Discussion:
[R-sig-phylo] Help Interpreting Phylogenetic ANOVA Results
d***@life.illinois.edu
2011-03-14 01:28:04 UTC
Permalink
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 ***@life.illinois.edu.
Thank you!




-Daniel


---- ><((((º> ----- ><((((º> ---- ><((((º> ---- ><((((º> ---- ><((((º> ----

Daniel P Welsh
University of Illinois at Urbana-Champaign
Champaign, IL, USA
Liam J. Revell
2011-03-14 20:22:58 UTC
Permalink
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: ***@umb.edu
blog: http://phytools.blogspot.com
Post by d***@life.illinois.edu
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
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
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.
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
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
t***@ucr.edu
2011-03-14 23:51:34 UTC
Permalink
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: ***@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" <***@umb.edu>
Subject: Re: [R-sig-phylo] Help Interpreting Phylogenetic ANOVA
Results
Post by Liam J. Revell
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
Post by Liam J. Revell
scenario of no effect of x on y. This "accounts for" the tree in
the
Post by Liam J. Revell
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
Post by Liam J. Revell
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/
blog: http://phytools.blogspot.com
Hi,
I am relatively new to phylogenetic methods. I'm hoping someone
can
Post by Liam J. Revell
help me to understand my results.
I am working with a group of 21 species of fish. I want to know
how
Post by Liam J. Revell
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
Post by Liam J. Revell
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
Post by Liam J. Revell
1. I am not sure I am interpreting what the phylogenetic p-value
means.
Post by Liam J. Revell
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
Post by Liam J. Revell
ANOVA) to significant (phylogenetic p-value)? Does it mean that
the
Post by Liam J. Revell
habitat does not have an effect on body shape if you don't
consider
Post by Liam J. Revell
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
Post by Liam J. Revell
lost.
Please feel free to respond directly to me at
Thank you!
-Daniel
----><((((º> -----><((((º> ----><((((º> ----><((((º>
----><((((º> ----
Post by Liam J. Revell
Daniel P Welsh
University of Illinois at Urbana-Champaign
Champaign, IL, USA
_______________________________________________
R-sig-phylo mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
_______________________________________________
R-sig-phylo mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
d***@life.illinois.edu
2011-03-16 20:38:54 UTC
Permalink
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
Post by t***@ucr.edu
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)
http://www.biology.ucr.edu/people/faculty/Garland.html
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
Subject: Re: [R-sig-phylo] Help Interpreting Phylogenetic ANOVA
Results
Post by Liam J. Revell
Hi Dylan.
The way the phylogenetic ANOVA (sensu Garland et al. 1993; Syst.
Biol.)
Post by Liam J. Revell
works is by first computing a standard ANOVA, and then comparing
the
Post by Liam J. Revell
observed F to a distribution obtained by simulating on the tree
under a
Post by Liam J. Revell
scenario of no effect of x on y. This "accounts for" the tree in
the
Post by Liam J. Revell
sense that it attempts to account for the possibility that species
may
Post by Liam J. Revell
have similar y conditioned on x because x influences y; or because
they
Post by Liam J. Revell
share common history and are thus similar by virtue of this history
(and
Post by Liam J. Revell
not at all due to x)
It is not particularly surprising that your P-value was lower in
the
Post by Liam J. Revell
phylogenetic ANOVA than in your regular ANOVA. In general, the
effect
Post by Liam J. Revell
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
Post by Liam J. Revell
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/
blog: http://phytools.blogspot.com
Hi,
I am relatively new to phylogenetic methods. I'm hoping someone
can
Post by Liam J. Revell
help me to understand my results.
I am working with a group of 21 species of fish. I want to know
how
Post by Liam J. Revell
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
Post by Liam J. Revell
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
Post by Liam J. Revell
1. I am not sure I am interpreting what the phylogenetic p-value
means.
Post by Liam J. Revell
Am I correct in saying that the phylogenetic p-value essentially
says
Post by Liam J. Revell
that, after "accounting for" phylogeny, the habitat has an effect
on body
Post by Liam J. Revell
shape (PC1)?
2. I am confused as to why it goes from non-significant (in the
standard
Post by Liam J. Revell
ANOVA) to significant (phylogenetic p-value)? Does it mean that
the
Post by Liam J. Revell
habitat does not have an effect on body shape if you don't
consider
Post by Liam J. Revell
phylogenetic relatedness?
I realize these might be very simple questions but I'd appreciate
it if
Post by Liam J. Revell
someone can help. I'm not well versed in phylogenetics, so I feel
a bit
Post by Liam J. Revell
lost.
Please feel free to respond directly to me at
Thank you!
-Daniel
----><((((º> -----><((((º> ----><((((º> ----><((((º>
----><((((º> ----
Post by Liam J. Revell
Daniel P Welsh
University of Illinois at Urbana-Champaign
Champaign, IL, USA
_______________________________________________
R-sig-phylo mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
_______________________________________________
R-sig-phylo mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
---- ><((((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
t***@ucr.edu
2011-03-17 21:32:30 UTC
Permalink
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:
Liam J. Revell
2011-03-21 19:31:16 UTC
Permalink
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: ***@umb.edu
blog: http://phytools.blogspot.com
Post by t***@ucr.edu
Dear Daniel,
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.
d***@life.illinois.edu
2011-03-22 20:17:02 UTC
Permalink
Hi Liam,
I've played around with your code and I see what you mean...
"tiny.edge" definitely influences whether it is significant or not. And
I re-ran my data playing with the edge length and that, too, is very
strongly influenced by the value of the edge length. And that makes me
very unsettled (and, frankly, a little depressed).
The only reason I put in an edge length is because, as far as I know,
the GEIGER program cannot work with branch lengths of zero. So, I
thought I could get around this by just putting in a nominal value. (I
hope my thought process makes sense).
Now, I don't know what to do. Is this analysis completely invalid?
Does anyone have a suggestion? Here's my original research question
again: I want to know if differences in body shape (geometric
morphometrics, "condensed" into PC scores) in a family of fish is
influenced by habitat (water velocity- moving water vs. still water)
and/or phylogeny (i.e. more closely related species look similar in
shape).
Thanks.




