File = PDTREE Mesquite.doc, copyright by Theodore Garland, Jr. This is version of 16 Nov. 2006.
Begun 18 March 2005 by modification of PDINSTRW.DOC, which is the documentation for the DOS PDAP programs.
This is just a start at documentation for the Mesquite version … needs much more work ….
PDAP:PDTREE module of Mesquite
This module is by Peter E. Midford, Theodore Garland, Jr., and Wayne P. Maddison.
Development of these programs was supported by various
National Science Foundation grants, including: DEB-0196384 to T.G. and Anthony R. Ives; and an NSF
Bioinformatics Postdoctoral Fellowship to P.E.M.
The main Mesquite programs may be downloaded from:
http://mesquiteproject.org/mesquite/mesquite.html
The PDTREE module may be downloaded from:
http://mesquiteproject.org/pdap_mesquite/index.html
When publishing, please use these citations:
Maddison, W.P. & D.R. Maddison. 2006. Mesquite: A modular system for evolutionary analysis.
Version 1.1. http://mesquiteproject.org
Midford, P. E., T. Garland Jr., and W. P. Maddison. 2005. PDAP Package of Mesquite. Version 1.07.
PDTREE analyzes data by the method of phylogenetically independent contrasts (PIC), as
described by Felsenstein (1985). It includes a series of diagnostics to check the inherent assumptions of
PIC (Garland et al., 1992; see also Garland, 1992, 1994; Garland et al., 1991, 1993; Garland and Janis,
1993; Garland and Adolph, 1994; Diaz-Uriarte and Garland, 1996, 1998). It can output a plain text
ASCII file of the raw independent contrasts (*.FIC file) and their associated standard deviations (plus
nodal values used during computation of the contrasts, corrected branch lengths, and heights of nodes).
PDTREE will also compute a variety of statistics with PIC.
Using independent contrasts, PDTREE also allows estimation of ancestral states (values at
internal nodes or at any point along a branch) and their standard errors (Garland et al., 1999). This
requires rerooting of your tree, as explained in Garland et al. (1999). PDTREE also performs bivariate
regression, confidence intervals, and prediction intervals as mapped back onto the original data space
(Garland and Ives, 2000). Note that, for most purposes, PIC are mathematically and statistically
equivalent to generalized least-squares (GLS) models (Grafen, 1989; Martins and Hansen, 1997;
Pagel, 1998; Butler et al., 2000; Garland and Ives, 2000; Rohlf, 2001; Blomberg et al., 2003; Garland et
al., 2005).
For information on the DOS version of PDTREE and other modules of the Phenotypic Diversity
Analysis Programs (PDAP), go here:
1
http://biology.ucr.edu/people/faculty/Garland/PDAP.html
2
Note that the DOS PDAP package contains many more modules in addition to PDTREE. We may put
more of these modules into Mesquite at some point, but for now you will need to use the DOS modules
for things besides independent contrasts, such as Monte Carlo simulations of character evolution and
associated hypothesis testing (e.g., see Martins and Garland, 1991; Garland et al., 1993).
For questions about PDTREE, please contact:
Theodore Garland, Jr.
Department of Biology
University of California, Riverside
Riverside, CA 92521
Phone: (951) 827-3524 = office
Phone: (951) 827-5724 = lab
FAX: (951) 827-4286 = Dept. office
Email: tgarland@ucr.edu
http://biology.ucr.edu/people/faculty/Garland.html
http://www.biology.ucr.edu/people/faculty/Garland/Garland2.html
http://www.biology.ucr.edu/people/faculty/Garland/GarlandCV.html
PDF files of almost all of my publications can be found here:
http://www.biology.ucr.edu/people/faculty/Garland/GarlandPublications.html
We are constantly updating and adding to these programs, so if you are going to use them then it
is best to download the latest versions.
We have also developed MatLab code (the PHYSIG package) to implements tests for
phylogenetic signal and branch length transformations as described in Blomberg et al. (2003; see also
Blomberg and Garland, 2002). These programs are available on request from T.G.
http://www.biology.ucr.edu/people/faculty/Garland/PHYSIG.html
Matlab programs to deal with within-species variation and measurement error in phylogenetic
comparative methods will be available shortly (see Ives et al., 2007).
A separate package of programs, PHYLOGR, produced by Ramon-Diaz-Uriarte and T.G., is
available at http://cran.r-project.org (click on Software, then Package Sources). PHYLOGR is written in
the free "R" language, and analyzes comparative data via Monte Carlo simulations (in combination with
the DOS PDSIMUL) or generalized least-squares (GLS) approaches. The package accompanies DíazUriarte and Garland (in revision). R is free, open-source software (similar to S+), available from the
Comprehensive R Archive Network at http://www.r-project.org/ and various mirror sites. As with other
R packages, PHYLOGR is available from CRAN in source code (tar.gz format) and as a zip file for
Windows systems. Installation is the same as for any other package (see Appendix 1 in our manuscript).
3
***** NOTE: If you find bugs in any of these programs, please contact Ted Garland
immediately! As well, please let me know about your uses of these programs and send
manuscripts or reprints when available. *****
4
GETTING STARTED
This section will get you started analyzing your data with Felsenstein’s (1985) method of
phylogenetically independent contrasts (PIC). We will assume that you want to perform the simple
task of testing for a relationship between two continuous-valued traits, as discussed in Felsenstein’s
(1985) original paper (see also Garland et al., 1992).
Aside from the original paper, only a few key references are cited here, in particular some that
deal with procedures ions involved in applying PIC to the analysis of real data. Emphasis is placed on
those that I have coauthored, simply because I know them best. Similar points can often be found in
works by others.
Let’s begin by assuming you have successfully entered a phylogenetic tree into Mesquite, and
that you also have data for two continuous-valued characters, such as log body mass and log home range
area (e.g., Garland et al., 1993). Further, let’s assume that you have no missing data, i.e., that you have
data for both traits for every single tip (e.g., species) on your phylogenetic tree.
The first thing you will want to do is get into Mesquite’s Tree Window. TIP: if you have
multiple trees in your file, pay close attention to which one you are displaying!!! To begin analyses
with PIC, do this:
1. From the top menu bar of the Tree Window, click on:
a. Analysis
b. New Chart for Tree
c. PDAP Diagnostic Chart
d. Stored Characters (OK)
2. This will give you the PDAP Diagnostic Chart Window
a. The first plot will be the absolute values of the standardized phylogenetically independent
contrasts (PIC) versus their standard deviations (Garland et al., 1991, 1992). This is the
most commonly used diagnostic check of whether the branch lengths of your
phylogenetic tree adequately fit the tip data (e.g., see Diaz-Uriarte and Garland, 1996,
1998). In particular, you want to see:
i. no significant correlation (a flat regression line with zero slope). If you click on
the Text tab and scroll to near the bottom, you will find the t (or F) statistic and
associated degrees of freedom for testing whether the least-squares linear
regression slope differs significantly from zero. If it does, then you can conclude
that your tree (topology, branch lengths, and assumed Brownian motion model of
character evolution) exhibit significant lack of fit to your tip data.
[Note: this is the one place where you examine a regression line for PIC that is
not computed through the origin.]
ii. viewed from the Y-axis, the distribution should appear approximately as ½ of a
normal (bell shaped) distribution. That is, you should tend to have more points
clustered near the bottom of the Y-axis and a thinning tail of points as you move
up along the Y-axis.
5
iii. no points that appear to be major “outliers” from the ½ normal or that appear to be
exerting a lot of “leverage” on the displayed regression line. In other words, you
don’t want one or a few points to be too “influential” in this plot. The exception
would be if they represent contrasts that you had specified a priori as being of
interest for testing particular hypotheses, such as between two major clades (see
Garland et al., 1993).
b. Use the arrows in the bottom left of the window to toggle between your two characters
and examine the above for both of them.
i. Often, one of your characters will be body size (e.g., log body mass) and the other
will be some trait that is expected to be fairly highly correlated with body size
based on general allometric principles, at least if you have a reasonably large
range of body sizes among the species in your data set. If so, then you probably
want to pay most attention to the diagnostics for body size.
ii. In other cases, you may find that the diagnostics for your two traits disagree to
some extent. In that case, the use of different branch lengths may be warranted
(e.g., Garland et al., 1992), but we will defer that scenario to a later point in the
documentation.
c. Additional diagnostic plots are available by clicking on the “PDAP.Chart” button at the
top of the Diagnostic Chart Window. These are named and have associated numbers
(3,4), (5,6), and (7,8). These numbers refer to their screen sequence in DOS PDTREE,
which only works with two characters at a time. These diagnostics may be useful for
various purposes, but have not been studied as much as the ones discussed above (1,2),
and so will not be considered further at this point.
3. Assuming that your diagnostic checks were OK, you are now ready to test for a relationship
between the two traits. Click on the “PDAP.Chart” button and choose “Y contrasts vs. X
Contrasts (positivized) (9).”
a. In the bottom left of the window, specify the X and Y trait.
b. The small gray text box in the upper left will show, among other things, the Pearson
product-moment correlation coefficient (computed through the origin) and its associated
P value (significance level). This and additional statistics can also be obtained from the
Text tab.
6
What the Field of
Conventional Statistics Assumes:
A Star Phylogeny
with Equal-Length Branches
\
What Evolution
Provides:
A Hierarchical Phylogeny
with Unequal Rates of Evolution
\
!
/
/
\
\
!
/
/
\
\
!
/
/
\
\
!
/
/
\ \
!
/ /
\ \ ! / /
\\ ! //
\!/
!
:
:
:
:
:
:
:____:
:
:
:
:
:
:____:
:______:
:
:
:
:_________:
:
"Phylogenies are fundamental to comparative biology;
there is no doing it without taking them into account."
(Felsenstein, 1985, p. 14)
Conventional, or phylogenetically uninformed ("PU" Garland, 2001, p. 120) statistics assume, in
effect, a star phylogeny with equal-length branches, as on the right, whereas phylogenetically
correct ("PC" Garland et al., 1993, p. 279) statistics can assume any topology and branch lengths
that are specified by the user, and can also incorporate estimation of the optimal transformation
of the branch lengths (e.g., Grafen, 1989; Freckleton et al., 2002; Blomberg et al., 2003).
7
CHARTS AVAILABLE IN PDAP Diagnostic Chart Window
As noted above, clicking on the “PDAP.Chart” pull-down menu allows you to access several
graphs. Here is a more detailed explanation of those graphs. The screen numbers follow from the DOS
version of PDTREE, and are indicated in parentheses in the Mesquite menu. In DOS PDTREE, which
only works with two traits at a time, you would see, for example, screens 1 and 2 in sequence for traits 1
and 2. In Mesquite, you need to indicate which trait you want in the bottom left of the window.
Screens 1+2 = absolute values of standardized contrasts (Y axis) versus their standard deviations (X
axis: square roots of sums of corrected branch lengths). For examples, see Figures 3 and 4 in Garland et
al., 1992; Figure 3 in Garland and Janis, 1993). This is the diagnostic proposed originally by Garland et
al. (1991) and more fully in Garland et al. (1992; see also Pagel, 1992, p. 441-442). This is the best
understood of existing diagnostics. Diaz-Uriarte and Garland (1996, 1998; see also Garland and DiazUriarte, 1999; Harvey and Rambaut, 2000; Diniz-Filho and Torres, 2002) have shown that it is indeed a
good thing to check.
The primary thing to check is the correlation between the Y and X variables. A statistically
significant correlation (2-tailed test) indicates significant lack of fit. Second, the distribution in the
vertical direction should approximate one-half of a normal distribution. Third, different clades within
the overall phylogeny should not differ, on average, with respect to the value of the Y axis variable. If
they do, this indicates significant differences in the average (minimum) rate of evolution among clades
(Garland, 1992; Garland and Ives, 2000; Hutcheon and Garland, 2004). Fourth, check for any single
points that are influential in the overall relationship.
In addition to this diagnostic, we recommend that you check the criterion of lowest variance of
contrasts or lowest Mean Squared Error in the GLS mode of operation. These checks can be performed
in the PHYSIG programs (Matlab) of Blomberg et al. (2003). Email Ted Garland for a copy.
Screen 3+4 = absolute values of standardized contrasts versus their estimated nodal values, as suggested
by Purvis and Rambaut (1995 [C.A.I.C. User's Guide]; e.g., Brandl et al., 1994, p. 111). Nobody has yet
explored its utility by computer simulations. (A simpler diagnostic was proposed by Freckleton [2000],
but it has several problems.)
Screen 5+6 = absolute values of standardized contrasts versus the heights of their base nodes (using
corrected branch lengths), as suggested by Purvis and Rambaut (1995 [C.A.I.C. User's Guide]).
Screen 7+8 = estimated nodal values versus heights of the base nodes of the contrasts (using corrected
branch lengths). This is fun to look at, but has not been suggested as a diagnostic. As discussed at the
end of the PDERROR section of the DOS PDAP documentation (PDINSTRW.DOC), the correlation of
this plot can be used to test for directional evolutionary trends.
Screen 9 = scatterplot of the standardized contrasts for the two traits, with an ordinary least-squares
regression through the origin plotted as a solid black line (e.g., Fig. 5 in Garland et al., 1992; Fig. 4c and
5 in Garland and Janis, 1993; Fig. 1 in Gray, 1996; Fig. 3 in Degen et al., 1998; Fig. 3b in Bonine and
Garland, 1999). A red line indicates the Reduced Major Axis (RMA) line and a green line indicates the
Major Axis (MA) line (see Garland et al., 1992). Note that the X variable has been “positivized”
(Garland et al., 1992).
8
The Text tab gives the corresponding statistics, and also reports the number of contrasts for the Y
variable that are positive, negative or zero, given that the X variable has been positivized: this
information can be used to perform a sign test (Sokal and Rohlf, 1981, pp. 449-450, 693), and the Pvalue for this test is also reported.
Screen 9A = estimated values for the two traits at the root (basal node) of the phylogeny, in addition to
their 95% confidence intervals. These can be interpreted as either (1) phylogenetically correct estimates
of the means of the tip values or (2) estimates of the ancestral states at the root of the tree (Garland et al.,
1999). Either interpretation is valid, but the latter requires that no directional trends have occurred
during character evolution from the root to the tips. Note that you can use Screen 9A to estimate
values for other (internal) nodes on your tree, but you first need to reroot the tree at that node (see
Garland et al., 1999). Other statistics can be accessed via the Text tab, and they correspond to the .RT
file of DOS PDTREE.
The Text tab also reports the statistics for the independent contrasts least-squares regression
equation, as mapped back onto the original data space (see Garland and Ives, 2000). Included are
95% confidence intervals for both the slope and the Y-intercept, again mapped back onto the original tip
data space. (Note that the slope on Screen 9A is the same as the least-squares regression slope reported
on Screen 9.)
xxAdd DF reduction as described in C:\Peattie\Peattie_Anne.doc
Screen 9B = the independent contrasts least-squares linear regression actually mapped back onto the
original tip data space (Garland and Ives, 2000; for examples, see their Figures 3 and 4). Other
published examples that have used this include: Perez-Barberia and Gordon, 2001; Reynolds, 2002;
Mermoz and Ornelas, 2004.xxTed check. The Text tab includes what corresponds to the .CI file of DOS
PDTREE:
Your Confidence/Prediction Interval (*.CI) file will contain the following columns:
1. Tip Name
2. X Value
3. Observed Y Value
4. Predicted Y Value (Yhat)
5. Lower 95% Confidence Interval
6. Upper 95% Confidence Interval
7. Lower 95% Prediction Interval
8. Upper 95% Prediction Interval
9. Lower 90% Confidence Interval
10. Upper 90% Confidence Interval
11. Lower 90% Prediction Interval
12. Upper 90% Prediction Interval
For "Tip Name," the last few rows may be for any user-defined values (named "usr"). The
several rows before those will be for the smallest actual tip X value -1, -2 ... -10% as well as the largest
actual tip X value +1, +2 ... +10%, with a value for X = 0 inserted in the middle.
Note that 95% and 90% are the default values, but these values can be changed by screen input.
Also, by default, the .CI file will contain one line for each data point in your data file. You will also be
9
asked if you want to add additional lines for other values of your X variable. This is useful for several
reasons. For example, you may wish to have the predicted Y value and associated confidence/prediction
intervals at the Y-intercept (enter a value of 0). Or, for purposes of graphing and extrapolation, you
may want to have values that extend beyond the range of your X variable.
***** NOTE: For computing the t-statistics used to compute confidence intervals, much of the
code was taken from Press et al. (1989). The results produced by these routines differ from the values
produced by SPSS/PC+ Version 5.0. The values usually differ in the fourth decimal place. We also
compared results from the routines used herein (from Press et al., 1989) with those produced by an HP21S calculator; they agree to more than 7 decimal places.
Screen 10 = a plot of residuals from the line shown in Screen 9 versus the X value contrasts, which
helps you check the assumptions of linear regression through the origin (e.g., homoscedasticity).
Screen 11 = absolute values of residuals from the least-squares linear regression through the origin (as
shown on Screen 9) plotted against heights of the corresponding base nodes (using corrected branch
lengths). This is another possible diagnostic, as suggested by Grafen (1989, p. 146).
