General

Multiple Copies are Conflicting

Q. Results from one analysis are referencing variables that aren’t in the currently open matrices. Then an error results and the program locks up.

A. You probably have two or more copies of PC-ORD on your computer. The most likely way that this could happen is if updates were installed to a different folder than the one in which the software was originally installed. The effects are very unpredictable and various error messages can result, because intermediate files from one task might be used for another task.

Steps to fix:

1. Close PC-ORD.
2. To search for multiple instances with Windows 7 or 10, open Windows Explorer, then type in PCORD7.exe into the Search box (upper right). You should select "advanced" and tell it to look in all of drive C. You should check the box to include "non-indexed, hidden, and system files".
3. If you find multiple folders with PCORD7.exe, figure out which one was the original folder, then delete the contents of the other one. Then reinstall the updates from www.pcord.com, being sure to select the original folder. If you have a 64-bit system, there should be "(x86)" in the folder name.
4. This takes care of the executable file, but you need to do the same with PCORD7.ini and PCORD7.opt, files that “remember” options and disk locations. Note that you can delete all instances of those files, but then PC-ORD will “forget” all of your previous settings and options.

Modules are Missing

Q. I received the error message, “PC-ORD modules are missing, contact mjm@pcord.com.” This happened after I updated my software to the latest version. What is wrong?

A. This message results from a partial installation. When downloading and installing updates, be sure to follow the instructions carefully. You must overwrite the original version when installing updates. If you try to install the updates to a new folder, then run from that folder, you will get the error that you describe. If you install the updates to the existing executable folder and launch PC-ORD from the existing location, there should not be a problem. If you suspect that you have two folders with PC-ORD, confirm this, and if so, then delete the more recent folder that has the partial installation (see the Help topic, Multiple Copies are Conflicting). Then repeat the update, being sure to select the correct folder for installation.

Decimal Separator Problems

Q. When trying to plot an ordination overlay in the Graph window an error comes up ('8.2' is not a valid floating point value) and the program stops responding. This even happens with the FoodHabitsMain.mjm example matrix. What is wrong?

A. If you are using a language option other than US English, you might encounter an error such as the one you describe, because many countries use a comma as a decimal separator rather than a period. First close any open files in PC-ORD then close PC-ORD. You can temporarily match the file's language platform by Start | Control Panel | Region | Additional Settings | Decimal Symbol or in Windows 10 use the search box for Regional Format (Exact path will vary depending on version of Windows). In Windows 7: Windows Control Panel | Region and Language | Formats | Additional settings. Click the tab or section that contains the settings that you want to modify, and make your changes. For example, to change part or all of a number format, click the Numbers tab and change the setting that you want. Then reopen PC-ORD and the data file.

There may still be a problem if PC-ORD rereads temporary files that it wrote in a previous session, if they have a conflicting decimal separator. You can clean these up by closing your data matrices, then going to Tools | View Application Data Folder and deleting everything there. Warning: this action will make PC-ORD forget your settings and options.

Empty variables or zero variance error

Q. I received an error message "Error: Empty variables; attempt to divide by zero."  What's wrong?

A. If your spreadsheet has rows or columns that are all zeros, many analyses will fail because in the underlying math, something is divided by sums or sums of squares that equal zero.  In general you should check for empty rows and columns before running analyses.  The easiest way to spot these is to run the Row & Column Summary under "Summary".  A related problem is when a column has a variance of zero (all values are the same in that column).  Any analysis requiring division by the variance or standard deviation of that column will, therefore, produce an error message.

Second matrix and graph file do not match

Q. We get the following error message.  "The number of items in your second matrix does not match the number of items in your graph file.  Second matrix will be ignored.  This error came after doing the ordination and while trying to graph the ordination.

A. The most common cause of this problem is when one or more sample units (rows) are deleted from the main matrix.  If you do this, you also need to delete the corresponding rows from the second matrix.  The easiest way to avoid this problem is to use Modify Data | Delete Rows | Both Matrices.

Negative CV's

Q. In Row and Column Summary I obtained a negative coefficient of variation (CV).  How can that be?

A. One can get wild results like CV = -833% if the data include negative numbers, or were standardized in some way that produces negative numbers (such as relativization by standard deviates). But the CV is always non-negative if the data are all non-negative. The CV makes sense only with non-negative data.