-Daniel
Post by Liam J. Revell
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/
blog: http://phytools.blogspot.com
Post by t***@ucr.edu
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,
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.
two approaches in evolutionary physiology. Pages 107-132 in R. C. Roach,
t***@ucr.edu
2011-03-22 20:21:11 UTC
Permalink
Hi Daniel,

Offline, I'd like to see your actual tree and tip data.

Cheers,
Ted


---- Original message ----

Date: Tue, 22 Mar 2011 15:17:02 -0500
From: ***@life.illinois.edu
Subject: Re: [R-sig-phylo] Help Interpreting Phylogenetic ANOVA
Results
Post by d***@life.illinois.edu
Hi Liam,
I've played around with your code and I see what you mean...
"tiny.edge" definitely influences whether it is significant or not.
And
Post by d***@life.illinois.edu
I re-ran my data playing with the edge length and that, too, is
very
Post by d***@life.illinois.edu
strongly influenced by the value of the edge length. And that makes
me
Post by d***@life.illinois.edu
very unsettled (and, frankly, a little depressed).
The only reason I put in an edge length is because, as far as I know,
the GEIGER program cannot work with branch lengths of zero. So, I
thought I could get around this by just putting in a nominal value.
(I
Post by d***@life.illinois.edu
hope my thought process makes sense).
Now, I don't know what to do. Is this analysis completely invalid?
Does anyone have a suggestion? Here's my original research question
again: I want to know if differences in body shape (geometric
morphometrics, "condensed" into PC scores) in a family of fish is
influenced by habitat (water velocity- moving water vs. still
water)
Post by d***@life.illinois.edu
and/or phylogeny (i.e. more closely related species look similar in
shape).
Thanks.
-Daniel
Post by Liam J. Revell
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
Post by d***@life.illinois.edu
Post by Liam J. Revell
it could be the case. For instance, try running the following
code for
Post by d***@life.illinois.edu
Post by Liam J. Revell
smaller (or larger) values of "tiny.edge." [Comments give you an
idea
Post by d***@life.illinois.edu
Post by Liam J. Revell
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$edge[,2]<=32]<-0
# simulate and add a little random error
y<-sim.char(tree,as.matrix(1))[,,1]+sqrt(error.variance)*rnorm(32)
Post by d***@life.illinois.edu
Post by Liam J. Revell
# create a factor
x<-as.factor(rep(c(0,1),16)); names(x)<-names(y)
# add a tiny little bit to the terminal edges
tree$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/
blog: http://phytools.blogspot.com
Post by t***@ucr.edu
Dear Daniel,
OK, then I think your results make sense. You have, in fact,
designed
Post by d***@life.illinois.edu
Post by Liam J. Revell
Post by t***@ucr.edu
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,
Garland, T., Jr., A. W. Dickerman, C. M. Janis, and J. A. Jones. 1993.
Phylogenetic analysis of covariance by computer simulation.
Systematic
Post by d***@life.illinois.edu
Post by Liam J. Revell
Post by t***@ucr.edu
Biology 42:265-292.
Vanhooydonck, B., and R. Van Damme. 1999. Evolutionary
relationships
Post by d***@life.illinois.edu
Post by Liam J. Revell
Post by t***@ucr.edu
between body shape and habitat use in lacertid lizards.
Evolutionary
Post by d***@life.illinois.edu
Post by Liam J. Revell
Post by t***@ucr.edu
Ecology Research 1:785-805.
two approaches in evolutionary physiology. Pages 107-132 in R. C. Roach,
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