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m Ew```֯֯_X```1ˇˇˇˇvv~~~~~~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: DEB0196384 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:
HYPERLINK "http://mesquiteproject.org/mesquite/mesquite.html" http://mesquiteproject.org/mesquite/mesquite.html
The PDTREE module may be downloaded from:
HYPERLINK "http://mesquiteproject.org/pdap_mesquite/index.html" 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; DiazUriarte 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 leastsquares (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:
HYPERLINK "http://biology.ucr.edu/people/faculty/Garland/PDAP.html" http://biology.ucr.edu/people/faculty/Garland/PDAP.html
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) 8273524 = office
Phone: (951) 8275724 = lab
FAX: (951) 8274286 = Dept. office
Email: tgarland@ucr.edu
HYPERLINK "http://biology.ucr.edu/people/faculty/Garland.html" http://biology.ucr.edu/people/faculty/Garland.html
HYPERLINK "http://www.biology.ucr.edu/people/faculty/Garland/Garland2.html" http://www.biology.ucr.edu/people/faculty/Garland/Garland2.html
HYPERLINK "http://www.biology.ucr.edu/people/faculty/Garland/GarlandCV.html" http://www.biology.ucr.edu/people/faculty/Garland/GarlandCV.html
PDF files of almost all of my publications can be found here:
HYPERLINK "http://www.biology.ucr.edu/people/faculty/Garland/GarlandPublications.html" 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.
HYPERLINK "http://www.biology.ucr.edu/people/faculty/Garland/PHYSIG.html" http://www.biology.ucr.edu/people/faculty/Garland/PHYSIG.html
Matlab programs to deal with withinspecies 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 RamonDiazUriarte and T.G., is available at HYPERLINK "http://cran.rproject.org" http://cran.rproject.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 leastsquares (GLS) approaches. The package accompanies DazUriarte and Garland (in revision). R is free, opensource software (similar to S+), available from the Comprehensive R Archive Network at HYPERLINK "http://www.rproject.org/" http://www.rproject.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).
***** 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. *****
GETTING STARTED
This section will get you started analyzing your data with Felsensteins (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 continuousvalued traits, as discussed in Felsensteins (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.
Lets begin by assuming you have successfully entered a phylogenetic tree into Mesquite, and that you also have data for two continuousvalued characters, such as log body mass and log home range area (e.g., Garland et al., 1993). Further, lets 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 Mesquites 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:
From the top menu bar of the Tree Window, click on:
Analysis
New Chart for Tree
PDAP Diagnostic Chart
Stored Characters (OK)
This will give you the PDAP Diagnostic Chart Window
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 DiazUriarte and Garland, 1996, 1998). In particular, you want to see:
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 leastsquares 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.]
viewed from the Yaxis, the distribution should appear approximately as of a normal (bell shaped) distribution. That is, you should tend to have more points clustered near the bottom of the Yaxis and a thinning tail of points as you move up along the Yaxis.
no points that appear to be major outliers from the normal or that appear to be exerting a lot of leverage on the displayed regression line. In other words, you dont 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).
Use the arrows in the bottom left of the window to toggle between your two characters and examine the above for both of them.
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.
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.
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.
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).
In the bottom left of the window, specify the X and Y trait.
The small gray text box in the upper left will show, among other things, the Pearson productmoment 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.
What the Field of What Evolution
Conventional Statistics Assumes: Provides:
A Star Phylogeny A Hierarchical Phylogeny
with EqualLength Branches 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 equallength 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).
CHARTS AVAILABLE IN PDAP Diagnostic Chart Window
As noted above, clicking on the PDAP.Chart pulldown 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. 441442). This is the best understood of existing diagnostics. DiazUriarte and Garland (1996, 1998; see also Garland and DiazUriarte, 1999; Harvey and Rambaut, 2000; DinizFilho 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 (2tailed test) indicates significant lack of fit. Second, the distribution in the vertical direction should approximate onehalf 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 leastsquares 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).
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. 449450, 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 leastsquares 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 Yintercept, again mapped back onto the original tip data space. (Note that the slope on Screen 9A is the same as the leastsquares regression slope reported on Screen 9.)
xxAdd DF reduction as described in C:\Peattie\Peattie_Anne.doc
Screen 9B = the independent contrasts leastsquares 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: PerezBarberia 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 userdefined 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 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 Yintercept (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 tstatistics 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 leastsquares 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. Tip Name
2. X Value
3. Observed Y Value
4. Predicted Y Value (Yhat)
5. Residual (Y  Yhat)
6. Standardized Residual (using actual SD of residuals, not MSE)
7. Leverage of X Value (using root value as Xmean)
8. 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.
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 pulldown menu.
You can also select Show columns in File of Independent Contrasts (FIC), which are:
FIC files contain the following columns:
1. Name of Contrast as Node  Node (e.g., 'Tm  Ta')
2. Name of Node at Base of Contrast
3. Unstandardized Contrast for Trait 1
4. Unstandardized Contrast for Trait 2
5. 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 (DescendantAncestor)
13. Corrected Length of First Daughter Branch
14. Name of Second Daughter Branch (DescendantAncestor)
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!!!
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.
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. Name of Contrast as Node  Node (e.g., 'Tm  Ta') CONTRAST (A)
2. Name of Node at Base of Contrast NODE (A)
3. Unstandardized Contrast for Trait 1 CLMASS *
4. Unstandardized Contrast for Trait 2 CLHOME *
5. Standard Deviation of Contrast SD
= square root of sum of corrected branch lengths
6. Nodal Value for Trait 1 NLMASS *
7. Nodal Value for Trait 2 NLHOME *
8. Uncorrected Height of Base Node from Root of Tree UHBNODE
9. Corrected Height of Base Node from Root of Tree CHBNODE
(as used in screens 5, 6, 7, 8, and 11)
10. Average Uncorrected Height of Daughter Nodes AUHDNODE
11. Average Corrected Height of Daughter Nodes ACHDNODE
12. Name of First Daughter Branch (DescendantAncestor) D1BNAME (A)
13. Corrected Length of First Daughter Branch D1LENGTH
14. Name of Second Daughter Branch (DescendantAncestor) D2BNAME (A)
15. Corrected Length of Second Daughter Branch 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'.
* 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
/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 = leastsquares 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
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 Pvalue for ROOT tests whether Carnivora and ungulates
* differ in masscorrected 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 crossproducts 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 Pvalue for SLOPE tests whether Carnivora and ungulates
* 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 masscorrected 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.
***** 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.
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, largerbodied species of mammals (e.g., elephants) have absolutely large hearts and brains, whereas smallbodied 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 logtransformed 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 DiazUriarte, 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.
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; DiazUriarte 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 DNADNA 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; DiazUriarte and Garland, 1996, 1998; Freckleton et al., 2002; Blomberg et al., 2003). Hence, PDTREE allows various branchlength diagnostics to be examined.
Figure 1. Three kinds of arbitrary branch lengths. All of these can be interconverted 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; PerezBarberia 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; CruzNeto et al., 2001; Ebensperger and Cofre, 2001; Iwaniuk and Nelson, 2001; Kohlsdorf et al., 2001; Mysterud et al., 2001; Porter and Hawkins, 2001; Szkely 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; PrezBarbera 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).
: : All equal (constant) branch lengths:
:_1_: all segments set equal to one (unity).
: : : :
: 2 : : 2 :
: :
: 3 :
:
: : : : : Pagel's (1992) arbitrary branch lengths.
:_1_: : : 1 : Tips are constrained to be contemporaneous
: : : (line up across the top)and then internode
: 2 : : segments are set equal to one in length.
: : Polytomies were not discussed by Pagel, but
: 3 : 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.
: : : : : Grafen's (1989) arbitrary branch lengths.
:_1_: : : 1 : Tips are contemporaneous and the depth of
: : : each node is set equal to one less than the
: 2 : : 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),
: 4 : in which depths of nodes are set equal to
: the log of the number of tip species that
descend from it.
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!"
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 squaredchange 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 N1 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 N1. 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 N1 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 squaredchange 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).
Worked example (see Martins and Garland, 1991, p. 557;
saved on disk as APPAMG91.PDI):
Trait A 15 9 18 35 28
Trait B 1 2 3 4 5
X1 X2 X3 X4 X5
0      
 v1 v2  v4 v5
  X7    X6 
1  ...  ...
  v3 
   