Resampling tests

Q. Are resampling or randomization tests (e.g., jackknife, bootstrap) provided for ordination procedures other than CCA?

A. Resampling or randomization procedures used in PC-ORD for several other applications (NMS, Indicator species analysis, Mantel test, PCA, and perMANOVA).  Jackknife estimates of species diversity are included.  But at present we have not included randomization tests for ordinations other than CCA, PCA, and NMS.

Spreadsheet Columns

Q. How many columns of data can I use?  My spreadsheet program allows a maximum 255 columns.  I want to enter a data set with more species than that.

A. In PC-ORD you can use up to 32,000 columns if your machine can handle it.  But most spreadsheet software is limited to many fewer columns than that (255 columns in old versions of Excel).  You can circumvent that by using compact format or database format. PC-ORD imports these into a spreadsheet.  Or, depending on the shape of your data matrix, it may be advantageous to enter the transpose of your matrix in a spreadsheet program.  For example, if you had 100 plots and 300 species, you could enter the species as rows and the plots as columns, then transpose the matrix in PC-ORD.  If you have a very large data set we recommend either compact format or database format.

To use the database format, first export your data from your database to a delimited text file. PC-ORD expects three columns, in the order:
SampleUnitID  SpeciesID  Abundance
Then PC-ORD will build a matrix from this.

PC-ORD crashes on laptop

Q. When I launch PC-ORD on the laptop the machine behaves strangely and eventually crashes.  Is there a known problem?

A. Check to see if you have a network printer as the default printer.  (Start | Settings | Control | Panel | Printers) A check mark will appear next to the default printer.  When you are not hooked up to the network, make sure the default printer is not a network printer.

Error reading PC-ORD options file

Q. I received an error message: Check for possible mixed or multiple version numbers of PC-ORD.  Error reading PCORD options file.  What is the solution?

A. Use Tools | View Application Data Folder.  Close PC-ORD, but leave the folder window open.  Delete the file Pcord7.opt.  Restart PC-ORD.  Then if you haven't already, download the latest fixes (Help | Check for software updates).

File not found error

Q. When attempting to run NMS using starting configuration I provide in a "graphrow" file PC-ORD is unable to open or read the file.  The error message I get is "Error reading graph file. Graph file not found."  What is wrong?

A. Any analysis related file has to be stored in a folder that has a filename (including the path) less then 240 characters long.  Open Windows Explorer and navigate to the folder where the file is stored to get the complete path in the Explorer Address window.  If the path plus file name is longer than this limit move the files not found to a shorter path and/or use a shorter file name.

Analyze second matrix

Q. How do I get row and columns summaries, outlier analyses, etc. on the second matrix?

A. Use "File | Switch Matrix" to swap the main and second matrices.  Think of the main matrix as the active matrix.  This is the matrix on which the operations are performed, unless an operation specifically requires the second matrix.

Editing spreadsheets

Q. Why doesn't PC-ORD allow cell-by-cell editing of spreadsheets?  I have to go back and forth between PC-ORD and a spreadsheet program when I am cleaning my data.

A. PC-ORD doesn't attempt to duplicate the spreadsheet functions.  However PC-ORD versions 4 and above allow simple editing of the main and second matrices.  More complicated editing and sorting is best done in your spreadsheet software.  Be sure to close a file in PC-ORD before editing it in spreadsheet software and vice-versa.   Otherwise file sharing conflicts may result that will cause problems in either Excel or PC-ORD.

Convert output to tables

Q. How can I convert tables in PC-ORD’s output files into tables in my word processor?

A. Your word processor probably has functions for converting tabular text files into tables.  For example, using Microsoft Word, you can highlight a table in a PC-ORD output file, then select Table | Convert Text To Table, to convert the output into a standard tabular format.  Be sure to set the delimiter to a space character and adjust the desired number of columns.

Convert Output to Spreadsheets

Q. How can I convert tables in PC-ORD’s result files into spreadsheets?

A. It is easy and fast to convert tables in your results file to columnar data in Excel.  That works really well with PC-ORD output, since the result file tables are fixed width, matching one of the options of Excel.

