-/-
>



-- 
-- 
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-
Ross Mounce, PhD
Software Sustainability Institute Fellow 2016
Dept. of Plant Sciences, University of Cambridge
www.rossmounce.co.uk <http://rossmounce.co.uk/>
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-

        [[alternative HTML version deleted]]

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