2    v6
   
   X8 
Branch Length 3   ...
  
(in units of   
expected 4  v7 
variance of   
character   
evolution) 5   v8
  
  
6   
  
  X9 
7  ...

Trait A Trait B
v4X5 + v5X4
X6 =  = 31.5 4.5
v4 + v5
v6' = v6 + v4v5/(v4 + v5) = 2.5 2.5
v2X1 + v1X2
X7 =  = 12.0 1.5
v1 + v2
v7' = v7 + v1v2/(v1 + v2) = 6.5 6.5
v6'X3 + v3X6
X8 =  = 25.3636 3.8182
v3 + v6'
v8' = v8 + v3v6'/(v3 + v6') = 5.3636 5.3636
v7'X8 + v8'X7
X9 =  = 19.3218 2.7701
v7' + v8'
__________________________________________________________________
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 = rate of evolution
5. the quantity ((v7' v8')/(v7' + v8')) = 2.9387, therefore:
66.6274 1.3680
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
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 2character species codes and data for preferred body temperature. This tree and tip data are in the file HB12C##.INP (dated 032698; 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 squaredchange 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 (28.0636.49) +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
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.
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
   Original Tree
  
 X  
\/ 
 
 
 
 
 Z 
\/

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
 Rerooted Tree used to estimate value at node X









9 7 

  
  
 X  Z 
\/

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 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.
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
  Rerooted Tree used to estimate value in lineage
  leading to species C one branch length unit
 X  in the past.
\/