Highlight the table that you want to export, then type Ctrl-c to copy.  Put the cursor on a single cell in Excel where you want the upper left corner of the table, then type Ctrl-v to paste. The results will all go in a single column.  Then, before doing anything else, while the column is still highlighted, use Data |Text to Columns | Fixed width, to create the separate columns.

Note that PC-ORD also provides direct conversion to spreadsheet in a number of cases, such as saving an ordination graph file (containing the ordination scores) as a spreadsheet.

Groups on ordinations

Q. I have a question about grouping. I have measurements of habitat along three transects of 250 plots, one transect along each of three creeks (total of 750 plots).   How can I make PC-ORD group these plots so I can best run a ordination on them?

A. Ordination doesn't necessarily have a built-in concept of groups, but you can overlay groups on any ordination.  To do this, create a second matrix with 750 rows and 1 column (or you can add this column to an existing second matrix).  Use this column to create a categorical ("C") variable that codes for "creek" (1, 2, 3). Open this as the second matrix and when graphing your ordination, select "creek" as an overlay variable.  You can use different colors and/or symbols to indicate each group.  If you want to compare species and communities among groups, consider MRPP and Indicator Species Analysis.

Multifactor Experimental Designs

Q. How can I using purely nonparametric perMANOVA or MRPP to analyze experimental designs with more than one or two factors in the design?

A. PC-ORD uses at most 2 factors in perMANOVA, 1 factor in MRPP, and 1 factor plus blocking in blocked MRPP. For more complicated designs, consider the following possiblities.

1. Aggregate subsamples by averaging.  This will decrease noise in the estimates.   This applies to nested designs.
   
   
2. Combine multiple levels of blocks or nesting into a single level representing control of spatial effects.  For example, with blocks nested within sites, use block/site combinations as a new compound blocking variable.
   
   
3. Identify weak factors by one-way analyses and drop the weakest factors from the design, in effect increasing replication.
   
   
4. Identify the strongest factor and split the analysis into a separate analysis within each factor.  This is particularly effective if the factor interacts with another (e.g. Factor 2 makes a difference only at one level of Factor 1).
   
   
5. With repeated sampling of the same design, calculate the statistic representing treatment effect at each date separately.  Then plot effect size (e.g. A from MRPP or F from perMANOVA) against date.
   
   
6. For repeated sampling subtracting the first date from the second, within each sample unit.  This results in values that represent the change in response variables. Accordingly, this matrix will have both positive and negative numbers.  If you do this, you need to use a Euclidean distance measure, or another distance measure that tolerates negative numbers, because the negative numbers resulting from the subtraction don't make sense with Sorensen distance or other proportional city-block distance measures.
   
   
7. Other kinds of subtraction-based data adjustments are also possible—for example, subtracting the mean (or median) for each variable in each block from each observations that block.  Thus each observation becomes a deviation from the block median or mean.   These adjusted observations could then be used in an analysis of a more complex design.  For example, if you had two-way factorial design with blocking, using the deviations from within-block means would allow a two-way perMANOVA.  What you would lose is a measure of the size of the block effect (since you have subtracted it out).
   

Mac version?

Q. Are versions of PC-ORD available for Macs?

A. No. There is only a Windows versions of PC-ORD. However, PC-ORD will run on Virtual PC for Mac, Parallels, other Windows emulators, and dual-boot Macs.

Linux version?

Q. Are versions of PC-ORD available for Linux?

A. PC-ORD will run with Wine on Linux machines..

Mac emulation 3D crash

Q. I am using PC-ORD with Mac OS X running Windows XP via Parallels. Graphing 3D ordinations makes PC-ORD crash. Is there a solution?

A. Open XP Control Panels | Appearance and Themes | Display Properties | Settings | Advanced | Troubleshoot and set the Hardware acceleration slider to the second position from the left that says "Disable all but basic accelerations. Use this setting to correct more severe problems". Note this position also disables DirectDraw and Direct3D used by any other software.