You will next be asked if you want to save a file of regression "residual" information. These
"residuals" are the vertical deviations, in the original data space, from the regression equation
estimated by independent contrasts (as shown graphically in Screen 9 and numerically in Screen 9A).
They are NOT independent contrast residuals!!! Hence, they are NOT free of phylogenetic effects
(see also Blomberg et al., 2003), and cannot be used in ordinary statistical procedures. (They also are
not uncorrelated with the X variable, so they do not remove the effects of, for example, body size.) They
may, however, be useful for making heuristic graphs. Screen 9C lists the contents of the .RSD file as
follows:
Your "Residual" file (*.RSD) will contain the following columns:
1.
2.
3.
4.
5.
6.
7.
8.
Tip Name
X Value
Observed Y Value
Predicted Y Value (Yhat)
Residual (Y - Yhat)
Standardized Residual (using actual SD of residuals, not MSE)
Leverage of X Value (using root value as Xmean)
Studentized Residual (Neter et al., 1989, p. 398)
Note: As of 21 May 1998, the .RSD file is a test version. Use only with caution.
10
11
EXPORTING YOUR CONTRASTS FOR USE IN A STATISTICS OR
GRAPHICS PROGRAM
Often, you will want to export your contrasts to make graphs or to perform other types of
statistical analyses. To do this, make sure you have “Y contrasts vs. X Contrasts (positivized) (9)”
displayed in your PDAP Diagnostic Chart Window, then click on “PDAP.Chart” and find the option
of “Generate File of Independent Contrasts (FIC)” near the bottom of the pull-down menu.
You can also select “Show columns in File of Independent Contrasts (FIC),” which are:
FIC files contain the following columns:
1.
2.
3.
4.
5.
Name of Contrast as Node - Node (e.g., 'Tm - Ta')
Name of Node at Base of Contrast
Unstandardized Contrast for Trait 1
Unstandardized Contrast for Trait 2
Standard Deviation of Contrast
= square root of sum of corrected branch lengths
6. Nodal Value for Trait 1
7. Nodal Value for Trait 2
8. Uncorrected Height of Base Node from Root of Tree
9. Corrected Height of Base Node from Root of Tree
(as used in screens 5, 6, 7, 8, and 11)
10. Average Uncorrected Height of Daughter Nodes
11. Average Corrected Height of Daughter Nodes
12. Name of First Daughter Branch (Descendant-Ancestor)
13. Corrected Length of First Daughter Branch
14. Name of Second Daughter Branch (Descendant-Ancestor)
15. Corrected Length of Second Daughter Branch
Note that exporting the FIC is linked to screen 9, which involves two traits, so you will need to export
multiple FIC files if you are analyzing more than two traits. Also, in the FIC file column 3 will
contain contrasts for the "X" trait as indicated on Screen 9 while column 4 will contain contrasts
for the "Y" trait as indicated on Screen 9. Hence, this may be a different order than occurs in
your Mesquite Character Matrix. Be very careful!!!
TIP: pay close attention to what you name the multiple FIC files so that you do not get columns
confused later when importing them into your spreadsheet or statistics program!!!
12
ANALYZING YOUR CONTRASTS IN A STATISTICS PROGRAM
As indicated above, the FIC file produced by PDTREE contains the raw contrasts. This is done
because for a few purposes, e.g., certain sorts of diagnostics, they may be of use. However, for
essentially all ordinary purposes you need to divide the raw contrasts (columns 3 and 4 of the FIC
file) by their standard deviations (column 5). You can do this is a program such as Excel or in your
statistics package. It is these “standardized contrasts” that will be used for computing correlations,
regressions, and so forth (always through the origin: Felsenstein, 1985; Garland et al., 1992).
PDTREE is not designed to be a comprehsnsive statistics package in and of itself. It will do
most of the things you might want to do with one or two traits, but beyond that (e.g., multiple regression,
ANOVA, principal components analysis), you will need to export your contrasts (the FIC file) and
merge them in a spreadsheet or statistics package.
Note that your FIC file includes two different sets of names for the individual contrasts, in
columns 1 and 2.
13
SPSS/PC+ (for DOS) CODE FOR ANALYZING
PHYLOGENETICALLY INDEPENDENT CONTRASTS
If you are analyzing more than two traits, e.g., for multiple regression or principal components
analysis, or if you are using different branch length transformations for each trait, then you will need to
enter two or more .FIC files into a commercial statistics/graphics package. SPSS/PC+ was once in
common use, and Windows, MacIntosh, and mainframe versions are now available. We therefore
provide some SPSS/PC+ commands to illustrate how to use the independent contrasts in a .FIC file. In
future versions of this documentation, syntax for the Windows version of SPSS will be provided.
We assume your .FIC file was created by use of the 49LBR70.PDI file that is appended at the
very bottom of this file (from Garland et al., 1993). The following commands will duplicate screens 111 that you can access from the PDAP.Chart tab of the PDAP Diagnostic Chart Window. Note that
the names given to the variables are entirely arbitrary, but here is how they match up with the FIC
contents. "(A)" denotes string (alphanumeric) variables.
1.
2.
3.
4.
5.
Name of Contrast as Node - Node (e.g., 'Tm - Ta')
Name of Node at Base of Contrast
Unstandardized Contrast for Trait 1
Unstandardized Contrast for Trait 2
Standard Deviation of Contrast
= square root of sum of corrected branch lengths
6. Nodal Value for Trait 1
7. Nodal Value for Trait 2
8. Uncorrected Height of Base Node from Root of Tree
9. Corrected Height of Base Node from Root of Tree
(as used in screens 5, 6, 7, 8, and 11)
10. Average Uncorrected Height of Daughter Nodes
11. Average Corrected Height of Daughter Nodes
12. Name of First Daughter Branch (Descendant-Ancestor)
13. Corrected Length of First Daughter Branch
14. Name of Second Daughter Branch (Descendant-Ancestor)
15. Corrected Length of Second Daughter Branch
CONTRAST (A)
NODE (A)
CLMASS *
CLHOME *
SD
NLMASS *
NLHOME *
UHBNODE
CHBNODE
AUHDNODE
ACHDNODE
D1BNAME (A)
D1LENGTH
D2BNAME (A)
D2LENGTH
* These four names are specific for traits 1 and 2. If you have more than two traits in your analysis, then
you would be repeating the procedure for those other traits, and you would obviously need to change the
names accordingly. If you are using the same branch lengths for all of the other traits, then you do not
need to change the other 11 names.
* Read in data and save as an SPSS for DOS system file.
* The .FIC file contains 15 columns, as indicated above.
DATA LIST FREE FILE = '49LBR70.FIC' / CONTRAST (A) NODE (A)
CLMASS CLHOME SD NLMASS NLHOME
UHBNODE CHBNODE AUHDNODE ACHDNODE
D1BNAME (A) D1LENGTH D2BNAME (A) D2LENGTH.
SAVE OUTFILE = '49LBR70.SYS'.
* Read in the SPSS system file.
GET FILE = '49LBR70.SYS'.
14
* Compute standardzied contrasts.
COMPUTE SCLMASS = CLMASS/SD.
COMPUTE SCLHOME = CLHOME/SD.
* "Positivize" contrasts for unambiguous graphs.
* This is NOT the same as simply taking the absolute
* values of both sets of contrasts.
* This does NOT affect slopes.
* See Garland et al. (1992).
IF (SCLMASS < 0) SCLHOME = -1 * SCLHOME.
IF (SCLMASS < 0) SCLMASS = -1 * SCLMASS.
* Compute absolute values of standardized contrasts.
COMPUTE ASCLMASS = ABS(SCLMASS).
COMPUTE ASCLHOME = ABS(SCLHOME).
* Diagnostics are screens 1 - 8.
* Screens 1 and 2 (see Garland et al., 1992).
REGRESSION
VARIABLES = ASCLMASS SD
/DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F
/DEP = ASCLMASS /METHOD = ENTER.
GRAPH SCATTERPLOT = ASCLMASS BY SD.
REGRESSION
VARIABLES = ASCLHOME SD
/DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F
/DEP = ASCLHOME /METHOD = ENTER.
GRAPH SCATTERPLOT = ASCLHOME BY SD.
* Screens 3 and 4 (see Purvis and Rambaut, 1995,
* and C.A.I.C. User's Guide).
REGRESSION
VARIABLES = ASCLMASS NLMASS
/DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F
/DEP = ASCLMASS /METHOD = ENTER.
GRAPH SCATTERPLOT = ASCLMASS BY NLMASS.
REGRESSION
VARIABLES = ASCLHOME NLHOME
/DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F
/DEP = ASCLHOME /METHOD = ENTER.
GRAPH SCATTERPLOT = ASCLHOME BY NLHOME.
* Screens 5 and 6 (see Purvis and Rambaut, 1995,
* and C.A.I.C. User's Guide).
REGRESSION
VARIABLES = ASCLMASS CHBNODE
/DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F
/DEP = ASCLMASS /METHOD = ENTER.
GRAPH SCATTERPLOT = ASCLMASS BY CHBNODE.
REGRESSION
VARIABLES = ASCLHOME CHBNODE
/DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F
/DEP = ASCLHOME /METHOD = ENTER.
GRAPH SCATTERPLOT = ASCLHOME BY CHBNODE.
* Screens 7 and 8 (may be useful in testing for directional trends).
REGRESSION
VARIABLES = NLMASS CHBNODE
15
/DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F
/DEP = NLMASS /METHOD = ENTER.
GRAPH SCATTERPLOT = NLMASS BY CHBNODE.
REGRESSION
VARIABLES = NLHOME CHBNODE
/DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F
/DEP = NLHOME /METHOD = ENTER.
GRAPH SCATTERPLOT = NLHOME BY CHBNODE.
* Screen 9 = least-squares linear regression through origin.
* Note that this was "positivized" above to allow
* consistency of graphs across programs (because
* the direction of subtraction with contrasts is arbitrary).
* However, positivization does not affect the slope.
GRAPH SCATTERPLOT = SCLHOME BY SCLMASS.
* Use regression through origin to compute residuals.
REGRESSION
VARIABLES = SCLHOME SCLMASS
/ORIGIN /DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F CHA SES TOL ZPP
/DEP = SCLHOME /METHOD = ENTER
/RESIDUALS /SAVE RESID(RSCLHOME).
* Screen 10 = a basic regression diagnostic.
REGRESSION
VARIABLES = RSCLHOME ASCLMASS
/ORIGIN /DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F
/DEP = RSCLHOME /METHOD = ENTER.
GRAPH SCATTERPLOT = RSCLHOME BY ASCLMASS.
* Screen 11 = a diagnostic suggested by Grafen (1989, p. 146).
COMPUTE ARSCLHOM = ABS(RSCLHOME).
REGRESSION
VARIABLES = ARSCLHOM CHBNODE
/DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F
/DEP = ARSCLHOM /METHOD = ENTER.
GRAPH SCATTERPLOT = ARSCLHOM BY CHBNODE.
***** NOTE: Some commercial statistics programs, when requested to perform a regression
through the origin, will report the correct slope but not the correct correlation coefficient or r2. In
other words, they report the ordinary values for r and r2!!! If you see differences between the numbers
reported by PDTREE and your statistics program, this may be the cause. I have heard such reports about
StatView, Excel (thanks to Per Christiansen for noting this), and possibly others.
* Analysis of Covariance (ANCOVA).
* Code to perform ANCOVA comparing the two sides of the
* tree, i.e., Carnivora (node 03) vs. ungulates (node 02).
* (code from ANOVA.RUN).
* Read in data and save as an SPSS system file.
* The .FIC file contains 15 columns, as indicated above.
DATA LIST FREE FILE = '49LBR70.FIC' / CONTRAST (A) NODE (A)
CLMASS CLHOME SD NLMASS NLHOME
UHBNODE CHBNODE AUHDNODE ACHDNODE
16
D1BNAME (A) D1LENGTH D2BNAME (A) D2LENGTH.
SAVE OUTFILE = '49LBR70.SYS'.
* Read in the SPSS system file.
GET FILE = '49LBR70.SYS'.
* Compute standardzied contrasts.
COMPUTE SCLMASS = CLMASS/SD.
COMPUTE SCLHOME = CLHOME/SD.
* Create a dummy variable that codes for the root (basal) contrast.
COMPUTE ROOT = 0.
* SPSS assumed default width for ASCII file variables is 8 characters.
IF (NODE = '01
') ROOT = 1.
* Check your computations.
FORMATS SCLMASS SCLHOME (F12.9).
LIST VARIABLES = CONTRAST NODE ROOT SCLMASS SCLHOME SD.
* Do the formal test by multiple regression through origin.
* Note that this was not "positivized" to allow
* consistency of graphs across programs, as
* "positivization" only affects graphs not regressions
* through the origin.
* The P-value for ROOT tests whether Carnivora and ungulates
* differ in mass-corrected home range area when one assumes
* parallel slopes: they do not (F1,46 = 2.428, P = 0.1260).
REGRESSION
VARIABLES = SCLHOME SCLMASS ROOT
/ORIGIN /DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F CHA SES TOL ZPP
/DEP = SCLHOME /METHOD = ENTER
/RESIDUALS /SAVE RESID(RSCLHOME).
* Compute cross-products term to test for difference in slopes.
COMPUTE CARNIV = 0.
IF (NODE = '03
') CARNIV = 1.
IF (NODE = '05
') CARNIV = 1.
IF (NODE = '06
') CARNIV = 1.
IF (NODE = '31
') CARNIV = 1.
IF (NODE = '95
') CARNIV = 1.
IF (NODE = '93
') CARNIV = 1.
IF (NODE = '92
') CARNIV = 1.
IF (NODE = '07
') CARNIV = 1.
IF (NODE = '21
') CARNIV = 1.
IF (NODE = '22
') CARNIV = 1.
IF (NODE = '28
') CARNIV = 1.
IF (NODE = '32
') CARNIV = 1.
IF (NODE = '34
') CARNIV = 1.
IF (NODE = '10
') CARNIV = 1.
IF (NODE = '18
') CARNIV = 1.
IF (NODE = '23
') CARNIV = 1.
IF (NODE = '35
') CARNIV = 1.
IF (NODE = '36
') CARNIV = 1.
COMPUTE SLOPE = CARNIV * SCLMASS.
FORMATS SCLMASS(F12.10) SCLHOME(F12.10) SD(F12.10).
LIST VARIABLES = CONTRAST NODE ROOT CARNIV SCLMASS SCLHOME SD.
* The P-value for SLOPE tests whether Carnivora and ungulates
17
* differ in the slope of the scaling relationship:
* they do not (F1,45 = 0.079, P = 0.7801).
REGRESSION VARIABLES = SCLHOME SCLMASS ROOT SLOPE
/DESCRIPTIVES = DEFAULTS STDDEV VARIANCE CORR SIG
/STATISTICS = DEFAULTS CI F CHA SES TOL ZPP
/ORIGIN /DEP = SCLHOME /METHOD = ENTER.
* Check graphically to see if the basal contrast is an "outlier."
* If so, then the clade difference in mass-corrected home
* range area is significant (see Fig. 5 of Garland et al., 1993).
* First, "positivize" contrasts for unambiguous graphs.
* This does NOT affect slopes. See Garland et al. (1992).
* This is same as Screen 9 in PDTREE.
IF (SCLMASS < 0) SCLHOME = -1 * SCLHOME.
IF (SCLMASS < 0) SCLMASS = -1 * SCLMASS.
GRAPH SCATTERPLOT = SCLHOME BY SCLMASS BY ROOT.
18
***** NOTE: When independent contrasts are used for multivariate statistical methods, such
as principal components analysis (PCA) or path analysis, all computations still must be computed
through the origin. This may or may not be easy to do in a given statistical program. For example,
SPSS/PC+ (for DOS) does not have such an option. However, it can nonetheless be accomplished by
reading a matrix of correlation coefficients, computed through the origin, into the SPSS PCA routine.
As it turns out, the REGRESSION routine in SPSS has an option for outputting a correlation matrix. If
you tell it to do regression through the origin, then the correlation matrix will also be through the origin.
Here is some code, modified from what was used in Clobert et al. (1998).
* Use regression through the origin to create a matrix of correlation
* coefficients that have also been computed through the origin.
* This assume that you have already read in an SPSS system file
* (*.SYS) that contains six variables as standardized independent
* contrasts, e.g., see example above.
* To run the regression routine, you actually need to compute any
* arbitrary regression, whose results can just be ignored.
REGRESSION VARIABLES X1CONT X2CONT X3CONT X4CONT X5CONT X6CONT
/WRITE CORR
/ORIGIN
/DEP = X1CONT
/METHIOD = ENTER.
* Now we reassign names to the variables that are associated with the
* correlation matrix because SPSS does not save them when writing it.
DATA LIST MATRIX FILE = 'SPSS.PRC'
X1CONT X2CONT X3CONT X4CONT X5CONT X6CONT.
* Perform the PCA, asking for as many principal components as there
* are original variables. This is the maximum possible, and we
* probably will not end up interpreting all of them, but it is good to
* see them nonetheless. Also, the command "NOROTATE" stops SPSS from
* doing a "factor analysis," which relaxes the orthogonality
* constraint of PCA. Social scientists often use factor analysis, as
* opposed to basic PCA, but many biologists stay away from it because
* of its arbitrary nature (e.g., how much to relax orthogonality).
