Just to add a little to this discussion, Luke Harmon suggested to me
off-list that adding arbitrarily short terminal branches to the tree
might perhaps *guarantee* a significant result. Indeed this seems like
it could be the case. For instance, try running the following code for
smaller (or larger) values of "tiny.edge." [Comments give you an idea
of what's being done.] - Liam
require(geiger)
# how long is your "tiny edge?"
tiny.edge<-0.0001
# is there error in measuring tip species
error.variance<-0.01
# create balanced tree
tree<-stree(n=32,type="balanced")
# create branch lengths
tree$edge.length<-rep(1,62)
# set all terminal branch lengths to zero
tree$edge.length[tree$edge[,2]<=32]<-0
# simulate and add a little random error
y<-sim.char(tree,as.matrix(1))[,,1]+sqrt(error.variance)*rnorm(32)
# create a factor
x<-as.factor(rep(c(0,1),16)); names(x)<-names(y)
# add a tiny little bit to the terminal edges
tree$edge.length[tree$edge[,2]<=32]<-tiny.edge
# compute phylogenetic anova
phy.anova(tree,y,x)
--
Liam J. Revell
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: liam.rev...@umb.edu
blog: http://phytools.blogspot.com
On 3/17/2011 5:32 PM, tgarl...@ucr.edu wrote:
Dear Daniel,
OK, then I think your results make sense. You have, in fact, designed
a comparative study in which the power to detect a statistical effect of
Habitat (i.e., a group difference) will be higher if analyzed phylogenetically
than if analyzed in the conventional fashion assuming a stat phylogeny. This
point has been made in various places, including:
Garland, T., Jr., A. W. Dickerman, C. M. Janis, and J. A. Jones. 1993.
Phylogenetic analysis of covariance by computer simulation. Systematic Biology
42:265-292.
Vanhooydonck, B., and R. Van Damme. 1999. Evolutionary relationships between
body shape and habitat use in lacertid lizards. Evolutionary Ecology Research
1:785-805.
Garland, T., Jr. 2001. Phylogenetic comparison and artificial selection: two
approaches in evolutionary physiology. Pages 107-132 in R. C. Roach, P. D.
Wagner, and P. H. Hackett, eds. Hypoxia: From Genes to the Bedside. Advances in
Experimental Biology and Medicine, volume 502. Kluwer Academic/Plenum
Publishers, New York.
In addition, you have made the within-species (and hence between
habitat) branch lengths arbitrarily very short relative to the among-species
branches in the rest f your tree. Hence, if you do have a Habitat effect, it
would be very unlikely to have occurred via Brownian motion character
evolution. So, you phylogenetic P values becomes (much) lower than your
non-phylogenetic P value.
As a reality check, I would run your analyses on a star phylogeny (a
giant hard polytomy) and see if you get P values that are the same (actually,
just very close to unless you do a lot of simulations) as for a nonphylogenetic
analysis.
Cheers,
Ted
Theodore Garland, Jr.
Professor
Department of Biology
University of California, Riverside
Riverside, CA 92521
Office Phone: (951) 827-3524
Wet Lab Phone: (951) 827-5724
Dry Lab Phone: (951) 827-4026
Home Phone: (951) 328-0820
Facsimile: (951) 827-4286 = Dept. office (not confidential)
Email: tgarl...@ucr.edu
Main Departmental page:
http://www.biology.ucr.edu/people/faculty/Garland.html
List of all Publications:
http://www.biology.ucr.edu/people/faculty/Garland/GarlandPublications.html
Garland and Rose, 2009
http://www.ucpress.edu/books/pages/10604.php
---- Original message ----
Date: Wed, 16 Mar 2011 15:38:54 -0500
From: dwe...@life.illinois.edu
Subject: Re: [R-sig-phylo] Help Interpreting Phylogenetic ANOVA
Results
To: tgarl...@ucr.edu
Cc: r-sig-phylo@r-project.org
>Hi Liam and Ted,
> My apologies for not writing sooner. I've been sick.