Exponential formats for numbers

Q. I’ve attached an output file from row and column summaries. Why are the numbers on my species summaries so odd?

       Summary of 53 species   N = 9 points
------------------------------------------------------------------------
No.   Name     Mean         Stand.Dev.  Sum           Minimum      Maximum (etc.)
------------------------------------------------------------------------
1     AGRPAR   0.111E+00   0.333E+00    0.1000E+01   0.000E+00   0.100E+01
2     ALLPET   0.100E+01   0.112E+01    0.9000E+01   0.000E+00   0.300E+01
3     ASPPLA   0.111E+00   0.333E+00    0.1000E+01   0.000E+00   0.100E+01

A. The numbers in your output are in exponential format ("E fields"). PC-ORD switches to this for row/column summaries when the number of decimal places in the regular format has insufficient precision in some portion of the table. In this specific case, you're on the borderline -- the regular format probably would have been ok too.

The following item from the built-in help system explains how to interpret the exponential format:

E Fields
Numbers are sometimes listed with the computer version of scientific notation. This is used for maximum flexibility in portions of the output. The numbers following the E are exponents. For example,

.7071E+01 = 7.071
.9169E+00 =  .9169
.1234E-05 =  .000001234

Discriminant Analysis

Q. Does PC-ORD contain Discriminant Analysis?  If not, why not?  I could use MRPP or perMANOVA but I am more interested in the graphs than the statistical tests.

A. PC-ORD does not contain discriminant analysis.  We have emphasized techniques that are more appropriate for community data, especially nonparametric techniques that are not readily available elsewhere.  So DA falls in the category of a parametric technique that is available in virtually every major statistical package and is seldom useful for community data.  If you are mainly interested in graphical approaches, you can use other ordination techniques, such as NMS, then superimpose group memberships on the symbols in the ordination.  If you are using community data, you should also consider indicator species analysis, which will perform better than discriminant analysis in telling you which species differ among groups.  MRPP has no graphical component, but when you have a priori groups MRPP makes a nice companion to a graphical approach such as ordination.

Won't work with Vista or Win 7

Q. I just installed PC-ORD and nothing seems to work.

A. The PCORD folder might not have write access.

1. Log in as Administrator
2. Right click the PC-ORD icon or menu item that you run PC-ORD
3. Select Properties
4. Select the Security tab
5. In the Permissions for SYSTEM box, check Allow for everything except Special Permissions
6. Click Apply and OK

Can't find saved files in Vista or Win 7

Q. Whether saving a matrix, graph, or results file, when I try to find the file, it is nowhere to be found.

A. Sounds like you are saving to the C:\Program Files\PCORD folder or a subfolder. (In 64-bit Windows: C:\Program Files(x86)\PCORD)  For security reasons Microsoft doesn't think you should write any files to the Program Folder or subfolders so it writes to a Virtual Store that you cannot see or get to.

Here are some solutions:

• Save your files to any folder other than a Program Files folder, for example, Documents.
  
  
• With Windows Explorer navigate to the Program Files\PCORD folder (with 64-bit Windows to Program Files (x86)\PCORD folder) and click Compatibility Files in the Windows Explorer bar.
  
  
• Run PC-ORD as Administrator.  Even if you are logged in as Administrator you still have to right click the PC-ORD icon on the Desktop or on the Start Menu and select Run as Administrator.
  
  
• One time, right click the PC-ORD icon and instead of selecting Run as Administrator, select Properties | Compatibility | Privilege Level and check Run this program as an administrator.

Out of memory

Q. I am running a large matrix and I get the "out of memory” error. What can I do?

A. PC-ORD can use all of your available memory. If you have plenty of memory and you get this error, your operating system has encountered some conflict in system resources and you may need to reboot.

There are several steps you can take to maximize the amount of available memory (check "Memory Requirements" under the File menu).

Avoid loading other memory-resident software, such as network drivers, if possible.

• Avoid loading other memory-resident software, such as network drivers, if possible.
• Reduce the size of your matrix by:

1. analyzing subsets of the data,
2. aggregating the observations to a higher level in your sampling design, or
3. eliminating rare species (say those in less than 5% of your sample units).

• Add more memory (RAM) to your machine.
• See additional suggestions for using large data sets.

Editing and Searching Result File

Q. How can I edit, search in, or insert comments in my result files?

A. Simple editing and commenting of your result file is possible directly within PC-ORD.  For more elaborate editing, just open the result file with the notepad or other text editor.  You can do this without closing down PC-ORD.