* Somewhat confusingly, the SPSS/PC+ procedure is named FACTOR.
FACTOR READ / VARIABLES = X1CONT X2CONT X3CONT X4CONT X5CONT X6CONT
/CRITERIA = FACTORS(6)
/ROTATION = NOROTATE
/PRINT = ALL.
19
ALLOMETRY AND CORRECTING FOR BODY SIZE
Body size is a common confounding factor in comparative studies. For example, suppose that
you wanted to correlated heart size and brain size across species of mammals. Obviously, larger-bodied
species of mammals (e.g., elephants) have absolutely large hearts and brains, whereas small-bodied
mammals (e.g., mice) have small organs. Hence, plotting heart mass against brain mass for a set of
species that included both mice and elephants would indicate a strong positive relationship, but one that
is probably not very interesting. In such cases, a common analytical procedure is to remove statistically
the effects of body size by computing residuals from regression lines.
Typically, one would do the following. First, compute log-transformed body and organ masses.
Second, regress log heart mass on log body mass and save the residuals (vertical deviations from the
regression line). Third, do the same for log brain mass. Fourth, correlate residual heart mass with
residual brain mass, perhaps removing two degrees of freedom for having estimated the appropriate
slopes.
The same procedure can be accomplished in a phylogenetically informed fashion by use of
independent contrasts (Garland et al., 1992: for some examples, see Garland and Janis, 1993; Bauwens
et al., 1995; Diaz et al., 1996; Bauwens and Diaz-Uriarte, 1997; Harris and Steudel, 1997; Clobert et al.,
1998; Bonine and Garland, 1999; Pyron, 2000; Rezende et al., 2002; xxadd others). With PDTREE, you
would do the following. First, save out two FIC files, one that contains log body mass and log heart
mass, the other log body mass and log brain mass.
Now load the FIC files into your statistics program. Compute the standardized contrasts,
perform a regression through the origin of log heart mass on log body mass, and ask it to save the
residuals. (Note that in regression through the origin, residuals are not constrained to sum to zero.) Do
the same for log brain mass and log body mass. Finally, test the residuals via a correlation through the
origin. This tests for an association between log heart mass and log brain mass, after having removed
statistically the association of both with log body mass.
20
BRANCH LENGTHS
When analyzing data by the method of phylogenetically independent contrasts (or most other
comparative methods for continuous traits), it is important to verify that branch lengths are adequate
in a statistical sense (see Garland et al., 1991; Garland, 1992; Garland et al., 1992; Garland and Janis,
1993; Diaz-Uriarte and Garland, 1996, 1998; Freckleton et al., 2002; Blomberg et al., 2003). Thus,
PDTREE can be used to transform branch lengths in a variety of ways, including both direct transforms
of each branch segment (see Garland et al., 1992) and the method described by Grafen (1989), for which
you must specify the value of the parameter rho (PDTREE will not estimate rho). Regardless of what
"starter" branch lengths you use when initially entering your tree, PDTREE also allows you to change all
branch lengths to equal one (consistent with a speciational model of character change, e.g., see Martins
and Garland, 1991; Price et al., 1997), to the arbitrary branch lengths of Grafen (1989), Pagel
(1992)(see Fig. 1) or S. Nee (cited in Purvis, 1995, p. 416). Checking for consistency of results with
different sets of branch lengths is useful as a sensitivity analysis.
For other ways of transforming branch lengths and an alternative criterion for determining which
branch lengths best fit a given set of tip data (minimum variance of contrasts or minimum MSE in the
GLS mode of operation), see Blomberg et al. (2003).
When available, "real" branch lengths should be tried in phylogenetic analyses. One example
would be divergence times, which can be estimated both from fossil and biogeographic evidence or
from molecular clocks (e.g., Garland et al., 1993; Bauwens et al., 1995; Purvis, 1995; Pitnick et al.,
1995; Brana, 1996; Pitnick, 1996; Harris and Steudel, 1997; Degen et al., 1998; Tobalske and Dial,
2000; Gibbs and Matzkin, 2001; Polly, 2001; Ross et al., 2004). Another example would be genetic
distances, such as those produced by DNA-DNA hybridization studies (e.g., Sibley and Ahlquist, 1990;
Bleiweiss et al., 1997; Kirsch et al., 1998), which have been used in many recent comparative studies of
birds (e.g., Dutenhoffer and Swanson, 1996; Gray, 1996; Reynolds and Lee, 1996; Williams, 1996;
Bleiweiss, 1997xxcheck and add; Thomson et al., 1998; Barbosa and Moreno, 1999b; Garland and Ives,
2000; Tieleman and Williams, 2000; Rezende et al., 2002). The number of character changes
estimated to have occurred along each branch segment can also be used for branch lengths, whether
those characters are morphological (e.g., Westneat, 1995a,b) or DNA sequences (e.g., Johnston et al.,
2003; Mermoz and Ornelas, 2004; xx). (In general, the characters used to construct the phylogeny and
branch lengths are assumed to be different from those that are to be analyzed by phylogenetically based
statistical methods [e.g., see de Queiroz, 1996, 2000).
Which branch lengths perform best for a comparative analysis of any particular data set is
generally an empirical question that can be approached through the use of various diagnostic statistics
and tests (e.g., see Garland et al., 1992; Diaz-Uriarte and Garland, 1996, 1998; Freckleton et al., 2002;
Blomberg et al., 2003). Hence, PDTREE allows various branch-length diagnostics to be examined.
21
Figure 1. Three kinds of arbitrary branch lengths. All of these can be inter-converted automatically
in PDTREE. Numbers above nodes indicate depth from highest tip. Arbitrary branch lengths have
been used many times in comparative analyses (e.g., xxadd; Huey and Bennett, 1987; Irschick et al., 1996; RodriguezRobles and Greene, 1996; Autumn et al., 1997; Garland et al., 1997; Price et al., 1997; Figs. 2 and 5 of Schluter et al., 1997; Clobert et al.,
1998; Ackerley and Donoghue, 1998; Janz and Nylin, 1998; Shine et al., 1998; Taylor, 1998; Ackerly and Reich, 1999; Autumn et al.,
1999; Bonine and Garland, 1999; Garland, 1999; Jackson et al., 1999; Perez-Barberia and Gordon, 1999b, 2001; Pyron, 1999, 2000; Van
Damme, 1999; Vanhooydonck and Van Damme, 1999; Blob, 2000; Colwell, 2000; Lovegrove, 2000, 2001, 2003; Shine, 2000; Zani,
2000; Ashton et al., 2000; Ashton, 2001; Bonine et al., 2001; Carrascal et al., 2001; Cruz-Neto et al., 2001; Ebensperger and Cofre, 2001;
Iwaniuk and Nelson, 2001; Kohlsdorf et al., 2001; Mysterud et al., 2001; Porter and Hawkins, 2001; Székely et al., 2000; Van Damme and
Vanhooydonck, 2001, 2002; Vanhooydonck et al., 2001; Aguirre et al., 2002; Canterbury, 2002; Herrel et al., 2002a,b; Lindenfors, 2002;
Pérez-Barbería et al., 2002; Perry and Garland, 2002; Rowe and Arnqvist, 2002; Vanhooydonck and Irschick, 2002; Ashton and Feldman,
2003; Cox et al., 2003; Goyman and Wingfield, 2003; Johnston et al., 2003; Toro et al., 2003; Vanhooydonck and Van Damme, 2003;
Hammond and Keller, 2004; Herrell et al., 2004; Ross et al., 2004; see also Purvis, 1995).
:
:
:_1_:
:
: 2
:
:
All equal (constant) branch lengths:
all segments set equal to one (unity).
:
:
:
:
: 2 :
:
3
:
:
:
:
:_1_:
:
: 2
:
:
:
:
:
:
:
:
: 1 :
:
:
:
3
:
:
Pagel's (1992) arbitrary branch lengths.
Tips are constrained to be contemporaneous
(line up across the top)and then internode
segments are set equal to one in length.
Polytomies were not discussed by Pagel, but
PDTREE sets them at the least possible depth,
subject to internodes being set to one.
All branch segments are integers, as they are
based on counts.
:
:
:_1_:
:
: 2
:
:
:
:
:
:
:
:
:
:
: 1 :
:
:
:
:
:
4
:
:
Grafen's (1989) arbitrary branch lengths.
Tips are contemporaneous and the depth of
each node is set equal to one less than the
number of tip species that descend from it.
A variant of this with some theoretical
justification is Nee's arbitrary branch
lengths (cited in Purvis, 1995, p. 416),
in which depths of nodes are set equal to
the log of the number of tip species that
descend from it.
22
EDITING TREES AND BRANCH LENGTHS: SOME
RECOMMENDATIONS
a. If you plan to edit a tree, save a copy of the original unedited version. To do this just save
the edited tree to a new name. The reason is that while you can undo many of the changes you make,
everything you do with a computer will produce rounding errors. For example, when you add a constant
to a branch length, then subtract it by adding the negative of it, you might not end up with exactly the
same number that you started with. The rounding errors will be on the order of a hundred billionth of
the value. They will only be in the 11th decimal place, but be warned that rounding errors are
cumulative and everything you do contributes.
b. Again with regard to rounding errors: if you require maximum accuracy, be warned that when
the program says something like enter one for no change there may in reality be an extremely small
change of a hundred billionth of the value. So, if you worry about the 10th or 11th decimal places in
your tip data or branch lengths, reload the tree and start over if you make unnecessary changes.
c. Extremely long branches (e.g., in units of billions of years) or extremely large (or small) tip
values can cause problems. Therefore, consider rescaling the total height of your tree if it is very tall.
d. Save your trees frequently. You do not want to be almost finished entering a tree with fifty
tips when the program crashes.
e. Be aware of the following when adding or trimming species from a tree in combination with
transforming branch lengths: the order in which you do things sometimes makes a difference! For
example, if you trim a species, then do a square root transform of the branch lengths (the proper
sequence), the length of the branch to which the trimmed species was formerly attached will not be the
same as if you do the procedure vice versa (because square roots aren't additive). Similarly, if you are
using Grafen's (1989) arbitrary method to assign branch lengths, then you need to reapply the transform
after you add or delete any species. To avoid going astray, just follow this motto: "trim then
transform!"
23
CONFIDENCE INTERVALS ON THE ROOT NODE (Garland et al.,
1999)
The simplest possible use of independent contrasts is to compute a phylogenetically weighted
estimate of the mean value for a set of species. This is simply the estimated value at the root (basal)
node of the phylogeny (Garland et al., 1993; Schluter et al., 1997). For most purposes, it is an extra
piece of information; hence, it was not mentioned by Felsenstein (1985; for example, his Fig. 9 and
Table 1 do not consider its computation).
The value at the root node can also be interpreted as an estimate of the phenotype of the
hypothetical ancestor of all species in the data set. This value also turns out to be exactly the same as the
value reconstructed by weighted squared-change parsimony (Maddison, 1991; Garland et al., 1997). For
either interpretation of the root node, the confidence interval of its estimator may be desirable. For
example, placing a confidence interval about the phylogenetically correct mean would allow tests of a
priori hypotheses concerning the phenotype of the hypothetical ancestor (see also Garland et al., 1997;
Schluter et al., 1997; Polly, 2001; Webster and Purvis, 2002; Johnston et al., 2003).
To compute a standard error and 95% confidence interval for the root node of a phylogeny,
perform the following steps, as listed on page 377 of Garland et al. (1999; see their Appendix for the
proof):
1. compute the N-1 standardized independent contrasts, where N = the number of tips in the phylogeny
(terminal taxa, which can be populations, species or higher taxa).
2. square the standardized independent contrasts.
3. sum the squared standardized independent contrasts.
4. divide quantity (3) by N-1. This is an estimate of r, the rate of character evolution.
5. multiply quantity (4) by (v1' v2')/(v1' + v2') where v1' and v2' are the corrected lengths of the two
branches that descend from the root (basal) node.
6. take the square root of quantity (5). This is a phylogenetically weighted estimate of the standard
error of the root node or, equivalently, of the phylogenetically weighted mean of the tip data.
7. multiply quantity (6) by the critical value from the t distribution for a = 0.025 and N-1 degrees of
freedom, where N = the number of tip species. This yields the + 95% confidence interval.
The foregoing procedure yields exactly the same estimate for the root node as described in
Schluter et al. (1997), but without the use of maximum likelihood. But unlike the maximum likelihood
approach, it does not apply to other internal nodes. The values computed by independent contrasts for
other internal nodes are not optimal by any criterion: they are a type of "local parsimony"
reconstruction, whereas the root node is a "global parsimony" reconstruction, which is the same as
computed by squared-change parsimony (Maddison, 1991; Garland et al., 1997). However, by rerooting
a phylogenetic tree at a given internal node (which produces a trichotomy), the procedure described
above can be used to obtain the appropriate estimates for any node. PDTREE can be used for this (see
below) and the values obtained will be identical to those produced by the ANCML program of Schluter
et al. (1997).
24
Worked example (see Martins and Garland, 1991, p. 557;
saved on disk as APPAMG91.PDI):
Branch Length
(in units of
expected
variance of
character
evolution)
X6
Trait A
15
9
18
35
28
Trait B
1
2
3
4
5
X1
X2
X3
X4
X5
0 -|
|
|
1 -|
|
|
2 -|
|
|
3 -|
|
|
4 -|
|
|
5 -|
|
|
6 -|
|
|
7 -|
v4X5 + v5X4
= ------------v4 + v5
|
|
|
|
|
v1|
v2|
|
v4|
v5|
| X7 |
|
| X6 |
.--.--.
.--.--.
|
|
v3|
|
|
|
|
|
|
v6|
|
|
|
|
|
X8 |
.----.---.
|
|
|
|
|
v7|
|
|
|
|
|
|
v8|
|
|
|
|
|
|
|
|
|
X9
|
.------.------.
|
v2X1 + v1X2
= ------------v1 + v2
Trait B
31.5
4.5
2.5
2.5
12.0
1.5
6.5
6.5
=
v6' = v6 + v4v5/(v4 + v5)
X7
Trait A
=
=
v7' = v7 + v1v2/(v1 + v2)
=
25
X8
v6'X3 + v3X6
= -------------v3 + v6'
=
v8' = v8 + v3v6'/(v3 + v6')
X9
v7'X8 + v8'X7
= --------------v7' + v8'
=
=
25.3636
3.8182
5.3636
5.3636
19.3218
2.7701
__________________________________________________________________
Squared
Standardized Contrast Standardized Contrast
Contrast Variance
_____________________ _____________________
Trait A
Trait B
Trait A
Trait B
__________________________________________________________________
X1 - X2
(v1 + v2)
4.2426
-0.7071
18.0000
0.5000
X4 - X5
(v4 + v5)
4.9497
-0.7071
24.5000
0.5000
X3 - X6
(v3 + v6')
-5.7564
-0.6396
33.1363
0.4091
X7 - X8
(v7' + v8')
-3.8799
-0.6730
15.0533
0.4530
__________________________________________________________________
Thus, for the seven steps listed above:
Trait A
Trait B
1. and 2. are as in above table
3.
90.6897
1.8621
4.
22.6724
0.4655
5.
the quantity ((v7' v8')/(v7' + v8')) = 2.9387, therefore:
66.6274
1.3680
= rate of evolution
6.
8.1626
1.1696
= Standard error; t4, 0.05 = 2.776
7.
22.6593
3.2468
= + 95% confidence interval
19.3218
2.7701
= Mean (from above)
Conventional (nonphylogenetic) statistics are as follows:
4.6583
0.7071
= Standard error
12.9315
1.9629
= + 95% confidence interval
21.0000
3.0000
= Mean
26
Below is a phylogenetic tree for 12 species of Australian skinks (from Fig. 1 of Garland et al.,
1991). Branch lengths are arbitrarily set equal to unity. Values at tips are 2-character species codes and
data for preferred body temperature. This tree and tip data are in the file HB12C##.INP (dated 03-26-98;
the second character is optimal body temperature for sprinting, from Table 1 of Garland et al., 1991).
Values at nodes are maximum likelihood estimates from ANCML.EXE of Schluter et al.
(1997): they are identical to those produced by weighted squared-change parsimony, as in the DOS
PDSQCHP program, and to those produced in PDTREE by use of independent contrasts after
rerooting (see next page). The tree was drawn using the PRINTREE.EXE program of Schluter et al.
(1997), then modified by word processor. For the root node (#13), the point estimate and its 95%
confidence interval are given: the latter can be obtained from PDTREE or the ANCML program. This
example is also presented in Fig. 2 of Garland et al. (1999).
+-----------1 ew 34.1
!
+----------14 33.19
!
!
+------------2 la 32.5
!
!
!
!
+----------15 33.20
!
!
!
+------------3 lb 33.9
!
!
+-----------4 hd 24.8
!
95% C.I.
!
-13 32.27 (28.06-36.49)
+-----------18 25.39
!
!
!
!
!
+-----------5 hp 23.5
!
+----------17 27.86
!
!
!
+-----------6 ef 24.4
!
!
!
!
!
!
+-----------19 26.85
!
!
!
+-----------7 sq 28.8
!
!
!
!
!
!
+----------20 28.28
+----------16 31.36
!
+-----------8 st 29.5
!
!
!
!
+----------21 29.19
!
!
!