 2

 Z 
\/

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 standin 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
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 continuousvalued 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 3category "factor" or you can perform a multiple regression with two independent (X) variables that are 01 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 C1 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 01, 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; DiazUriarte and Garland, 1996, 1998) you should be able to perform adequate analyses when you have a 01 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 continuousvalued 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 3category 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 continuousvalued 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, continuousvalued data are to be preferred, as they should typically increase statistical power to detect relations (Garland et al., 1993; empirical examples in Alkahtani et al., 2004; MuozGarcia 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 phylogenyrelated 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 (1tailed P = 0.3107), but in the corresponding analysis with phylogenetically independent contrasts it was (1tailed 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).
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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 DazUriarte, 1997; Bleiweiss, 1997; Harris and Steudel, 1997; Jackman et al., 1997; Pitnick et al., 1997; Reynolds, 1997; PerezBarberia and Gordon, 1999a,b; Barbosa and Moreno, 1999a,b; Bleiweiss, 1999; de Repentigny, 2000
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 0length 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 zerolength, 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 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.
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. 809812; 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 nonphylogenetic "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. 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.
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 withintip 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 fibertype 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.
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 0length 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 zerolength, 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 zerolength 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 18 in PDTREE, would be affected (cf. Garland et al., 1992; Garland and DiazUriarte, 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 (Pvalues) when correlating independent contrasts.
Recently, Garland and DiazUriarte (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 equallength branches) by independent contrasts, then the estimate of the correlation coefficient will be identical to an ordinary Pearson productmoment 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 noncontemporaneous 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 nonzero 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 computersimulated 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 DiazUriarte, 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.
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 2character 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 twocharacters. These can be any ASCII printing characters, such as A, b, 5, (, ], *, _, #, ^, ~, ', ?, etc., but not spaces! If PDTREE finds a duplicate 2character 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 0length branches to some positive number).
Here are some stepbystep 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.
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 dropdown 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 2character 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 47tip tree instead of a 49tip tree.
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
cleanedup 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.
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 RodriguezRobles 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 2tailed Pvalue for this test (by comparison with the binomial distribution [Sokal and Rohlf, 1981, pp. 449450, 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 Yvariable contrasts that are greater than, less than, and equal to zero (see Tables 2 and 3 above, columns 911), given that the Xtrait 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 onetailed test).