Help system not working

Q. I'm trying to use the Help | Contents in PCORD and it will not open for me. Why?

A. The most common reason for this is that Windows is blocking access to the Help file, which is an executable file and therefore can be suspicious for Windows. First, check in the folder containing the PC-ORD software for the file PCORD7.chm. If it is not there, then there was a problem with the installation and you should redo the update, being sure to install to the same folder as the previous installation. However, most likely the file is there, and you can make sure that Windows will let you use it by right clicking the file name, then Properties | General tab. At the bottom right if you see an "Unblock" button, click on that. If there is no Unblock button then that probably isn't the problem. In that case, try changing the way you launch PC-ORD. Close PC-ORD, go to the icon from which you launch it, then right click, go to the Compatibility tab, and check "Run this program as an administrator."

Data Structure

Analyses and transformations of the second matrix

Q. How do I get row and columns summaries, outlier analyses, etc. on the second matrix?

A. Use File | Switch Matrix to swap the main and second matrices.  Think of the main matrix as the active matrix -- the matrix on which the operations are performed, unless an operation specifically requires the second matrix.  Alternatively, you can get a quick summary or profile of main and second matrices by selecting Advisor | Show Current Profile.

Delete rare species

Q. Is there an easy way to delete rare species from a matrix?

A. Assume that species are columns.  Select Modify | Delete Columns | Fewer Than N Non-zero Values.  Then you enter a value for N.  If N=1 then empty columns are deleted.

Delete rows from second matrix

Q. I deleted rows from my main matrix, but when I performed an analysis, I received an error message that the second matrix didn't match the main matrix. How can I delete the corresponding rows from the second matrix?

A. To delete rows from both matrices, use Modify | Delete Rows | Both Matrices.

Missing data

Q. What can I do about missing data (cells in my matrices for which I have no data)?

A. You must take steps to replace missing cells with numerical values, or you must delete the offending rows or columns.  If you ignore warnings about missing data, they are most likely to be interpreted as zeros, which may or may not be reasonable.   There are several approaches to substituting values for missing cells.  We recommend reading Tabachnik and Fidell (1989) for a good discussion of the pros and cons of various remedies for missing data. PC-ORD expects you to deal with the missing value problem rather than having an automatic way of dealing with it.  The reason for this is that for most multivariate analyses there simply is no good universal way of handling missing values.

Error message about a cell outside data matrix

Q. When PC-ORD reads my data I get an error message about a cell that is outside of my data matrix. Why?

A. There is something in your spreadsheet outside the matrix.  Even if the cell looks blank, there may be something there.  For example, if you go to a cell in a spreadsheet, hit the space bar, then move to another cell, the cell will look blank, but there are actually data written in that cell: first a code saying there is a label field, next the "blank" character.  When you put the cursor on the cell in question the spreadsheet will display one of the characters that signals a label field: usually ' " or ^.  This is displayed not in the cell itself, but in the separate display that shows the contents and any imbedded codes in the current cell.  You can get rid of these by erasing the cell in question or a whole block of cells.

Error in species file, number not first in line

Q. I entered my data in the compact format.  When I run "Summary" or attempt to import the data I get an error on ever line: "Error in species file, line 1, Species number not first in line."  My species file looks correct.  What is wrong?

A. In this particular case, one possibility is that each line begins with a TAB character.  PC-ORD is looking for a number but finding something that is not a number.  Check for and remove TAB characters (or other non-numeric character) at the beginning of each line.

Subplots in each plot

Q. I have 40 plots and 60 subplots in each plot.  Each of the plots has been recorded at 3 dates.  How can I enter and analyze this large data set in PC-ORD?

A. Your data set has a nested structure which is best handled in PC-ORD with the compact data format using "break groups."  If each combination of date/plot/subplot is analyzed separately, then you will have way too many rows for analysis (40 x 60 x 3 = 7200 sample units).  We suggest combining some of the sample units -- essentially collapsing the nested structure somewhat.  How you do this depends on the question of interest.  For example, if you are interested in the differences between dates, you might aggregate the 60 subplots within each combination of date/plot, leaving you with a manageable 80 sample units.  This would be done by creating a compact format file.  If you already have the data in spreadsheets, you can export the data to compact format, then use a text editor to append the break groups that you choose, then import the data into PC-ORD, selecting aggregation of subsamples.   The groups of plots to be combined are separated by the keyword "break".   However you set up your main matrix, you should set up a corresponding second matrix that codes for each level in your design.