+-----------9 sk 29.8
!
!
+-----------10 cr 35.6
!
!
+----------22 33.93
!
+----------11 ct 35.3
!
!
+-----------23 34.84
!
+----------12 cu 35.3
27
CONFIDENCE INTERVALS ON OTHER INTERNAL NODES (Garland
et al., 1999)
ANCML automatically produces estimates and standard errors for all of the internal nodes,
including the root. PDTREE, on the other hand, only produces values for the root node because it is
using the mathematics of independent contrasts (as described in Garland et al., 1999). Nevertheless,
PDTREE can also be used to obtain the values listed below for the other internal nodes by rerooting
the tree so that the node of interest is at the base. If you reroot along a branch, rather than at a node per
se, then you can estimate values for an ancestor that is anywhere along a branch, not just at a node!
If you want to use ANCML and PRINTREE (from Schluter et al., 1997) on files from
PDTREE, follow these steps. First, use DOS PDTREE to save your file in the .BRK format and with
floating point values (i.e., no exponents: this is necessary because ANCML and PRINTREE won't accept
scientific notation). Rename the .BRK file as TREEFILE. Second, edit the .TIP file that was also
automatically saved when you saved the .BRK file. Delete the second character because ANCML only
handles one. You don't have to get rid of the scientific notation. However, you must insert spaces
before the data so that the data begin in column 11. Finally, insert a first line that indicates the number
of species followed by a 1. Save this as INFILE. PRINTREE uses TREEFILE only, but ANCML uses
both TREEFILE and INFILE as input.
To run ANCML, just type "ANCML > file.ext" at the DOS prompt. This will direct results to an
ASCII file named file.ext. If you just type "ANCML" the output will only appear on your screen.
PRINTREE works the same way.
28
Here is a simple example of using PDTREE to reroot a tree to get
a confidence interval for an internal node. We have three species,
named A, B, and C, with phenotypes (tip values) of 9, 7, and 2.
A
B
C
9
7
2
|
|
|
|
X
|
|
\-------/
|
|
|
|
|
Z
|
\-----------/
|
Original Tree
PDTREE indicates values of -4.81 < 5.33 < 15.47 for the root node (Z)
and its 95% confidence interval. Below is the tree redrawn to put
node X at the root.
2
|
|
|
|
|
9
7
|
|
|
|
|
X
|
Z
|
\---------------/
|
Rerooted Tree used to estimate value at node X
Note that for this very simple tree, "rerooting" just required
collapsing the branch between X and Z to zero, and then adding this
length to the branch between Z and C. With this tree, PDTREE gives
values of 0.92 < 7.33 < 13.75 for the root node (Z) and its 95%
confidence interval. However, because the branch length between nodes
29
Z and X is zero, they are effectively a single node. Thus, we have
actually estimated values for node X in the first tree. Note that the
two confidence intervals (for nodes Z and X) are not joint confidence
intervals for simultaneous inference. Rather, they are what you would
want to use for making an inference about one node or the other, not
both at once.
30
The foregoing procedure can also be used to estimate the value
and its confidence interval at any point along a branch. Suppose, for
example, that we wanted to know what the ancestor of species C was
like one branch length unit in the past. We can again reroot the
Original Tree.
9
7
|
|
|
X
|
\-------/
|
|
|
|
|
|
2
|
Z
|
\-----------/
|
Rerooted Tree used to estimate value in lineage
leading to species C one branch length unit
in the past.
In this tree, we have effectively just moved node Z up along the
branch leading to tip species C. (Note that in all three trees the
total amount of branch length remains the same.) With this tree,
PDTREE gives values of -3.75 < 2.67 < 9.08 for the root node (Z) and
its 95% confidence interval. But this root node is actually just a
stand-in for the ancestor of species C one branch length unit ago.
As you estimate the value for hypothetical ancestors that are
closer and closer along the branch leading to tip C, the point
estimate converges towards the tip value (2 in this example) and the
confidence intervals shrink to a width of zero. For example, the
estimate for a point 0.001 branch length units below species C is
1.786 < 2.001 < 2.216; for a point 0.0000001 branch length units below
species C, values are 1.998 < 2.000 < 2.002
31
FAQ
A. What about categorical traits?
As with conventional statistical analyses, categorical traits as independent variables are easy
to deal with when using phylogenetically based statistical methods. Think about conventional
statistics for a moment. If you have a continuous-valued dependent variable (e.g., body size) and a
categorical independent variable (e.g., diet scored as carnivore, omnivore, herbivore), then you can either
perform an ANOVA with a 3-category "factor" or you can perform a multiple regression with two
independent (X) variables that are 0-1 dummy variables. If the concept of dummy variables and multiple
regression is not familiar to you, then please consult a statistics text. You should be able to find a
section that lays out the formal equivalence of ANOVA and multiple regression with dummy variables.
(Note that for any categorical variable you will need C-1 dummy variables, where C is the number of
categories. One category is arbitrarily chosen as the "base" group for the coding scheme.)
If you are trying to work through an example in your favorite "canned" statistics package, then
note that you may need to specify an "option" in the ANOVA routine so that it uses "regression" or
"simultaneous" or "Type III" sums of squares (different terms for the same thing). Once you do that, you
should be able to get out exactly the same F statistics, P values, etc. However, the regression routine
will give you P values separately for each of your independent variables (the dummy variables you have
coded), so you will need to do a hand calculation to get the combined F test and P value (some statistics
packages, such as SPSS, have an option in the regression routine to "test" the significance of several X
variables at once, which can save you the trouble of the hand calculations).
Anyway, once you understand the concept of ANOVA, etc., please read the paper by Garland et
al. (1993) for how to do such tests phylogenetically.
Note that the above is not the same as logistic regression. I have not done logistic regression
very many times, and am not an expert, but as I remember it logistic regression is designed for the case
in which your dependent (Y) variable is binary and you want to "predict" it from one or more continuous
independent variables (and you could also have some categorical independent variables). When your
dependent variable is 0-1, your residuals are unlikely to be normally distributed, although they may come
close if you have several independent variables. In any case, logistic regression is designed to allow you
to specify other distributions besides normal for your residuals, and then give you the correct P values,
etc.
Logistic regression per se cannot be implemented in PDTREE. It could be implemented in the
GLS mode of operation, similar to our Matlab REGRESSION.M program that accompanies Blomberg et
al. (2003), but we have not yet done that. Also, by judicious use of Monte Carlo simulations (e.g., via
PDSIMUL: see Garland et al., 1993; Diaz-Uriarte and Garland, 1996, 1998) you should be able to
perform adequate analyses when you have a 0-1 dependent variable.
Another important point is that many traits people score in just two or three categories are
really just representing crude data for what is an inherently continuous-valued underlying trait.
For example, diet is often scored into three categories of herbivore, omnivore, carnivore. Typically, this
is because quantitative data on % meat in the diet are not available for all species in the analysis.
However, if one treats the 3-category variable as a quantitative with states of 1, 2, and 3 (respectively),
then it can be analyzed just as for any other variable available in a truly continuous-valued form. (The
same argument applies even if the variable is scored only in two categories, such as mesic and arid to
represent variation in water availability, or low and high altitude.) When available, continuous-valued
32
data are to be preferred, as they should typically increase statistical power to detect relations (Garland et
al., 1993; empirical examples in Al-kahtani et al., 2004; Muñoz-Garcia and Williams, 2005).
Finally, remember that the nodal values computed with phylogenetically independent
contrasts should be thought of just as intermediate steps in the algorithm, not estimates of
ancestral values. Many people have become quite disturbed when they realize that traits are averaged
and "smeared" across nodes, especially hen those traits are "categorical" in their view. But the nodal
values are not actually used for anything when you correlated (or regress) traits. (an exception applies
for the root node, which can be viewed as an estimate of the common ancestor for the entire
phylogenetic tree. This is explained in detail in Garland et al. (1999, 2005) and above in this
documentation.
If you need to analyze relationships between two characters that are truly discrete characters, then
see Pagel (1994, 1999), MacClade (Maddison and Maddison, 2000), and Mesquite
(http://mesquiteproject.org/mesquite/mesquite.html; see also Paradis and Claude, 2002), and papers and
programs by Alan Grafen (http://users.ox.ac.uk/~grafen/). For a general listing of phylogeny-related
programs, see the website maintained by Joe Felsenstein
(http://evolution.genetics.washington.edu/phylip/software.html).
B. What if I don't have any branch lengths?
Search for "arbitrary" branch lengths above.
C. What if the diagnostic checks are conflicting?
[insert example from 282 seminar]
E. Very often it seems that results become "less significant" (larger P values) when I perform
phylogenetic analyses. Are there any examples in which results become more significant?
Yes. One example is in this paper, in which log kidney mass was regressed on log body mass
and a variable indicating (crudely) habitat aridity. In the conventional multiple regression, the effect of
habitat was not significant (1-tailed P = 0.3107), but in the corresponding analysis with phylogenetically
independent contrasts it was (1-tailed P = 0.0346).
Many other such examples do exist, although I have not compiled. A couple that come to mind
are Promislow's (1991) study of mammalian blood traits and the relation between body size and
longevity in bats (Joao Pedro de Magalhaes, pers. comm. April 2006).
33
REFERENCES
NOTE: Not all of the following are specifically cited in this document.
Abouheif, E. 1998. Random trees and the comparative method: a cautionary tale. Evolution 52:11971204.
Abouheif, E. 1999. A method for testing the assumption of phylogenetic independence in comparative
data. Evolutionary Ecology Research 1:895-909.
Abouheif, E., and D. J. Fairbairn. 1997. A comparative analysis of allometry for sexual size dimorphism:
assessing Rensch's rule. American Naturalist 149:540-562.
Ackerly, D. D. 2000. Taxon sampling, correlated evolution, and independent contrasts. Evolution
54:1480-1492.
Ackerly, D. D., and M. J. Donoghue. 1998. Leaf size, sapling allometry, and Corner's rules: phylogeny
and correlated evolution in maples (Acer). American Naturalist 152:767-791.
Ackerly, D. D., and P. B. Reich. 1999. Convergence and correlations among leaf size and function in
seed plants: a comparative test using independent contrasts. American Journal of Botany
86:1272-1281.
Aguirre, L. F., A. Herrel, R. van Damme, and E. Matthysen. 2002. Ecomorphological analysis of trophic
niche partitioning in a tropical savannah bat community. Proc. R. Soc. Lond. B 269:1271–1278.
Al-kahtani, M. A., C. Zuleta, E. Caviedes-Vidal, and T. Garland, Jr. 2004. Kidney mass and relative
medullary thickness of rodents in relation to habitat, body size, and phylogeny. Physiological and
Biochemical Zoology 77:346-365. (plus online Appendix B).
Alroy, J. 1998. Cope's rule and the dynamics of body mass evolution in North American fossil
mammals. Science 280:731-734.
Ashton, K. G. 2001. Body size variation among mainland populations of the western rattlesnake
(Crotalus viridis). Evolution 55:2523-2533. [PDTREE, arbitrary branch lengths]
Ashton, K. G. 2004. Comparing phylogenetic signal in intraspecific and interspecific body size datasets.
Journal of Evolutionary Biology 17:1157-1161. [PDTREE, PDRANDOM, PDERROR, PDDIST,
PHYSIG]
Ashton, K. G. 2004. Sensitivity of intraspecific latitudinal clines of body size for tetrapods to sampling,
latitude and body size. Integrative and Comparative Biology 44:403-412. [PDTREE, PHYSIG]
Ashton, K. G., and C. R. Feldman. 2003. Bergmann's Rule in nonavian reptiles: turtles follow it, lizards
and snakes reverse it. Evolution 57:1151-1163. [PDTREE, PDSIMUL, RDRANDOM,
PDERROR, PDTIPS]
Ashton, K. G., M. C. Tracy, and A. de Queiroz. 2000. Is Bergmann's rule valid for mammals? American
Naturalist 156:390-415. [results of regular and independent contrasts analyses differ]
Autumn, K., C. T. Farley, M. Emshwiller, and R. J. Full. 1997. Low cost of locomotion in the banded
gecko: a test of the nocturnality hypothesis. Physiological Zoology 70:660-669.
Autumn, K., D. Jindrich, D. DeNardo, and R. Mueller. 1999. Locomotor performance at low
temperature and the evolution of nocturnality in geckos. Evolution 53:580-599.
Barbosa, A. 1993. Morphometric variation of the hindlimb of waders and its evolutionary implications.
Ardeola 1993:65-75.
Barbosa, A., and E. Moreno. 1999a. Hindlimb morphology and locomotor performance in waders: an
evolutionary analysis. Biological Journal of the Linnean Society 67:313-330.
Barbosa, A., and E. Moreno. 1999b. Evolution of foraging strategies in shorebirds: an ecomorphological
approach. The Auk 116:712-725.
34
Bauwens, D., and R. Diaz-Uriarte. 1997. Covariation of life-history traits in lacertid lizards: a
comparative study. American Naturalist 149:91-111.
Bauwens, D., T. Garland, Jr., A. M. Castilla, and R. Van Damme. 1995. Evolution of sprint speed in
lacertid lizards: morphological, physiological, and behavioral covariation. Evolution 49:848-863.
Bjorklund, M. 1994. The independent contrast method in comparative biology. Cladistics 10:425-433.
Bleiweiss, R. 1997. Covariation of sexual dichromatism and plumage colours in lekking and non-lekking
birds: A comparative analysis. Evolutionary Ecology 11:217-235.
Bleiweiss, R. 1999. Joint effects of feeding and breeding behavior on trophic dimorphism in
hummingbirds. Proc. Roy. Soc. B. 266:2491-2498.
Bleiweiss, R., J. A. W. Kirsch, and J. C. Matheus. 1997. DNA hybridization evidence for the principal
lineages of hummingbirds (Aves: Trochilidae). Mol. Biol. Evol. 14:325-343.
Blob, R. W. 2000. Interspecific scaling of the hindlimb skeleton in lizards, crocodilians, felids and
canids: does limb bone shape correlate with limb posture? Journal of Zoology, London 250:507531.
Blomberg, S. P. 2000. Fels-Rand: An Xlisp-Stat program for the comparative analysis of data under
phylogenetic uncertainty. Bioinformatics 16:1010-1013.
Blomberg, S. P., and T. Garland, Jr. 2002. Tempo and mode in evolution: phylogenetic inertia,
adaptation and comparative methods. Journal of Evolutionary Biology 15:899-910.
Blomberg, S. P., T. Garland, Jr., and A. R. Ives. 2003. Testing for phylogenetic signal in comparative
data: behavioral traits are more labile. Evolution 57:717-745.
Blomberg, S. P., A. R. Ives, and T. Garland, Jr. 2001. Detecting phylogenetic signal in comparative data.
American Zoologist 41:1395. Abstract.
Bonine, K. E. 2001. Morphological and physiological predictors of lizard locomotor performance: a
phylogenetic analysis of trade-offs. Unpublished Ph.D. dissertation, University of WisconsinMadison. v + 222 pages.
Bonine, K. E., and T. Garland, Jr. 1999. Sprint performance of phrynosomatid lizards, measured on a
high-speed treadmill, correlates with hindlimb length. Journal of Zoology, London 248:255-265.
Bonine, K. E., T. T. Gleeson, and T. Garland, Jr. 2001. Comparative analysis of fiber-type composition
in the iliofibularis muscle of phrynosomatid lizards (Sauria). Journal of Morphology 250:265280.
Brana, F. 1996. Sexual dimorphism in lacertid lizards: male head increase vs female abdomen increase?
Oikos 75:511-523.
Branquart, E. 1999. In review.
Brashares, J., T. Garland, Jr., and P. Arcese. 2000. The ecology, behavior, and phylogeny of the African
antelope. Behavioral Ecology 11:452-463.
Butler, M. A., T. W. Schoener, and J. B. Losos. 2000. The relationship between sexual size dimorphism
and habitat use in Greater Antillean Anolis lizards. Evolution 54:259-272.
Canterbury, G. 2002. Metabolic adaptation and climatic constraints on winter bird distribution. Ecology
83:946-957.
Carranza, J. 1996. Sexual selection for male body mass and the evolution of litter size in mammals.
American Naturalist 148:81-100.
Carrascal, L. M., E. Moreno, and I. Mozetich. 2001. The link between leg morphology, locomotion and
habitat preferences: a phylogenetic and ecomorphological study in Passeriformes. Avian Science
1:in press.
35
Chevalier, C. D. 1991. Aspects of thermoregulation and energetics in the Procyonidae (Mammalia:
Carnivora). Unpubl. Ph.D. dissertation, Univ. of Calif., Irvine. 202 pp.
Cheverud, J. M., and M. M. Dow. 1985. An autocorrelation analysis of genetic variation due to lineal
fission in social groups of rhesus macaques. American Journal of Physical Anthropology 67:113121.
Cheverud, J. M., M. M. Dow, and W. Leutenegger. 1985. The quantitative assessment of phylogenetic
constraints in comparative analyses: sexual dimorphism in body weight among primates.
Evolution 39:1335-1351.
Christian, A., and T. Garland, Jr. 1996. Scaling of limb proportions in monitor lizards (Squamata:
Varanidae). Journal of Herpetology 30:219-230.