> First off, let me thank you both for helping to clarify what the
>phylogenetic ANOVA is and what it means.
> I thought I would explain a little more than I did in my initial
post
>since Ted seemed curious to know more.
> I am using geometric morphometrics to analyze body shape in a
family of
>freshwater fish (topminnows). I ran a PCA to "condense" the
>morphometric analyses into PC scores. I'm using the PC scores in
the
>phylogenetic ANOVA. Because I would like to know how phylogeny
>"effects" habitat-specific differences in body shape, I run the
>phylogenetic ANOVAs with the tips being a species-habitat
combination.
>Essentially, it looks like this:
>
> |---- Species A Habitat 1
> |
> |------|
> | |
>---| |---- Species A Habitat 2
> |
> |
> |
> | |---- Species B Habitat 1
> | |
> |-----|
> |
> |---- Species B Habitat 2
>
> The tree for these species was made in Mesquite and based off of a
tree
>from a recent molecular phylogeny that came out (Whitehead 2010
>Evolution paper). The tree for the phylogenetic ANOVA includes
branch
>lengths, obviously. Because I don't know if there is any genetic
>distance between the same species from the two different habitats,
I set
>the branch lengths to a really small value (0.00001) in R.
> All of the 21 species used to run the phylogenetic ANOVA have
>populations in both habitats, so in that sense it's "balanced".
Where
>the species fall on the tree is pretty scattered, throughout the
tree
>(the tree contains about 20 more species that I did not include in
this
>analysis, so I don't know if that matters). Just visually glancing
at
>it, there are two main clades in the tree and 14 come from one
clade and
>7 come from the other clade, so, if anything, I would think they'd
be
>more "clumped" than overdispersed. However, I could be wrong.
> I would be happy to share the real tree and my data with anyone
who is
>interested.
>
>
>
>
>
>-Daniel
>
>
>
>> Exactly as Liam wrote, except that it is usually uncommon to find
real
>> data that are "overdispersed phylogenetically," so normally one
finds that
>> the P values when done phylogenetically are larger (less
significant) than
>> when done via conventional, non-phylogenetic ANOVA. I'd be
curious what
>> your data are and how they appear to be scattered across the tips
of your
>> phylogeny. Are they really overdispersed?
>>
>> Cheers,
>> Ted
>>
>> Theodore Garland, Jr.
>> Professor
>> Department of Biology
>> University of California, Riverside
>> Riverside, CA 92521
>> Office Phone: (951) 827-3524
>> Wet Lab Phone: (951) 827-5724
>> Dry Lab Phone: (951) 827-4026
>> Home Phone: (951) 328-0820
>> Facsimile: (951) 827-4286 = Dept. office (not confidential)
>> Email: tgarl...@ucr.edu
>>
>> Main Departmental page:
>> http://www.biology.ucr.edu/people/faculty/Garland.html
>>
>> List of all Publications:
>>
http://www.biology.ucr.edu/people/faculty/Garland/GarlandPublications.html
>>
>> Garland and Rose, 2009
>> http://www.ucpress.edu/books/pages/10604.php
>>
>>
>> ---- Original message ----
>>
>> Date: Mon, 14 Mar 2011 16:22:58 -0400
>> From: "Liam J. Revell"<liam.rev...@umb.edu>
>> Subject: Re: [R-sig-phylo] Help Interpreting Phylogenetic ANOVA
>> Results
>> To: dwe...@life.illinois.edu
>> Cc: r-sig-phylo@r-project.org
>>
>> >Hi Dylan.
>> >
>> >The way the phylogenetic ANOVA (sensu Garland et al. 1993; Syst.
>> Biol.)