Using numbers as row labels

Q. I wish to label my sample units with numbers, but PC-ORD insists on character data in the first column. It seems that the only way to get number labels into PC-ORD is to either enter them in compact format and import, or reformat each cell by hand in Quattro or Lotus, or insert a character before the first number in Excel.

A. This is a problem with the Excel export to *.wk1. It is too smart for its own good, converting numbers defined as characters into numbers defined as numbers.  The problem is irrelevant for PC-ORD 7, because it no longer uses the *.wk1 format by default.

One solution to this and many other data formatting problems is to export the file from Excel in comma-separated-values format (*.csv).  This pure-text format strips out all formatting codes. Then import the *.csv file into PC-ORD.

Compact format vs. spreadsheet

Q. I have a large data set in a spreadsheet program.  The help file states that the compact data format should be used to optimize storage of this type of data.  Do I need to convert my spreadsheet to compact format?

A. Compact format is mainly a time saver with data entry.  You CAN use it to store data in a more compact way, but unless you are low on disk space, it is usually more convenient to keep the data in spreadsheet format.  There are, however, a number of situations in which using compact format can be very helpful.  If you are managing large data sets with many subsets, you will find compact format convenient for combining subsets in various ways.  You can easily combine different subsets of a large data set, just by appending the compact-format text files to each other.  But if you (a) have plenty of disk space, and (b) don't need to fiddle a lot with subsets of data, and (c) don't need to compact format for data entry, then you should stick with the spreadsheet format.

Export compact format with breakpoints

Q. I have a large spreadsheet data set that I wish to export to compact format.  How can I insert breakpoints in the compact format file?

A. When you export to compact format, breakpoints are not inserted.  If you wish to insert those, do so with a text editor after you have created the compact file.

Append matrix

Q. How can I append one species matrix to another in PC-ORD?

A. Combine two spreadsheets by selecting Modify | Append Matrix.

How many columns of data can I use

Q. How many columns of data can I use?  My spreadsheet program allows a maximum 255 columns. I  want to enter a data set with more species than that.

A. In PC-ORD you can use up to 32,000 columns if your machine can handle it. But most spreadsheet software is limited to many fewer columns than that (255 columns in old versions of Excel).  You can circumvent that by using compact format or database format. PC-ORD imports these into a spreadsheet.  Or, depending on the shape of your data matrix, it may be advantageous to enter the transpose of your matrix in a spreadsheet program.  For example, if you had 100 plots and 300 species, you could enter the species as rows and the plots as columns, then transpose the matrix in PC-ORD.  If you have a very large data set we recommend either compact format or database format.

To use the database format, first export your data from your database to a delimited text file.  PC-ORD expects three columns, in the order:

SampleUnitID  SpeciesID  Abundance

Then PC-ORD will build a matrix from this.  Both compact format and database (list) format are described in detail in the on-line help system.

Bad entry in cell x. Expecting number

Q. I get the error: "Bad entry in cell x. Expecting number."  I looked at the spreadsheet and can find nothing wrong.  What is the problem?

A. PC-ORD is expecting a number but finding something else.  Sometimes the problem can be "invisible." Examples:
- the letter o instead of the number zero
- an imbedded space in a number (the spreadsheet automatically considers this character data)
- an equation instead of a number

If you can't see the problem, re-enter the data in the cell and explicitly format the cell to be a number.  This problem can also produce the error message: "Error reading main matrix. row x. Label encountered in spreadsheet when expecting number."

Another way to quickly remove all cell formatting that PC-ORD does not recognize is to save the file in Excel as a .CSV (comma delimited) file type rather than .wk1 and then import that file into PC-ORD.

Combining two spreadsheets

Q. My dataset is in Excel, and is contained in two worksheets, one for each year of data.  Each worksheet has a slightly different species list, and the species are not in the same order.  How can I combine the worksheets?