Clobert, J., T. Garland, Jr., and R. Barbault. 1998. The evolution of demographic tactics in lizards: a test
of some hypotheses concerning life history evolution. Journal of Evolutionary Biology 11:329364.
Colwell, R. K. 2000. Rensch's rule crosses the line: convergent allometry of sexual size dimorphism in
hummingbirds and flower mites. American Naturalist 156:495-510.
Conroy, G. C. 2003. The inverse relationship between species diversity and body mass: do primates play
by the “rules”? Journal of Human Evolution 45:783–795.
Cox, R. M., S. L. Skelly, and H. B. John-Alder. 2003. A comparative test of adaptive hypotheses for
sexual size dimorphism in lizards. Evolution 57:1653–1669.
Crespi, B., and M. Worobey. 1998. Comparative analysis of gall morphology in Australian gall thrips:
the evolution of extended phenotypes. Evolution 52:1686-1696. [uses PDAP for simulations]
Crowley, P. H. 1992. Resampling methods for computation-intensive data analysis in ecology and
evolution. Annual Review of Ecology and Systematics 23:405-447.
Cruz-Neto, A. P., T. Garland, Jr., and A. S. Abe. 2001. Diet, phylogeny, and basal metabolic rate in
phyllostomid bats. Zoology 104:49-58.
Degen, A. A., M. Kam, I. S. Khokhlova, B. R. Krasnov, and T. G. Barraclough. 1998. Average daily
metabolic rate of rodents: habitat and dietary comparisons. Functional Ecology 12:63-73.
de Queiroz, K. 1996. Including the characters of interest during tree reconstruction and the problems of
circularity and bias in studies of character evolution. American Naturalist 148:700-708.
de Queiroz, K. 2000. Logical problems associated with including and excluding characters during tree
reconstruction and their implications for the study of morphological character evolution. Pages
192-212 in J. J. Wiens, ed. Phylogenetic analysis of morphological data. Smithsonian Institution
Press, Washington, D.C.
de Repentigny, Y. 2000. Song versus plumage in some North American Oscines: Testing Darwin's
hypothesis. Ecoscience 7:137-148.
Diaz, J. A., D. Bauwens, and B. Asensio. 1996. A comparative study of the relation between heating
rates and ambient temperatures in lacertid lizards. Physiological Zoology 69:1359-1383.
Diaz-Uriarte, R., and T. Garland, Jr. 1996. Testing hypotheses of correlated evolution using
phylogenetically independent contrasts: sensitivity to deviations from Brownian motion.
Systematic Biology 45:27-47.
Diaz-Uriarte, R., and T. Garland, Jr. 1998. Effects of branch length errors on the performance of
phylogenetically independent contrasts. Systematic Biology 47:654-672.
Diaz-Uriarte, R., and T. Garland, Jr. In revision. PHYLOGR: An R package for the analysis of
comparative data via Monte Carlo simulations or generalized least-squares approaches.
Bioinformatics.
36
Diniz-Filho, J. A. F., and N. M. Torres. 2002. Phylogenetic comparative methods and the geographic
range size-body size relationship in new world terrestrial carnivora. Evolutionary Ecology
16:351-367. [PDSIMUL, PDERROR]
Donoghue, M. J., and D. D. Ackerley. 1996. Phylogenetic uncertainties and sensitivity analyses in
comparative biology. Philosophical Transactions of the Royal Society of London B, Biological
Sciences 351:1241-1249.
Ebensperger, L. A., and H. Cofre. 2001. On the evolution of group-living in the New World cursorial
hystricognath rodents. Behavioral Ecology 12:227-236.
Felsenstein, J. 1985. Phylogenies and the comparative method. American Naturalist 125:1-15.
Felsenstein, J. 1988. Phylogenies and quantitative characters. Annual Review of Ecology and
Systematics 19:445-471.
Ferguson, S. H., J. A. Virgl, and S. Lariviere. 1996. Evolution of delayed implantation and associated
grade shifts in life history traits of North American carnivores. Ecoscience 3:7-17.
Frappell, P. F., D. S. Hinds, and D. F. Boggs. 2001. Scaling of respiratory variables and the breathing
pattern in birds: an allometric and phylogenetic approach. Physiological and Biochemical
Zoology 74:75-89.
Freckleton, R. P. 2000. Phylogenetic tests of ecological and evolutionary hypotheses: checking for
phylogenetic independence. Functional Ecology 14:129-134.
Freckleton, R. P., P. H. Harvey, and M. Pagel. 2002. Phylogenetic analysis and comparative data: a test
and review of evidence. Am. Nat. 160:712-726.
Futuyma, D. J. 1998. Evolutionary biology. 3rd ed. Sinauer Associates, Sunderland, Mass.
Garland, T., Jr. 1992. Rate tests for phenotypic evolution using phylogenetically independent contrasts.
American Naturalist 140:509-519.
Garland, T., Jr. 1994. Phylogenetic analyses of lizard endurance capacity in relation to body size and
body temperature. Pages 237-259 (+ references) in Lizard Ecology: Historical and Experimental
Perspectives, L. J. Vitt and E. R. Pianka, eds. Princeton University Press, Princeton.
Garland, T., Jr. 1999. Laboratory endurance capacity predicts variation in field locomotor behaviour
among lizard species. Animal Behaviour 57:77-83.
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.
Garland, T., Jr. 2003. Selection experiments: an under-utilized tool in biomechanics and organismal
biology. Pages 23-56 in V. L. Bels, J.-P. Gasc, and A. Casinos, eds. Vertebrate Biomechanics
and Evolution. BIOS Scientific Publishers, Oxford, U.K.
Garland, Jr., and S. C. Adolph. 1994. Why not to do 2-species comparative studies: limitations on
inferring adaptation. Physiological Zoology 67:797-828.
Garland, T., Jr. and R. Díaz-Uriarte. 1999. Polytomies and phylogenetically independent contrasts: an
examination of the bounded degrees of freedom approach. Systematic Biology 48:547-558.
Garland, T., Jr., and A. R. Ives. 2000. Using the past to predict the present: Confidence intervals for
regression equations in phylogenetic comparative methods. American Naturalist 155:346-364.
Garland, T., Jr., and C. M. Janis. 1993. Does metatarsal/femur ratio predict maximal running speed in
cursorial mammals? Journal of Zoology, London 229:133-151.
Garland, T., Jr., et al. In preparation. Statistical comparisons of phenotypic diversity among
monophyletic or ecologically defined groups.
37
Garland, T., Jr., P. H. Harvey, and A. R. Ives. 1992. Procedures for the analysis of comparative data
using phylogenetically independent contrasts. Systematic Biology 41:18-32.
Garland, T., Jr., R. B. Huey, and A. F. Bennett. 1991. Phylogeny and thermal physiology in lizards: a
reanalysis. Evolution 45:1969-1975.
Garland, T., Jr., A. F. Bennett, and E. L. Rezende. 2005. Phylogenetic approaches in comparative
physiology. Journal of Experimental Biology 208:3015-3035.
Garland, T., Jr., K. L. M. Martin, and R. Diaz-Uriarte. 1997. Reconstructing ancestral trait values using
squared-change parsimony: plasma osmolarity at the origin of amniotes. Pages 425-501 in
Amniote Origins: Completing the Transition to Land, S. S. Sumida and K. L. M. Martin, eds.
Academic Press, San Diego.
Garland, T., Jr, P. E. Midford, and A. R. Ives. 1999. An introduction to phylogenetically based statistical
methods, with a new method for confidence intervals on ancestral states. American Zoologist
39:374-388.
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.
Gibbs, A. G., and L. M. Matzkin. 2001. Evolution of water balance in the genus Drosophila. Journal of
Experimental Biology 204:2331-2338.
Gittleman, J. L., and M. Kot. 1990. Adaptation: statistics and a null model for estimating phylogenetic
effects. Syst. Zool. 39:227-241.
Gittleman, J. L., C. G. Anderson, M. Kot, and H.-K. Luh. 1996. Phylogenetic lability and rates of
evolution: a comparison of behavioral, morphological and life history traits. Pages 166-205 in E.
P. Martins, ed. Phylogenies and the comparative method in animal behavior. Oxford University
Press, Oxford.
Goyman, W., and J. C. Wingfield. 2003. Allostatic load, social status, and stress hormones – the costs of
social status matter. Animal Behaviour. In press. [arbitrary branch lengths]
Grafen, A. 1989. The phylogenetic regression. Philosophical Transactions of the Royal Society of
London B 326:119-157.
Gray, D. A. 1996. Carotenoids and sexual dichromatism in North American passerine birds. American
Naturalist 148:453-480.
xxcite: Hale, M. E., J. H. Long, Jr., M. J. McHenry, and M. W. Westneat. 2002. Evolution of behavior
and neural control of the fast-start escape response. Evolution 56:993–1007.
Hammond, R. L., and L. Keller. 2004. Conflict over male parentage in social insects. PLoS Biology
2(9):e248. [PDTREE and CAIC, all branch lengths = 1]
Hansen, T. F., and E. P. Martins. 1996. Translating between microevolutionary process and
macroevolutionary patterns: The correlation structure. Evolution 50:1404-1417.
Harmon, L. J., J. A. Schulte II, A. Larson, and J. B. Losos. 2003. Tempo and mode of evolutionary
radiation in iguanian lizards. Science 301:961-964. [PDSIMUL]
Harris, M. A., and K. Steudel. 1997. Ecological correlates of hind-limb length in the Carnivora. Journal
of Zoology, London 241:381-408.
Harvey, P. H., and M. D. Pagel. 1991. The comparative method in evolutionary biology. Oxford
University Press, Oxford. 239 pp.
Harvey, P. H., and A. Rambaut. 2000. Comparative analyses for adaptive radiations. Philosophical
Transactions of the Royal Society of London B 355:1599-1605.
Herrel, A., J. J. Meyers, and B. Vanhooydonck 2002a. Relations between microhabitat use and limb
shape in phrynosomatid lizards. Biological Journal of the Linnean Society 77:149–163.
38
Herrel, A., J. C. O'Reilly, and A. M. Richmond. 2002b. Evolution of bite performance in turtles. Journal
of Evolutionary Biology 15:1083-1094.
Herrel, A., B. Vanhooydonck, and R. Van Damme. 2004. Omnivory in lacertid lizards: adaptive
evolution or constraint? Journal of Evolutionary Biology 17:974-984.
Huelsenbeck, J. P., and B. Rannala. 2003. Detecting correlation between characters in a comparative
analysis with uncertain phylogeny. Evolution 57:1237-1247.
Huey, R. B. and A. F. Bennett. 1987. Phylogenetic studies of coadaptation: preferred temperatures
versus optimal performance temperatures of lizards. Evolution 41:1098-1115.
Hutcheon, J. M., and T. Garland, Jr. 2004. Are megabats big? Journal of Mammalian Evolution 11:257276.
Hutcheon, J. M., J. A. W. Kirsch, and T. Garland, Jr. 2002. A comparative analysis of brain size in
relation to foraging ecology and phylogeny in the Chiroptera. Brain, Behavior and Evolution
60:165-180.
Irschick, D. J., C. C. Austin, K. Petren, R. N. Fisher, J. B. Losos, and O. Ellers. 1996. A comparative
analysis of clinging ability among pad-bearing lizards. Biological Journal of the Linnaen Society
59:21-35.
Ives, A. R., P. E. Midford, and T. Garland, Jr. 2006. Within-species variation and measurement error in
phylogenetic comparative methods. Systematic Biology. In press.
Iwaniuk, A. N., and J. E. Nelson. 2001. A comparative analysis of relative brain size in waterfowl
(Anseriformes). Brain, Behavior and Evolution 57:87-97.
Jackson, J. F., D. C. Adams, and U. B. Jackson. 1999. Allometry of constitutive defense: a model and a
comparative test with tree bark and fire regime. American Naturalist 153:614-632.
Janz, N., and S. Nylin. 1998. Butterflies and plants: a phylogenetic study. Evolution 52:486-502.
Johnston, I. A., D. A. Fernandez, J. Calvo, V. L. A. Vieira, A. W. North, M. Abercomby, and T.
Garland, Jr. 2003. Reduction in muscle fibre number during the adaptive radiation of
notothenioid fishes: a phylogenetic perspective. Journal of Experimental Biology 206:2595-2609.
Kingsolver, J. G., and D. W. Pfennig. 2004. Individual-level selection as a cause of Cope's rule of
phyletic size increase. Evolution 58:1608-1612.
Kirsch, J. A. W., and F.-J. Lapointe. 1997. You aren't (always) what you eat: evolution of nectar-feeding
among Old World fruitbats (Megachiroptera: Pteropodidae). Pages 313-330 in T. J. Givnish and
K. J. Sytsma, eds. Molecular evolution and adaptive radiation. Cambridge University Press, New
York.
Kirsch, J. A., J. M. Hutcheon, D. G. P. Byrnes, and B. D. Lloyd. 1998. Affinities and historical
zoogeography of the New Zealand short-tailed bat, Mystacina tuberculata Gray 1843, inferred
from DNA-hybridization comparisons. Journal of Mammalian Evolution 5:33-64.
Knouft, J. H., and L. M. Page. 2003. The evolution of body size in extant groups of North American
freshwater fishes: speciation, size distributions, and Cope's Rule. American Naturalist 161:413421.
Kohlsdorf, T., C. A. Navas, and T. Garland, Jr. 2001. Limb and tail lengths in relation to substrate usage
in Tropidurus lizards. Journal of Morphology 248:151-164.
Langer, P. 2002. The digestive tract and life history of small mammals. Mammal Rev. 32:107–131.
Langer, P. 2003. Lactation, weaning period, food quality, and digestive tract differentiations in Eutheria.
Evolution 57:1196-1215. [uses PDTREE, "residuals," and Abouheif (1999) test]
Lapointe, F.-J., and T. Garland, Jr. 2001. A generalized permutation model for the analysis of crossspecies data. Journal of Classification 18:109-127.
39
Laurin, M. 2004. The evolution of body size, Cope’s Rule and the origin of amniotes. Syst. Biol. 53:594622.
Lindenfors, P. 2002. Sexually antagonistic selection on primate size. Journal of Evolutionary Biology
15:595-607.
Losos, J. B. 1990. Ecomorphology, performance capability, and scaling of West Indian Anolis lizards:
An evolutionary analysis. Ecological Monographs 60:369-388.
Losos, J. B. 1994. An approach to the analysis of comparative data when a phylogeny is unavailable or
incomplete. Systematic Biology 43:117-123.
Losos, J. B., and L. Chu. 1998. Examination of factors potentially affecting dewlap size in Caribbean
anoles. Copeia 1998:430-438.
Lovegrove, B. G. 2000. The zoogeography of mammalian basal metabolic rate. American Naturalist
156:201-219.
Lovegrove, B. G. 2001. The evolution of body armour in mammals: plantigrade constraints of large body
size. Evoluton 55:1464–1473.
Lovegrove, B. G. 2003. The influence of climate on the basal metabolic rate of small mammals: a slowfast metabolic continuum. J. Comp. Physiol. B 173:87-112. [Pagel's (1992) arbitrary branch
lengths. Wolf et al. (1998) for climate on a star phylogeny.]
Maddison, D. R., D. L. Swofford, and W. P. Maddison. 1997. Nexus: an extensible file format for
systematic information. Systematic Biology 46:590-621.
Maddison, W. P. 1989. Reconstructing character evolution on polytomous cladograms. Cladistics 5:365377.
Maddison, W. P. 1991. Squared-change parsimony reconstructions of ancestral states for continuousvalued characters on a phylogenetic tree. Systematic Zoology 40:304-314.
Maddison, W. P., and D. R. Maddison. 1992. MacClade. Analysis of phylogeny and character evolution.
Version 3. Sinauer Associates, Sunderland, Mass. 398 pp.
Martin, T. E., and J. Clobert. 1996. Nest predation and avian life history evolution in Europe versus
North America: a possible role of humans? American Naturalist 147:1028-1046.
Martins, E. P. 1993. A comparative study of the evolution of Sceloporus push-up displays. American
Naturalist 142:994-1018.
Martins, E. P. 1994. Estimating the rate of phenotypic evolution from comparative data. American
Naturalist 144:193-209.
Martins, E. P. 1996a. Conducting phylogenetic comparative studies when the phylogeny is not known.
50:12-22.
Martins, E. P. 1996b. Phylogenies, spatial autoregression and the comparative method: a computer
simulation test. Evolution 50:1750-1765.
Martins, E. P., ed. 1996c. Phylogenies and the comparative method in animal behavior. Oxford
University Press, Oxford. x + 415 pp.
Martins, E. P., and T. Garland, Jr. 1991. Phylogenetic analyses of the correlated evolution of continuous
characters: a simulation study. Evolution 45:534-557.
Martins, E. P., and T. F. Hansen. 1996. The statistical analysis of interspecific data: a review and
evaluation of comparative methods. Pages 22-75 in E. P. Martins, ed. Phylogenies and the
comparative method in animal behavior. Oxford University Press, Oxford.
Martins, E. P., and T. F. Hansen. 1997. Phylogenies and the comparative method: a general approach to
incorporating phylogenetic information into the analysis of interspecific data. American
Naturalist 149:646-667.
40
Martins, E. P., and J. Lamont. 1998. Estimating ancestral states of a communicative display: a
comparative study of Cyclura rock iguanas. Animal Behaviour 55:1685-1706.