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)
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
***** NOTE: You must use 2character 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.
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 2character 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 $$ 0.0000000000E+00
03 01 1.2000000000E+01
05 03 6.0000000000E+00
06 05 8.0000000000E+00
31 06 3.9000000000E+01
95 31 3.0000000000E+00
Tm 95 2.0000000000E+00
Ur 95 2.0000000000E+00
Um 31 5.0000000000E+00
93 06 1.3000000000E+01
92 93 2.6000000000E+01
Nn 92 5.0000000000E+00
pl 92 5.0000000000E+00
07 93 1.1000000000E+01
Mp 07 2.0000000000E+01
Ml 07 2.0000000000E+01
21 05 4.2500000000E+01
22 21 5.0000000000E01
28 22 3.0000000000E+00
32 28 3.0000000000E+00
34 32 5.0000000000E01
Cp 34 2.5000000000E+00
Ct 34 2.5000000000E+00
Lp 32 3.0000000000E+00
Ca 28 6.0000000000E+00
Uc 22 9.0000000000E+00
Vf 21 9.5000000000E+00
10 03 3.2000000000E+01
18 10 2.1000000000E+01
Hh 18 5.0000000000E+00
Cc 18 5.0000000000E+00
23 10 1.7000000000E+01
Aj 23 9.0000000000E+00
35 23 6.5000000000E+00
Pp 35 2.5000000000E+00
36 35 5.0000000000E01
Pt 36 2.0000000000E+00
Pl 36 2.0000000000E+00
02 01 4.0000000000E+00
04 02 1.0000000000E+01
99 04 6.0000000000E+00
Tb 99 5.0000000000E+01
16 99 3.7000000000E+01
Cs 16 1.3000000000E+01
Db 16 1.3000000000E+01
26 04 4.9000000000E+01
Eh 26 7.0000000000E+00
29 26 1.0000000000E+00
Ec 29 6.0000000000E+00
Eb 29 6.0000000000E+00
88 02 2.3000000000E+01
77 88 2.5500000000E+01
Lg 77 1.7500000000E+01
Cd 77 1.7500000000E+01
08 88 2.2500000000E+01
Gc 08 2.0500000000E+01
09 08 5.0000000000E01
12 09 5.0000000000E01
24 12 5.0000000000E01
98 24 9.0000000000E+00
Sc 98 1.0000000000E+01
Bb 98 1.0000000000E+01
To 24 1.9000000000E+01
13 12 3.5000000000E+00
19 13 5.0000000000E+00
90 19 4.0000000000E+00
27 90 4.5000000000E+00
Gg 27 2.5000000000E+00
Gt 27 2.5000000000E+00
Ac 90 7.0000000000E+00
Mk 19 1.1000000000E+01
14 13 5.0000000000E01
97 14 1.1500000000E+01
Oa 97 4.0000000000E+00
Oc 97 4.0000000000E+00
91 14 6.5000000000E+00
He 91 9.0000000000E+00
20 91 2.5000000000E+00
Am 20 6.5000000000E+00
30 20 1.0000000000E+00
Cu 30 5.5000000000E+00
33 30 2.0000000000E+00
Dl 33 3.5000000000E+00
Ab 33 3.5000000000E+00
11 09 5.0000000000E01
Aa 11 1.9500000000E+01
17 11 8.5000000000E+00
96 17 7.0000000000E+00
cc 96 4.0000000000E+00
Dd 96 4.0000000000E+00
37 17 5.5000000000E+00
Al 37 5.5000000000E+00
38 37 5.0000000000E01
Rt 38 5.0000000000E+00
39 38 4.0000000000E+00
Ov 39 1.0000000000E+00
Oh 39 1.0000000000E+00
Tm 2.4232458740E+00 2.0629578340E+00
Ur 2.4001924890E+00 1.9180303370E+00
Um 1.9703468760E+00 1.7543483360E+00
Nn 6.4345267650E01 2.1189299100E02
pl 8.4509804000E01 5.6904851300E02
Mp 3.9794000870E01 3.9794000870E01
Ml 1.0644579890E+00 6.0480747000E02
Cp 1.5477747050E+00 2.3070679510E+00
Ct 1.1238516410E+00 1.6532125140E+00
Lp 1.3010299960E+00 2.2041199830E+00
Ca 9.4448267220E01 9.5904139230E01
Uc 5.6820172410E01 4.1392685200E02
Vf 6.8124123740E01 5.8771096500E01
Hh 1.4281347940E+00 2.1841233540E+00
Cc 1.7160033440E+00 1.3979400090E+00
Aj 1.7693773260E+00 1.7930916000E+00
Pp 1.7193312870E+00 1.3654879850E+00
Pt 2.2068258760E+00 1.8426092400E+00
Pl 2.1925674530E+00 2.3729120030E+00
Tb 2.3979400090E+00 3.0102999570E01
Cs 3.3010299960E+00 8.2282164530E01
Db 3.0791812460E+00 1.1931245980E+00
Eh 2.3010299960E+00 1.5440680440E+00
Ec 2.5440680440E+00 1.3521825180E+00
Eb 2.3710678620E+00 2.2174839440E+00
Lg 1.9777236050E+00 3.0102999600E01
Cd 2.7403626890E+00 2.0000000000E+00
Gc 3.0314084640E+00 1.9273703630E+00
Sc 2.7923916890E+00 2.1398790860E+00
Bb 2.9370161070E+00 2.1238516410E+00
To 2.7084209000E+00 1.9420080530E+00
Gg 1.7958800170E+00 1.3010299960E+00
Gt 1.3117538610E+00 7.2427586960E01
Ac 1.5740312680E+00 8.1291335660E01
Mk 6.9897000430E01 1.3665315400E+00
Oa 2.0549958620E+00 1.3569814010E+00
Oc 1.9294189260E+00 1.1562461900E+00
He 2.3550682060E+00 1.9030899870E+00
Am 1.7263196120E+00 5.7978359660E01
Cu 2.3344537510E+00 1.8750612630E+00
Dl 2.1139433520E+00 3.4242268080E01
Ab 2.1335389080E+00 6.9897000430E01
Aa 1.6989700040E+00 1.0000000000E+00
cc 2.4771212550E+00 1.1115985250E+00
Dd 1.7403626890E+00 1.1394335230E01
Al 2.5843312240E+00 1.2068258760E+00
Rt 2.0000000000E+00 1.4771212550E+00
Ov 1.7558748560E+00 2.9225607140E01
Oh 1.8692317200E+00 4.5484486000E01
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