>> >works is by first computing a standard ANOVA, and then comparing
>> the
>> >observed F to a distribution obtained by simulating on the tree
>> under a
>> >scenario of no effect of x on y. This "accounts for" the tree in
>> the
>> >sense that it attempts to account for the possibility that
species
>> may
>> >have similar y conditioned on x because x influences y; or
because
>> they
>> >share common history and are thus similar by virtue of this
history
>> (and
>> >not at all due to x)
>> >
>> >It is not particularly surprising that your P-value was lower in
>> the
>> >phylogenetic ANOVA than in your regular ANOVA. In general, the
>> effect
>> >of the phylogenetic ANOVA on P depends on the distribution of
the
>> >factor, x. If x is clumped on the tree, than the P-value of a
>> >phylogenetic ANOVA will tend to be higher than a regular ANOVA.
By
>> >contrast, if x is overdispersed phylogenetically, the P-value of
>> the
>> >phylogenetic ANOVA will tend to be lower than the regular ANOVA.
>> >
>> >I hope this is of some help.
>> >
>> >- Liam
>> >
>> >--
>> >Liam J. Revell
>> >University of Massachusetts Boston
>> >web: http://faculty.umb.edu/liam.revell/
>> >email: liam.rev...@umb.edu
>> >blog: http://phytools.blogspot.com
>> >
>> >On 3/13/2011 9:28 PM, dwe...@life.illinois.edu wrote:
>> >> Hi,
>> >> I am relatively new to phylogenetic methods. I'm hoping
someone
>> can
>> >> help me to understand my results.
>> >> I am working with a group of 21 species of fish. I want to
know
>> how
>> >> their habitat may influence body shape and whether
phylogenetic
>> >> relatedness may influence body shape as well. I performed a
>> >> phylogenetic ANOVA using the GEIGER package in R. My "metric"
of
>> body
>> >> shape is a PC score. Here's the output:
>> >>
>> >> Standard ANOVA:
>> >> Analysis of Variance Table
>> >>
>> >> Response: td$data
>> >> Df Sum Sq Mean Sq F value Pr(>F)
>> >> group 1 4.01 4.0134 0.4595 0.5017
>> >> Residuals 40 349.35 8.7337
>> >>
>> >>
>> >> Phylogenetic p-value: 0.000999001
>> >>
>> >> I'm a bit uncertain as to how to properly interpret the
result. I
>> think
>> >> my confusion is two fold:
>> >>
>> >> 1. I am not sure I am interpreting what the phylogenetic
p-value
>> means.
>> >> Am I correct in saying that the phylogenetic p-value
essentially
>> says
>> >> that, after "accounting for" phylogeny, the habitat has an
effect
>> on body
>> >> shape (PC1)?
>> >>
>> >> 2. I am confused as to why it goes from non-significant (in
the
>> standard
>> >> ANOVA) to significant (phylogenetic p-value)? Does it mean
that
>> the
>> >> habitat does not have an effect on body shape if you don't
>> consider
>> >> phylogenetic relatedness?
>> >>
>> >> I realize these might be very simple questions but I'd
appreciate
>> it if
>> >> someone can help. I'm not well versed in phylogenetics, so I
feel
>> a bit
>> >> lost.
>> >> Please feel free to respond directly to me at
>> dwe...@life.illinois.edu.
>> >> Thank you!
>> >>
>> >>
>> >>
>> >>
>> >> -Daniel
>> >>
>> >>
>> >> ----><((((º> -----><((((º> ----><((((º> ----><((((º>
>> ----><((((º> ----
>> >>
>> >> Daniel P Welsh
>> >> University of Illinois at Urbana-Champaign
>> >> Champaign, IL, USA
>> >>
>> >> _______________________________________________
>> >> R-sig-phylo mailing list
>> >> R-sig-phylo@r-project.org
>> >> https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
>> >
>> >_______________________________________________
>> >R-sig-phylo mailing list
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>>
>
>
>----><((((º> -----><((((º> ----><((((º> ----><((((º> ----
><((((º> ----
>
>Daniel P Welsh
>PhD Student
>Teaching Assistant
>Department of Animal Biology
>University of Illinois at Urbana-Champaign
>202 Shelford Vivarium
>606 E. Healey Street
>Champaign, IL 61821
>lab phone: (217) 333-5323
>
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