McArdle, B., and A. G. Rodrigo. 1994. Estimating the ancestral states of a continuous-valued character
using squared-change parsimony: an analytical solution. Systematic Biology 43:573-578.
McKechnie, A. E., and B. O. Wolf. 2004. The allometry of avian basal metabolic rate: good predictions
need good data. Physiological and Biochemical Zoology. In press.
McPeek, M. A. 1995. Testing hypotheses about evolutionary change on single branches of a phylogeny
using evolutionary contrasts. American Naturalist 145:686-703.
McShea, D. W. 1994. Mechanisms of large-scale evolutionary trends. Evolution 48:1747-1763.
McShea, D. W. 1998. Possible largest-scale trends in organismal evolution. Annual Review of Ecology
and Syustematics 29:293-318.
Mermoz, M. E., and J. F. Ornelas. 2004. Phylogenetic analysis of life-history adaptations in parasitic
cowbirds. Behavioral Ecology 15:109-119.
Miles, D. B., and A. E. Dunham. 1992. Comparative analyses of phylogenetic effects in the life history
patterns of iguanid reptiles. American Naturalist 139:848-869.
Miles, D. B., and A. E. Dunham. 1996. The paradox of the phylogeny: character displacement of
analyses of body size in island Anolis. Evolution 50:594-603.
Mooers, A. O., S. M. Vamosi, and D. Schluter. 1999. Using phylogenies to test macroevolutionary
hypotheses of trait evolution in cranes (Gruinae). American Naturalist 154:249-259.
Mysterud, A., F. J. Pérez-Barbería, and I. J. Gordon. 2001. The effect of season, sex and feeding style on
home range area versus body mass scaling in temperate ruminants. Oecologia 127:30–39.
Neter, J., W. Wasserman, and M. H. Kutner. 1989. Applied linear regression models. 2nd ed. Richard D.
Irwin, Inc., Homewood, Illinois. xv + 667 pp.
Nunn, C. L., and R. A. Barton. 2000. Allometric slopes and independent contrasts: a comparative test of
Kleiber's Law in primate ranging patterns. American Naturalist 156:519-533.
Oakley, T. H., and C. W. Cunningham. 2000. Independent contrasts succeed where ancestor
reconstruction fails in a known bacteriophage phylogeny. Evolution 54:397-405.
Pagel, M. D. 1992. A method for the analysis of comparative data. Journal of Theoretical Biology
156:431-442.
Pagel, M. D. 1993. Seeking the evolutionary regression coefficient: an analysis of what comparative
methods measure. Journal of Theoretical Biology 164:191-205.
Pagel, M. D. 1994. Detecting correlated evolution on phylogenies: a general method for the comparative
analysis of discrete characters. Proceedings Royal Society of London B 255:37-45.
Pagel, M. 1998. Inferring evolutionary processes from phylogenies. Zoologica Scripta 26:331-348.
Perez-Barberia, F. J., and I. J. Gordon. 1999a. The functional relationship between feeding type and jaw
and cranial morphology in ungulates. Oecologia 118:157-165.
Perez-Barberia, F. J., and I. J. Gordon. 1999b. The relative roles of phylogeny, body size and feeding
style on the activity time of temperate ruminants: a reanalysis. Oecologia 120:193-197.
Pérez-Barbería, F. J., and I. J. Gordon. 2001. Relationships between oral morphology and feeding style
in the Ungulata: a phylogenetically controlled evaluation. Proc. Roy. Soc. Lond. B 268:10211030.
Pérez-Barbería, F. J., I. J. Gordon, and M. Pagel. 2002. The origins of sexual dimorphism in body size in
ungulates. Evolution 56:1276-1285.
Perry, G., and T. Garland, Jr. 2002. Lizard home ranges revisited: effects of sex, body size, diet, habitat,
and phylogeny. Ecology 83:1870-1885.
41
Pierce, V. A., and D. L. Crawford. 1997. Phylogenetic analysis of glycolytic enzyme expression. Science
276:256-259.
Pianka, E. R. 1995. Evolution of body size: varanid lizards as a model system. American Naturalist
146:398-414.
Pitnick, S. 1996. Investment in testes and the cost of making long sperm in Drosophila species.
American Naturalist 148:57-80.
Pitnick, S., T. A. Markow, and G. S. Spicer. 1995. Delayed male maturity is a cost of producing large
sperm in Drosophila. Proc. Natl. Acad. Sci. USA 92:10614-10618.
Pitnick, S., G. S. Spicer, and T. A. Markow. 1997. Phylogenetic examination of female incorporation of
ejaculate in Drosophila. Evolution 51:833-845.
Polly, P. D. 2001. Paleontology and the comparative method: ancestral node reconstructions versus
observed node values. American Naturalist 157:596-609.
Porter, E. E., and B. A. Hawkins. 2001. Latitudinal gradients in colony size for social insects: termites
and ants show different patterns. American Naturalist 157:97-106.
Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. 1989. Numerical recipes in Pascal.
Cambridge University Press, Cambridge.
Price, T. D., A. J. Helbig, and A. D. Richman. 1997. Evolution of breeding distributions in the Old
World leaf warblers (Genus Phylloscopus). Evolution 51:552-561.
Purvis, A. 1995. A composite estimate of primate phylogeny. Philosophical Transactions of the Royal
Society of London B 348:405-421.
Purvis, A., and T. Garland, Jr. 1993. Polytomies in comparative analyses of continuous characters.
Systematic Biology 42:569-575.
Pyron, M. 1999. Relationships between geographical range size, body size, local abundance, and habitat
breadth in North American suckers and sunfishes. Journal of Biogeography 26:549-558.
Pyron, M. 2000. Testes mass and reproductive mode of minnows. Behavioral Ecology and Sociobiology
48:132-136.
Reynolds, P. S. 1997. Phylogenetic analysis of surface areas of mammals. Journal of Mammalogy
78:859-868.
Reynolds, P. S. 2002. How big is a giant? The importance of methodology in estimating body size of
extinct mammals. Journal of Mammalogy 83:321–332. [uses Garland and Ives, 2000 prediction
method]
Reynolds, P. S., and R. M. Lee, III. 1996. Phylogenetic analysis of avian energetics: passerines and
nonpasserines do not differ. American Naturalist 147:735-759.
Rezende, E. L., and T. Garland, Jr. 2003. Comparaciones interespecíficas y métodos estadísticos
filogenéticos. Pages 79-98 in F. Bozinovic, ed. Fisiología Ecológica & Evolutiva.Teoría y casos
de estudios en animales. Ediciones Universidad Católica de Chile, Santiago.
Rezende, E. L., F. Bozinovic, and T. Garland, Jr. 2004. Climatic adaptation and the evolution of basal
and maximum rates of metabolism in rodents. Evolution 58:1361-1374. [different branch lengths
for different traits, one set being a star; results of conventional and contrasts analyses differ]
Rezende, E. L., D. L. Swanson, F. F. Novoa, and F. Bozinovic. 2002. Passerines versus nonpasserines:
so far, no statistical differences in the scaling of avian energetics. J. Exp. Biol. 205:101-107.
Rheindt, F. E., T. U. Grafe, and E. Abouheif. 2004. Rapidly evolving traits and the comparative method:
how important is testing for phylogenetic signal? Evolutionary Ecology Research 6:377-396.
[different branch lengths for different traits, one set being a star]
42
Ridley, M., and A. Grafen. 1996. How to study discrete comparative methods. Pages 76-103 in E. P.
Martins, ed. Phylogenies and the comparative method in animal behavior. Oxford University
Press, Oxford.
Rodriguez-Robles, J. A., and H. W. Greene. 1996. Ecological patterns in Greater Antillean
macrostomatan snake assemblages, with comments on body-size evolution in Epicrates (Boidae).
Pages 339-357 in R. Powell and R. W. Henderson, eds. Contributions to West Indian
herpetology: A tribute to Albert Schwartz. Society for the Study of Amphibians and Reptiles,
Ithaca, New York. Contributions to Herpetology, vol. 12.
Rohlf, F. J. 2001. Comparative methods for the analysis of continuous variables: geometric
interpretations. Evolution 55:2143-2160.
Rohlf, F. J., and R. R. Sokal. 1981. Statistical tables. 2nd ed. W. H. Freeman and Co., San Francisco.
219 pp.
Ross, C. F., M. Henneberg, M. J. Ravosa, and S. Richard. 2004. Curvilinear, geometric and phylogenetic
modeling of basicranial flexion: is it adaptive, is it constrained? Journal of Human Evolution
46:185-213.
Rowe, L., and G. Arnqvist. 2002. Sexually antagonistic coevolution in a mating system: combining
experimental and comparative approaches to address evolutionary processes. Evolution 56:754767.
Schluter, D., T. Price, A. O. Mooers, and D. Ludwig. 1997. Likelihood of ancestor states in adaptive
radiation. Evolution 51:1699-1711.
Schultz, B. B. 1985. Levene's test for relative variation. Systematic Zoology 34:449-456.
Shine, R. 2000. Vertebral numbers in male and female snakes: the roles of natural, sexual and fecundity
selection. Journal of Evolutionary Biology 13:455-465.
Shine, R., S. Keogh, P. Doughty, and H. Giragossyan. 1998. Costs of reproduction and the evolution of
sexual dimorphism in a 'flying lizard' Draco melanopogon (Agamidae). Journal of Zoology,
London 246:203-213.
Sibley, C. G., and J. E. Ahlquist. 1990. Phylogeny and classification of birds: a study in molecular
evolution. Yale Univ. Press, New Haven, Conn. 1008 pp.
xxcite: Smith, R. J., and J. M. Cheverud. 2002. Scaling of sexual size dimorphism in body mass: a
phylogenetic analysis of Rensch's rule in primates. International Journal of Primatology 23:10951135.
Sokal, R. R., and F. J. Rohlf. 1981. Biometry. 2nd ed. W. H. Freeman and Co., San Francisco. 859 pp.
Stamps, J. A., J. B. Losos, and R. M. Andrews. 1997. A comparative study of population density and
sexual size dimorphism in lizards. American Naturalist 149:64-90.
Székely, T., J. D. Reynolds, and J. Figuerola. 2000. Sexual size dimorphism in shorebirds, gulls and
alcids: the influence of sexual and natural selection. Evolution 54:1404-1413.
Taylor, J. R. E. 1998. Evolution of energetic strategies in shrews. Pages 309-346 in J. M. Wojcik and M.
Wolsan, eds. Evolution of shrews. Mammal Research Institute, Polish Academy of Sciences,
Bialowieza, Poland.
Thomson, D. L., P. Monaghan, and R. W. Furness. 1998. The demands of incubation and avian clutch
size. Biol. Rev. 73:293-304.
Tieleman, B. I., and J. B. Williams. 2000. The adjustment of avian metabolic rates and water fluxes to
desert environments. Physiological and Biochemical Zoology 73:461-479.
Tobalske, B. W., and K. P. Dial. 2000. Effects of body size on take-off flight performance in the
Phasianidae (Aves). Journal of Experimental Biology 203:3319-3332.
43
Tobalske, B. W., D. L. Altshuler, and D. R. Powers. 2004. Take-off mechanics in hummingbirds
(Trochilidae). Journal of Experimental Biology 207:1345-1352. [PDTREE, RMA]
Toro, E., A. Herrel, B. Vanhooydonck, and D. J. Irschick. 2003. A biomechanical analysis of intra- and
interspecific scaling of jumping and morphology in Caribbean Anolis lizards. J. Exp. Biol.
206:2641-2652.
Traveset, A., M. F. Willson, and M. Verdu´. 2004. Characteristics of fleshy fruits in southeast Alaska:
phylogenetic comparison with fruits from Illinois. Ecography 27:41-48.
Van Cakenberghe, V., A. Herrel, and L. F. Aguirre. 2002. Evolutionary relationships between cranial
shape and diet in bats (Mammalia: Chiroptera). Pages 205-236 in P. Aerts, K. D’Août, A. Herrel,
and R. Van Damme, eds. Topics in functional and ecological vertebrate morphology. Shaker
Publishing. ISBN 90-423-0204-6. [PDSIMUL, PDANOVA]
Van Damme, R. 1999. Evolution of herbivory in lacertid lizards: effects of insularity and body size.
Journal of Herpetology 33:663-674.
Van Damme, R., and B. Vanhooydonck. 2001. Origins of interspecific variation in lizard sprint capacity.
Functional Ecology 15:186-202. [PDSIMUL, PDANOVA, All BL = 1]
Van Damme, R., and B. Vanhooydonck. 2002. Speed versus manoeuvrability: association between
vertebral number and habitat structure in lacertid lizards. J. Zool., Lond. 258:327-334.
[PDSIMUL, PDANOVA, All BL = 1]
Vanhooydonck, B., and D. J. Irschick. 2002. Is evolution predictable? Evolutionary relationships of
divergence in ecology, performance and morphology in Old and New World lizard radiations.
Pages 191-204 in P. Aerts, K. D’Août, A. Herrel, and R. Van Damme, eds. Topics in functional
and ecological vertebrate morphology. Shaker Publishing. ISBN 90-423-0204-6. [All BL = 1]
Vanhooydonck, B., and R. Van Damme. 1999. Evolutionary relationships between body shape and
habitat use in lacertid lizards. Evolutionary Ecology Research 1:785-805.
Vanhooydonck, B., and R. Van Damme. 2003. Relationships between locomotor performance,
microhabitat use and antipredator behaviour in lacertid lizards. Functional Ecology 17:160–169.
[all BL = 1]
Vanhooydonck, B., R. Van Damme, and P. Aerts. 2001. Speed and stamina trade-off in lacertid lizards.
Evolution 55:1040-1048. xxcite above
Wagner, P. J. 1996. Contrasting the underlying patterns of active trends in morphologic evolution.
Evolution 50:990-1007.
Walton, M. 1993. Physiology and phylogeny: the evolution of locomotor energetics in hylid frogs.
American Naturalist 141:26-50.
Ward, D., and M. K. Seely. 1996. Adaptation and constraint in the evolution of the physiology and
behavior of the Namib Desert tenebrionid beetle genus Onymacris. Evolution 50:1231-1240.
Weathers, W. W. 1992. Scaling nestling energy requirements. Ibis 134:142-153.
Weathers, W. W., and R. B. Siegel. 1995. Body size establishes the scaling of avian postnatal metabolic
rate: an interspecific analysis using phylogenetically independent contrasts. Ibis 137:532-542.
Webster, A. J., and A. Purvis. 2002. Testing the accuracy of methods for reconstructing ancestral states
of continuous characters. Proc. R. Soc. Lond. B. 269:143-150.
Westneat, M. W. 1995. Feeding, function, and phylogeny: analysis of historical biomechanics and
ecology in labrid fishes using comparative methods. Systematic Biology 44:361-383.
Westneat, M. W. 1995. Phylogenetic systematics and biomechanics in ecomorphology. Environmental
Biology of Fishes 44:263-383.
Williams, J. B. 1996. A phylogenetic perspective of evaporative water loss in birds. The Auk 113:457472.
44
Wolf, C. M., T. Garland, Jr., and B. Griffith. 1998. Predictors of avian and mammalian translocation
success: reanalysis with phylogenetically independent contrasts. Biological Conservation
86:243-255.
Zani, P.A. 2000. The comparative evolution of lizard claw and toe morphology and clinging
performance. Journal of Evolutionary Biology 13:316-325.
xxNeed to insert these (in appropriate places) as examples that have used PDAP (some with arbitrary
branch lengths):
Barbosa, 1993; Walton, 1993; Jordano, 1995; Konarzewski, 1995; Pitnick et al., 1995; Steudel and
Beattie, 1995; Weathers and Siegel, 1995; Westneat, 1995a,b; Dutenhoffer and Swanson, 1996; Pitnick,
1996; Reynolds and Lee, 1996; Williams, 1996; Ricklefs et al., 1996; Abouheif and Fairbairn, 1997;
Bauwens and Díaz-Uriarte, 1997; Bleiweiss, 1997; Harris and Steudel, 1997; Jackman et al., 1997;
Pitnick et al., 1997; Reynolds, 1997; Perez-Barberia and Gordon, 1999a,b; Barbosa and Moreno,
1999a,b; Bleiweiss, 1999; de Repentigny, 2000
45
THE FOLLOWING SECTIONS ARE TAKEN DIRECTLY FROM THE DOCUMENTATION
FOR DOS PDTREE (PDINSTRW.DOC) AND HAVE NOT YET BEEN MODIFIED FROM
Mesquite PDTREE:
6. Branch Length Manipulations
Your third option in the Editing Module is (B)ranch length manipulations. This allows
changes to all the branches at once, such as a direct exponential or logarithmic transformation of each
branch segment, or transformation by Grafen's (1989) rho method.
Be cautious about using branch length transformations, especially when your tree has
polytomies (see below). For example, you cannot apply a log transform if any of your branches are <
1.0 in length, because this would yield negative values. The exception to this rule is that if you start with
some 0-length branches (i.e., intentional polytomies), then you can still apply the log transform, provided
none of the other branches are between zero and one in length. Note also that if your tree has branch
lengths that equal exactly one, then a log transform will turn those into branches of zero-length, thus
creating artificial polytomies that you don't want! However, you can avoid this by first rescaling the
total height of the tree. Some of the complications of the log transform can be avoided by instead
transforming by raising all of the branch lengths to a power < unity, which will accomplish something
similar, depending on the power you choose (e.g., 0.5 = square root, 0.25 = fourth root, 0.1 = tenth root).
PDTREE also allows you to reset all branch lengths to one of four arbitrary conditions, three of
which are shown in Figure 1: (C)onstant sets all branch segments to a length of 1.0; (G)rafen changes
the lengths to Grafen's (1989, Figure 2) arbitrary method (cardinality); (P)agel changes the lengths to
Pagel's (1992, 7th paragraph on page 441) arbitrary method (this is like most rectangular cladograms are
drawn, as if lined up on graph paper). Note that for what we are calling Pagel's arbitrary method, we
have arbitrarily set the branch lengths around polytomous nodes so as to minimize length between the
polytomous node and the tips of the tree, which also minimizes the total length of the tree (how to treat
the branch lengths for polytomies was not discussed by Pagel [1992]). A fourth set of arbitrary branch
lengths is similar to Grafen's (1989), but uses the logarithm (base 10 in PDTREE) of the number of
species descended from each node to set the node depth. This is indicated as (N)ee in PDTREE, because
Sean Nee suggested it in a personal communication to Purvis (1995, p. 416). Note that if you have
polytomies (constructed by setting some internal branch lengths to zero), then using C, G, N or P will
leave them as polytomies.
(F)ull screen print is the fourth option. This is intended for performing a screen dump of the
tree; it will eliminate the information box at the bottom of the Editing screen (see below). This output,
in combination with a list of species (tip) names (and perhaps tip data) produced in a word processor,
can be used to literally cut and paste together a labeled phylogenetic tree (see also above).
Finally, you can choose to (R)eturn to the Main Menu when you are done editing the tree. In
summary, from the Editing Module you can choose to edit the tip data, branch lengths or whole tree, or
get a full screen print of the tree.
If you select (E) from the Editing Module menu, you see your tree on the screen with some
descriptive data below it. "num" is the total length of all branches on the tree; "starnum" is what the
total branch length would be if it were a star phylogeny (instantaneous radiation from the root) of the
same height; "ratio" is num/starnum. Use the arrow keys to move around the tree as described at the
bottom of the Editing Module menu screen. The branch that blinks and is a different color than the rest
is the branch you are on. From here you can (T)rim off the branch you are on and all its children. You
can (A)dd a branch to the branch you are on. This will require you to know where along the current
46
branch you want the new one to branch off, plus data for the newly created tip. Don't worry if you are
unsure of what to enter here, because you can change it later. If you are on a tip, you can (C)hange the
name and/or values of it. You can do a (L)ength change on the current branch. You can do a (S)calar
extension of all the branches at the current height. This option is a little confusing, but what happens is
this: an imaginary line is drawn across the entire tree at the height of the top of the current branch.
Every branch that this line touches is extended the amount you input. You can (D)raw a horizontal line
through the current node. This is useful to see if all the nodes line up at the top. You can zoom in on a
subclade of the tree that you are working on (without changing the whole tree) by using the (E)dit just
the subtree command. You will then be working with just the subclade that the current branch forms
when it is viewed as the root. To undo this, select (P)op and you will again be working with the whole
tree. Finally, you can select (R)eturn to return to the Editing Module menu.
47
8. Computing Felsenstein's (1985) Independent Contrasts
This includes option to save regression confidence and prediction intervals.
(S)ave .STA file {screen display statistics and contrasts}
This writes the statistics from both sets of stats (V and W in
sequence).
Before you see Screen 1 or 9, you will be asked if you want to display a single contrast in a
different symbol. This is useful for testing a priori hypotheses about particular contrasts (e.g., see
Garland and Adolph, 1994, pp. 809-812; Reynolds and Lee, 1996) or for exploratory data analysis (e.g.,
Fig. 4c in Garland and Janis, 1993; Fig. 3 in Pianka, 1995). You will also be asked if you want to
display all of the contrasts within a given clade (as named by its basal node) in a different symbol. This
is useful for checking for clade differences in the average (minimum) rate of evolution (Garland, 1992;
examples in Barbosa, 1993; Clobert et al., 1998; Barbosa and Moreno, 1999b; Garland and Ives, 2000;
Hutcheon and Garland, 2004; xxothers).
If you are not satisfied with the various graphs, then Return to the main menu, go to the Editing
Module, and transform your tip data and/or your branch lengths. Note that different branch length
transformations might be appropriate for each trait in an analysis (see Garland et al., 1992; Pagel,
1992; for empirical examples, see Garland, 1994; Bonine and Garland, 1999; Lovegrove, 2003; Rezende
et al., 2004; Rheindt et al., 2004). This is especially true when some of the independent variables are
non-phylogenetic "nuisance" variables, such as method of calculation of home range area (Wolf et al.,
1998; Perry and Garland, 2002). However, PDTREE only lets you compute contrasts with a single set of
(possibly transformed) branch lengths for both traits. So, if you want to use different branch lengths
transformations for the two traits in your data file, then you will need to save two different .FIC files,
one with each set of transformed branches, and then use only the appropriate contrasts from each one.
Also note that, for a given character, a single branch length transformation may not work for
an entire phylogeny. That is, for a given set of branches, rates of evolution may vary among clades.
One such example involves limb proportions (e.g., metatarsal/femur ratio) in Carnivora and ungulates
(Garland, 1992; Figures 3c, 4b, 5, and 6a in Garland and Janis, 1993). Another involves body mass and
basal metabolic rate of birds (Garland and Ives, 2000; McKechnie and Wolf, 2004). If, for a given set of
branches, rates of evolution differ in different subclades, then statistical tests based on contrasts from the
entire tree may not be appropriate, because the "identically distributed" part of the standard i.i.d.
assumption will be violated. One solution would be to separate the subclades for all statistical analyses.
Another possibility is to transform the branch lengths differently in different subclades (see
Garland and Ives [2000] for a reanalysis of the Reynolds and Lee [1996] data on body masses and basal
metabolic rates of passerine versus other birds). This can be done as follows. First, Edit your tree.
From the editing screen, put the cursor on the node at the base of the clade whose branches you want to
transform differently. Then type E, which will zoom you into that clade only. Next type R to return to
the main editing menu. Now type B for branch length manipulations. You will only be working on the
zoomed subclade. Thus, any transformation that you specify will be applied only to that subclade!
When finished, return to the main editing menu, and then Edit the tree again. Type P for pop and you
will again see the entire phylogeny, which should have the subclade's branches differently transformed.
48
Now, you can go back to the Analyze with Felsenstein module and recheck all of the diagnostics -- make
sure to put the specially transformed subclade in a different symbol. If you save a .FIC or .STA (next
paragraph) or other file of computations, it will be based on the differently transformed branches.
Once you are satisfied that you have adequate branch lengths, then choose either Save to get a
.STA file, containing statistics as shown on all the 11 graphs plus the contrasts listed at the bottom of the
file (as in the .FIC file, but including column names), or Just save to obtain a .FIC file (for Felsenstein's
Independent Contrasts). The .FIC file is all you need to enter into a commercial statistics/graphics
package (note that it does not include column names).
Note that a copy of the .FIC file is also saved at the bottom of the .STA file. This copy of the
.FIC file includes column names.
49
13. Measurement Error
All of the above discussion of independent contrasts has assumed that the data available for
analysis are mean values for a series of different species (perhaps separated by sex). Thus, we ignore
information on the magnitude of individual variation within species (i.e., the amount of variation that
remains after separating individuals into sex and/or age categories) as well as the magnitude of
measurement error per se. Most comparative studies that have been presented to date operate in exactly
this way (review in Martins and Hansen, 1996). Methods are now available that can use information on
individual variation, measurement error, and so forth (e.g., Martins and Lamont, 1998). We have
recently worked out how to incorporate measurement error in analyses with independent contrasts.
Essentially, this involves lengthening each terminal branch by an amount proportional to the amount of
within-tip error, which results in differential weighting on contrasts with more or less measurement
error. We plan to write a manuscript on this soon, and to incorporate this option into PDAP (planned as
the PD_SE.EXE module, which has to date [10 March 2004] only been used in Kevin E. Bonine's
[2001] Ph.D. dissertation work on lizard muscle fiber-type composition).
For now, it is important to note that incorporation of measurement error does not necessarily
affect point estimates of parameters in any predictable direction. In other words, when
measurement error is incorporated into the analysis, estimates of correlations between traits, values at
ancestral nodes, etc., will not necessarily be either increased or decreased consistently. In general,
however, standard errors of these estimates will tend to decrease. xxcheck this! Hence, effects on Pvalues are not consistent.
50
14. Unresolved Nodes (polytomies)
PDTREE and PDSIMUL (see below) can handle unresolved nodes (multifurcations). In
PDTREE, it is often easiest to initially enter a tree as completely binary, then return to some internode
branches and change their length to zero. (Use the "(L)ength change" option while editing the tree
graphically.)
Be cautious about using branch length transformations, especially when your tree has
polytomies. For example, you cannot apply a log transform if any of your branches are < 1.0 in length.
The exception to this rule is that if you do start with some 0-length branches (i.e., intentional
polytomies), then you can still apply the log transform, provided none of the other branches are between
zero and one in length. Note also that if your tree has branch lengths that equal exactly one, then a log
transform will turn those into branches of zero-length, thus creating artificial polytomies that you don't
want! However, you can avoid this by first rescaling the total height of the tree. Some of the
complications of the log transform can be avoided by instead transforming by raising all of the branch
lengths to a power < unity, which will accomplish something similar, depending on the power you
choose (e.g., 0.5 = square root, 0.25 = fourth root, 0.1 = tenth root).
Note that if you change all branches to one of the four sets of arbitrary branch lengths, i.e.,
using the (C)onstant, (P)agel, (G)rafen or (N)ee option under (B)ranch length manipulations, they will
leave your polytomies intact; that is, they will not affect your zero-length branches. Thus, it is easy to try
different sets of branches, even if you have polytomies.
For computing correlations with Felsenstein's (1985) independent contrasts (Purvis and Garland,
1993) or for simulating data with PDSIMUL (Garland et al., 1993), the way a polytomy is arbitrarily
"resolved" for initial tree entry will not matter. When computing independent contrasts, different pairs
of species or nodes will be subtracted depending on the way a polytomy is "resolved" for initial entry,
but once the appropriate internode branch lengths are set to zero and a correlation or regression through
the origin is used to analyze the standardized contrasts (as in PDTREE and CMSINGLE), the estimate
of the correlation or regression will be identical. Amazing but true. Of course, graphs of independent
contrasts, including the diagnostic plots 1-8 in PDTREE, would be affected (cf. Garland et al., 1992;
Garland and Diaz-Uriarte, 1999).
For hypothesis testing a correlation through the origin based on independent contrasts, the
degrees of freedom available from a polytomous node range between a minimum of one and a maximum
of the number of contrasts minus one (the number of contrasts is always the number of species minus
one), depending on whether the polytomy is "soft" (sensu Maddison, 1990), representing ignorance of
the true branching sequence), or "hard," indicating true instantaneous speciation. Thus, for an entire
phylogenetic tree with some polytomous nodes, the degrees of freedom for a correlation range between a
minimum of the number of nodes minus one (except for a completely unresolved tree -- a star phylogeny
-- which has one degree of freedom rather than zero) and a maximum of the number of contrasts minus
one (i.e., the number of species minus two). Thus, for trees with soft polytomies, it makes sense to
report a range of significance levels (P-values) when correlating independent contrasts.
Recently, Garland and Diaz-Uriarte (1999) have shown by computer simulations that the method
of Purvis and Garland (1993) does indeed lead to a bounding of Type I error rates when testing for the
correlation between two traits. Several empirical studies have used this approach (e.g., xx add Christian
and Garland, 1996; Carranza, 1996; Stamps et al., 1997; Mysterud et al., 2001).
***** NOTE: If you analyze a completely unresolved tree (a star phylogeny with equal-length
branches) by independent contrasts, then the estimate of the correlation coefficient will be identical to
51
an ordinary Pearson product-moment correlation of the tip data! You may want to verify this on your
own data. It is a good way to make sure that your tip data have been correctly entered. Similarly, if you
estimate the value at the root node (see above) of a star phylogeny it will be identical to the simple mean
of the data.
***** NOTE: You can create a star phylogeny very easily from the (B)ranch length
manipulations module (in the Editing Module menu). First, if your tree has any non-contemporaneous
tips, then make them line up across the top by choosing either Grafen's arbitrary or Pagel's arbitrary
branch lengths. Second, choose (T)ransform by Grafen's (1989) rho, and enter a rho value of zero; this
yields a star. Third, choose (C)onstant; this will change all of the non-zero branches to length of one.
PDSIMUL also handles polytomies. Any branches with zero length just receive no change.
When hypothesis testing against computer simulated data (e.g., Martins and Garland, 1991; Garland et
al., 1993), degrees of freedom per se are not used for determining significance levels (cf. Crowley,
1992), although the nominal d.f. are used in computing F statistics, etc., for both the real and the
simulated data. As discussed in Garland et al. (1993), the relative lengths of the branches below and
above a polytomy will affect the critical values obtained from computer-simulated data. If branches
between a polytomous node and its descendants are set to be relatively long, this is tantamount to
treating the descendants as relatively statistically independent, which will yield relatively liberal critical
values. Setting the branches to be relatively short will be conservative, because the descendants are
being treated as close relatives, expected to be relatively similar phenotypically, as if degrees of freedom
were reduced. These points should be remembered when using arbitrary branch lengths.
Polytomies can also be dealt with simply by omitting species whose relationships are uncertain or
by performing the analysis with several alternative topologies (Losos, 1994; Donoghue and Ackerley,
1996; Abouheif, 1998; Ackerley and Donoghue, 1998: for empirical examples, see Bauwens et al.,
1995; Bauwens and Diaz-Uriarte, 1997; Irschick et al., 1996; Vanhooydonck and Van Damme, 1999).
Note that if you simulate data up a completely unresolved tree (a star phylogeny) and analyze
them by comparing two or more groups by ANOVA or ANCOVA (e.g., using PDNOVA), the F
statistics obtained will on average be the same as conventional tabular values (see Garland et al., 1993).
Speciational Brownian Motion evolution in PDSIMUL is equivalent to Gradual Brownian
Motion performed on a phylogeny with all branch lengths set equal to one. If you specify Speciational
evolution on a tree with polytomies, then they will remain as polytomies (i.e., in effect, only the nonzero branches are set to unity).
***** NOTE: You cannot simulate under the Punctuated Equilibrium model with a tree
containing polytomies. This makes sense in terms of the original formulation of the model, which
envisioned a small daughter population budding off from a large mother population, with change
occurring only in the daughter. Thus, with bifurcations, PDSIMUL simply chooses at random which
daughter will change and which will remain constant (stasis); this general procedure is necessary
because, for a given tree, we will not know which branch represented the mother and which the daughter
during past evolution. With a polytomy, it is unclear which branch should be viewed as the big mother
population and which as the daughters, and even a random choosing procedure is difficult to implement
in the present program.
52
15. Input/Output Formats (MacClade, PAUP, PHYLIP)
Importing tree files to PDTREE:
In addition to the .PDI and .INP formats, PDTREE can import files produced by other
phylogenetic programs. PDTREE can read a file containing one tree saved in the bracket format (the
standard "New Hampshire" or "Newick" tree format). The file must use the extension .BRK. Because
most phylogenetic programs can export tree files in this bracket format, no other formats are currently
accepted by PDTREE.
Note that .BRK format files do not contain node names. Therefore, when reading in a .BRK file,
PDTREE will name the internal nodes, beginning with 1A ... 1Z, then 2A ... 2Z, and eventually 1a ... 1z,
and so forth. Any conflicting tip name results in the program asking the user to change the tip name.
When reading a .BRK file, PDTREE will also look for a .TIP file containing the tip data. If a
.TIP file with the same root name as the .BRK is not found, then PDTREE will set all character values to
zero. The format of the .TIP file is a column of 2-character tip names, a column of tip data for trait one,
and finally a column of data for trait two: columns must be separated by one or more spaces.
Also, note that all of your tip names should start with a unique, combination of two-characters.
These can be any ASCII printing characters, such as A, b, 5, (, ], *, _, #, ^, ~, ', ?, etc., but not spaces! If
PDTREE finds a duplicate 2-character combinations starting a name, then it will generate unique 2character combinations sequentially, after the first one.
You can actually read in a .BRK file with tip names longer than two characters; PDTREE will
just ignore anything beyond the first two characters. However, if you write the file back out with
PDTREE, you will lose everything except the first two characters.
The following is an acceptable description of a rooted, fully bifurcating tree for PDTREE:
(s1:1.24,(s2:3.76,(s3:1.02,s4:3.11):1.41):2.77);
In this example, s1, s2, s3, and s4 are names of tips. The numbers following the colons (1.24, 3.76, 1.02,
3.11, 1.41, and 2.77) are branch lengths. Note that internal nodes do not have names; PDTREE will
generate these anew each time it reads in such a file.
If PDTREE finds missing branch lengths in a .BRK file that you attempt to input, then it will set
them equal to one in length unless they are part of a polytomy. Thus, a tree that had contemporaneous
tips in the MacClade display screen will not when it is read into PDTREE. However, you can change
the branch lengths globally in the (B)ranch length manipulation option of the main Editing Module, or
you can change them individually in the (E)dit the tree graphically option of the main Editing Module
(where you can also resolve polytomies by changing 0-length branches to some positive number).
53
Here are some step-by-step instructions for getting trees into PDTREE.
How to go from PHYLIP to PDTREE ?
1. save your tree in a TREEFILE
2. rename that file with the extension .BRK
3. Input the tree to PDTREE
How to go from PAUP to PDTREE ?
1. save your tree with BRANCH LENGTHS and using the PHYLIP 3.5 format
2. name that file with the extension .BRK
3. Input the tree to PDTREE
How to go from MacClade 3.01 to PDTREE ?
These instructions have been tested with version 3.01 of MacClade.
1. In MacClade, go to the menu item File:Options for saving:Nexus Format. If the box for "include
translation table in TREEs block" is checked, uncheck it. Select "CR+LF" as the line delimiter (the
default for MacIntosh files is just "CR").
2. Save the file and transfer it to a PC that has PDTREE. Because DOS file names are limited to 8+3
characters, we suggest the extension .NEX.
3. Open the file in your favorite word processor and locate the appropriate tree in the file. To do this,
search for "BEGIN TREES". This will indicate the start of the set of trees in the file. If you know the
name of a specific named tree, then you can search for the start of that tree by name. Otherwise, the last
tree created in the file will occur at the end, usually titled "UNTITLED."
4. Once you have located this tree, copy the Newick description (i.e., the tree in bracket format), which
starts with an open parenthesis and ends with a semicolon, and paste it into a new file with the extension
.BRK. Do not include the initial portion of the line (which will look like "TREE * UNTITLED =
[&R]") or any initial spaces.
5. Save the new file with the .BRK extension, which you should then be able to load into PDTREE.
(Because Nexus files are so large, it is usually more efficient to paste the tree into a new file, rather than
cut out the remainder of the Nexus file.)
6. Note that MacClade does not save trees with branch lengths, so they will be set to one as described on
the previous page.
54
Exporting tree files from PDTREE:
When PDTREE saves a file with the .BRK extension, three files
are created:
The .BRK file contains the tree in bracket format with branch lengths
The .TIP file contains the tip data, as presented in a .PDI file
The .NAM file contains a list of taxon names (2 characters) and a
vector filled with zeros.
The .TIP and .NAM are used to export data from PDTREE to other programs. The .NAM file allows the
user to export (at least) the taxon names to other programs that can only deal with qualitative characters
(e.g., PAUP and MacClade). Some phylogeny reconstruction programs don't accept continuous traits, so
they cannot read a .TIP file when it contains data for quantitative characters. Thus, if you try to open a
.TIP file containing real numbers in these programs, it will not work, so use the .NAM file instead!
MacClade will accept PDTREE files directly, with one caveat, as noted below. To use other
programs, you can go through MacClade first.
1. start MacClade. When it prompts for a file to open, you have two options:
A. if the .TIP file contains integers only, then open it. MacClade will ask what format it is in,
with a drop-down menu. Select the Simple Table format.
B. if the .TIP file contains real values, then open the .NAM file instead, and do as described for
a.
MacClade will now display an empty character matrix with the 2-character names of the tips of
the tree.
2. select Go To Tree Window from the display menu, and tell it to Open Treefile
3. select the .BRK file corresponding to the .NAM file
4. choose the file format PHYLIP, which will bring up another menu, from which you select "1. PHYLIP
1" and click on Get Tree. Some warning messages may appear, but eventually ...
5. the tree that will appear on screen has the same topology as in PDTREE. The difference is that branch
lengths are ignored! New branch lengths can be computed by relating this tree to a new data set,
using the same taxon names.
MacClade 3.01 does not always distinguish between upper and lower case in tip names. Therefore, if
you read in a .BRK file (such as one made from 49LBR.INP), it will find apparent duplicate tip names
and will drop one of each duplicate from the tree; that is, you would end up with a 47-tip tree instead of
a 49-tip tree.
55
PHYLIP will also accept PDTREE files, with a little modification.
1. Use PDTREE to save a .BRK file
2. PHYLIP won't accept branch lengths in scientific notation,
so change them in your .BRK file using a text editor.
3. use PHYLIP's RETREE program. Input the .BRK file and, accepting
the defaults, Write a Rooted tree; then quit the program.
This file will be called OUTTREE by default, and it is a
cleaned-up version of the .BRK file from PDTREE.
You can also use PHYLIP's DRAWTREE and DRAWGRAM programs to print out the tree in various
and wonderful formats. For example, input the OUTTREE file into either program, choose the
appropriate printer, and then Write the file; it will be called PLOTFILE by default. Finally, type "COPY
PLOTFILE PRN:" to send the file to your printer.
56
5. Sign tests with independent contrasts and simulated data
A very conservative way to test for an association between two traits using standardized
independent contrasts is to perform a simple sign test, rather that computing a Pearson correlation
through the origin (e.g., see Felsenstein, 1985, p. 13; Felsenstein, 1988, p. 457; Grafen, 1989, p. 148; for
examples, see Rodriguez-Robles and Greene, 1996; xxadd others). On screen 9, for example, PDTREE
reports the number of contrasts for the Y variable that are positive, negative or zero, given that the X
variable has been "positivized" (Garland et al., 1992), along with the 2-tailed P-value for this test (by
comparison with the binomial distribution [Sokal and Rohlf, 1981, pp. 449-450, 693]).
Alternatively, one could compare the results for their one real data set with a distribution created
by analysis of simulated data sets. PDERROR includes in its output the number of Y-variable contrasts
that are greater than, less than, and equal to zero (see Tables 2 and 3 above, columns 9-11), given that
the X-trait contrasts have been positivized. For example, one could make a histogram of the number of
positive contrasts and see if the number of positive contrasts for the real data set was greater than the
95th percentile (this would be a one-tailed test).
57
6. Testing for directional trends in character evolution
In combination with PDSIMUL (or RDRANDOM), PDERROR could be used to test for
directional trends in character evolution. Columns 17 and 18 (see tables above) report the correlation of
estimated nodal values for traits 1 and 2, respectively, with the base node height (tip values are excluded
from the computation). The same correlation is reported in screens 7 and 8 of PDTREE, within "(V)iew
diagnostics" option of the "(A)nalyze data with Felsenstein's (1985) contrasts" module. Thus, one can
(1) simulate data with PDSIMUL, (2) analyze them in PDERROR, (3) make a histogram of the
correlations for the simulated data, and (4) compare the distribution with the correlation for the real data.
(See work by Etienne Branquart, Miguel Verdu.)
Other options are available when data for fossil taxa are available, and various analyses can be
performed in Mesquite (e.g., see Laurin, 2004)
58
TABLE OF CONTENTS
I. PDTREE.........................................................9
1. Entering Trees and File Formats.............................9
2. Branch Lengths.............................................10
Figure 1. Three kinds of arbitrary branch lengths........12
3. The Main Menu..............................................13
4. Entering Tip Data..........................................16
5. Printing Trees.............................................17
6. Branch Length Manipulations................................19
7. Recommendations for using PDTREE to Edit Trees.............21
8. Computing Felsenstein's (1985) Independent Contrasts.......22
Contents of the .FIC file of contrasts....................26
Contents of the .CI file..................................27
Contents of the .RSD file of "residuals"..................28
9. Allometry and Correcting for Body Size.....................29
10. SPSS/PC+ Code for analyzing independent contrasts..........30
Regression................................................30
ANCOVA....................................................32
Principal Components Analysis (PCA).......................34
11. Confidence Intervals on the Root Node......................35
Worked Example............................................37
12. Confidence Intervals on other Internal Nodes...............40
13. Measurement Error..........................................43
14. Unresolved Nodes (polytomies)..............................44
15. How to Create a Star Phylogeny.............................45
16. Input/Output Formats (MacClade, PAUP, PHYLIP)..............47
Phylogenetically correct ("PC") vs. uninformed ("PU") stats.......85
K. Testing for Phylogenetic Signal in Comparative Data..........108
REFERENCES....................................................110
59
***** NOTE: You must use 2-character names for tip species and nodes (e.g., Cf for Canis
familiaris, rt for the root node, 01 for the first node to the left of the root). Upper and lower case are
recognized as different by the programs, and any combination of key symbols is allowed (e.g., aa,
AA, aA, a@, *9, =+, ^/, ?$, 1!, -9).
If you are editing a tree that contains a large number of species, then it may become difficult to
see exactly where you are as you move around in the tree. PDTREE allows you to zoom in on a subset
of the tree: with the cursor on any internal node, just type E (for edit) and you will then just see that
subclade on the screen. To resume editing the entire tree, just type P (for pop).
The zoom feature allows differential transformation of the branch lengths within a
particular part (subclade) of your phylogenetic tree. That is, if you zoom in on a subclade, then
return to the main menu of the Editing Module, then enter Branch length manipulations, anything you do
will apply only to the subclade! You can then return to the Edit screen and pop to again view the entire
tree, with just the branches of one subclade changed. This is an important feature because clades may
vary in rate of evolution (Garland, 1992; examples in Barbosa, 1993; Clobert et al., 1998; Barbosa and
Moreno, 1999b; Garland and Ives, 2000; Hutcheon and Garland, 2004; xxothers), which may in turn
necessitate differential branch length transformations (Grafen, 1989, p. 146; Garland and Ives, 2000).
(T)ip data manipulations is your second choice. This allows you to change the value of the tip
traits one at a time, or all at once. You can reenter one value, or log transform all of them. You can also
see a scatterplot of the two characters, along with conventional statistics, such as regression. We
will not list all the options here, because they are explained in the Tip Data Edit Module menu. Note
that a copy of the statistics produced under the (V)iew: XY plot of Trait 1 vs. Trait 2 is also saved at the
beginning of the .STA file.
4. Entering Tip Data
The easiest way to enter data is by pasting blocks of text from your word processor, using the
column editing feature. (In WORD for Windows, put the cursor at the corner of a column that you want
to select, hold down the 'Ctrl' and 'Alt' keys simultaneously, and then move the mouse to highlight the
column. Release the two keys and click on Edit, Copy. Move to the new place and choose Edit, Paste.)
Note that the current version of PDTREE only uses two characters at once. So, if you want to
make copies of the same tree but with completely different tip data, then it will also be easiest to do so
using the column editing feature of a word processor.
60
EXAMPLE DATA FILE
49LBR70.PDI
This file can be read directly into Mesquite. It is in the preferred format of DOS PDTREE. The
phylogeny block is at the start, from Garland et al. (1993). The data block includes 2-character tip
names, log10 body mass, and log10 home range area. You can paste out the file below, save it as a plain
ASCII text file with the name 49LBR70.PDI, and import it to Mesquite.
49
01
03
05
06
31
95
Tm
Ur
Um
93
92
Nn
pl
07
Mp
Ml
21
22
28
32
34
Cp
Ct
Lp
Ca
Uc
Vf
10
18
Hh
Cc
23
Aj
35
Pp
36
Pt
Pl
02
04
99
Tb
16
Cs
Db
26
Eh
29
$$
01
03
05
06
31
95
95
31
06
93
92
92
93
07
07
05
21
22
28
32
34
34
32
28
22
21
03
10
18
18
10
23
23
35
35
36
36
01
02
04
99
99
16
16
04
26
26
0.0000000000E+00
1.2000000000E+01
6.0000000000E+00
8.0000000000E+00
3.9000000000E+01
3.0000000000E+00
2.0000000000E+00
2.0000000000E+00
5.0000000000E+00
1.3000000000E+01
2.6000000000E+01
5.0000000000E+00
5.0000000000E+00
1.1000000000E+01
2.0000000000E+01
2.0000000000E+01
4.2500000000E+01
5.0000000000E-01
3.0000000000E+00
3.0000000000E+00
5.0000000000E-01
2.5000000000E+00
2.5000000000E+00
3.0000000000E+00
6.0000000000E+00
9.0000000000E+00
9.5000000000E+00
3.2000000000E+01
2.1000000000E+01
5.0000000000E+00
5.0000000000E+00
1.7000000000E+01
9.0000000000E+00
6.5000000000E+00
2.5000000000E+00
5.0000000000E-01
2.0000000000E+00
2.0000000000E+00
4.0000000000E+00
1.0000000000E+01
6.0000000000E+00
5.0000000000E+01
3.7000000000E+01
1.3000000000E+01
1.3000000000E+01
4.9000000000E+01
7.0000000000E+00
1.0000000000E+00
61
Ec
Eb
88
77
Lg
Cd
08
Gc
09
12
24
98
Sc
Bb
To
13
19
90
27
Gg
Gt
Ac
Mk
14
97
Oa
Oc
91
He
20
Am
30
Cu
33
Dl
Ab
11
Aa
17
96
cc
Dd
37
Al
38
Rt
39
Ov
Oh
Tm
Ur
Um
Nn
pl
Mp
Ml
Cp
Ct
Lp
Ca
Uc
29
29
02
88
77
77
88
08
08
09
12
24
98
98
24
12
13
19
90
27
27
90
19
13
14
97
97
14
91
91
20
20
30
30
33
33
09
11
11
17
96
96
17
37
37
38
38
39
39
6.0000000000E+00
6.0000000000E+00
2.3000000000E+01
2.5500000000E+01
1.7500000000E+01
1.7500000000E+01
2.2500000000E+01
2.0500000000E+01
5.0000000000E-01
5.0000000000E-01
5.0000000000E-01
9.0000000000E+00
1.0000000000E+01
1.0000000000E+01
1.9000000000E+01
3.5000000000E+00
5.0000000000E+00
4.0000000000E+00
4.5000000000E+00
2.5000000000E+00
2.5000000000E+00
7.0000000000E+00
1.1000000000E+01
5.0000000000E-01
1.1500000000E+01
4.0000000000E+00
4.0000000000E+00
6.5000000000E+00
9.0000000000E+00
2.5000000000E+00
6.5000000000E+00
1.0000000000E+00
5.5000000000E+00
2.0000000000E+00
3.5000000000E+00
3.5000000000E+00
5.0000000000E-01
1.9500000000E+01
8.5000000000E+00
7.0000000000E+00
4.0000000000E+00
4.0000000000E+00
5.5000000000E+00
5.5000000000E+00
5.0000000000E-01
5.0000000000E+00
4.0000000000E+00
1.0000000000E+00
1.0000000000E+00
2.4232458740E+00
2.4001924890E+00
1.9703468760E+00
6.4345267650E-01
8.4509804000E-01
3.9794000870E-01
1.0644579890E+00
1.5477747050E+00
1.1238516410E+00
1.3010299960E+00
9.4448267220E-01
5.6820172410E-01
2.0629578340E+00
1.9180303370E+00
1.7543483360E+00
2.1189299100E-02
5.6904851300E-02
3.9794000870E-01
-6.0480747000E-02
2.3070679510E+00
1.6532125140E+00
2.2041199830E+00
9.5904139230E-01
4.1392685200E-02
62
Vf
Hh
Cc
Aj
Pp
Pt
Pl
Tb
Cs
Db
Eh
Ec
Eb
Lg
Cd
Gc
Sc
Bb
To
Gg
Gt
Ac
Mk
Oa
Oc
He
Am
Cu
Dl
Ab
Aa
cc
Dd
Al
Rt
Ov
Oh
6.8124123740E-01
1.4281347940E+00
1.7160033440E+00
1.7693773260E+00
1.7193312870E+00
2.2068258760E+00
2.1925674530E+00
2.3979400090E+00
3.3010299960E+00
3.0791812460E+00
2.3010299960E+00
2.5440680440E+00
2.3710678620E+00
1.9777236050E+00
2.7403626890E+00
3.0314084640E+00
2.7923916890E+00
2.9370161070E+00
2.7084209000E+00
1.7958800170E+00
1.3117538610E+00
1.5740312680E+00
6.9897000430E-01
2.0549958620E+00
1.9294189260E+00
2.3550682060E+00
1.7263196120E+00
2.3344537510E+00
2.1139433520E+00
2.1335389080E+00
1.6989700040E+00
2.4771212550E+00
1.7403626890E+00
2.5843312240E+00
2.0000000000E+00
1.7558748560E+00
1.8692317200E+00
5.8771096500E-01
2.1841233540E+00
1.3979400090E+00
1.7930916000E+00
1.3654879850E+00
1.8426092400E+00
2.3729120030E+00
3.0102999570E-01
8.2282164530E-01
1.1931245980E+00
1.5440680440E+00
1.3521825180E+00
2.2174839440E+00
-3.0102999600E-01
2.0000000000E+00
1.9273703630E+00
2.1398790860E+00
2.1238516410E+00
1.9420080530E+00
1.3010299960E+00
7.2427586960E-01
8.1291335660E-01
-1.3665315400E+00
1.3569814010E+00
1.1562461900E+00
1.9030899870E+00
5.7978359660E-01
1.8750612630E+00
3.4242268080E-01
6.9897000430E-01
1.0000000000E+00
1.1115985250E+00
1.1394335230E-01
1.2068258760E+00
1.4771212550E+00
2.9225607140E-01
4.5484486000E-01
63