A. Use Modify Data | Append Matrices to append a matrix of your choice to the main matrix.  The combined matrix is then offered for approval (as temp.wk1) as the new main matrix.  The main use of this procedure will be to combine community matrices that differ somewhat in the species present.  Using Append Matrix will correctly align the columns of the matrices, regardless of the order of species in the two matrices.

Standardizing data

Q. When I use Ward's method with the Euclidean distance as similarity index to cluster my data, are my column variables then automatically standardized?  Or doesn't it standardize my variables?

A. Your column variables are not automatically standardized.  If you wish to do that, you should use Modify data | Relativizations, then choose the method for relativization that you want.

Cornell full format tables

Q. Am I correct that PC-ORD does not include importing Cornell full format tables (species x frequency/abundance)?

A. A. PC-ORD imports Cornell condensed files but does not import the Cornell full format table directly.  That format is, however, easy to place directly into a wk1 spreadsheet, using one of the data tools with your spreadsheet.  With Excel, paste the data into a single column, then use Data | Text-to-columns (fixed-width fields), then add the header rows and save as a .wk1 file

Error reading main matrix.  Data read error

Q. I have had no success in importing a CSV file into PC-ORD.  I get the message "Error reading main matrix. Data read error."  How can I correct the problem?

A. Check to be sure you have included the header rows. See the help system under CSV format.  Also, you can look at the text file "tempdat.tmp" in the Application Data folder.  You can easily find this file by selecting Tools | Application Data Folder.  You can open this plain text file with Notepad.   This file contains information for the the last item at the time the import failed.   This file contains one data item per line.  You should be able to see the data for the row that failed or any other information out of place.

Number of rows

Q. I'm having some problems reading my data matrix (*.wk1) and I'm hoping you can help.  The matrix is 13228 rows X 12 columns.  When I try to open it, I get an error message saying that "13228 rows" doesn't match the actual number of rows (8188).  There are no missing data values and no apparent reason why it should stop at row 8188.  It always stops at that exact row, no matter what I try.

A. Some older versions of Excel export only the first 8192 rows (8188 not counting the 4 header rows).  You can get all 13228 rows (actually up to 32,000 rows) of your data into PC-ORD by saving the file from excel in CSV format.  Then, the first time you open it in PC-ORD, you will need to import it (File | Import | CSV).  Then save it in PC-ORD file.  From then on you can use it as a normal data matrix in PC-ORD.   But if you reopen it and change it with that same version of Excel, you will need to go the CSV route again to get it to save the whole thing.

Can not import Excel

Q. I get an "Invalid variant operation" when I try to import an Excel .xls or .xlsx file.  Is there a solution?

A. First download the latest modules and see if that solves the problem.

Microsoft Excel must be on the computer in order to import.  (Open Office will not work.)  During import, Excel is loaded into memory invisible and sent instructions to open the file, and copy the data to the clipboard in text format so it can be accessed.  On a few systems this does not work for unknown reasons.  If you continue to have problems, save the file from Excel in CSV format and then import as CSV.

Can not import CSV

Q. I received a data file from a colleague overseas and cannot import the file.   What is the problem?

A. It sounds like the problem is due to the difference in the list and decimal separators, one using comma and period respectively, and the other using semicolon and comma.  You can temporarily match your colleague's language platform by Start | Control Panel | Regional and Language | Regional Options.  Then import the file.

Error exporting to Excel spreadsheet

Q. When I try to export a matrix to *.xls or *.xls I get an "OLE error" if there are more than 256 columns.  This happens in both Excel 2007 and Excel 2010.   What is wrong?

A. You may have set the default format for saving to *.xls (Excel 2003).  This will cause an error in later versions of Excel if there are more than 256 columns.   To fix this:

In Excel 2007:

1. Click the Office button in the upper left corner
2. Click the Excel Options button at the bottom of the drop-down menu
3. Select Save | Save file in this format: Excel Workbook (*.xlsx).

In Excel 2010:

1. Select File tab
2. Options
3. Save | Save file in this format: Excel Workbook (*.xlsx).

Then in PC-ORD, export as .xlsx file type.

Convert Database Format to Spread

Q. How can I convert my data in a database to PC-ORD spreadsheet format?

A. PC-ORD versions 4 and above allow you to import/export files in a list (or database) format. You can choose your field delimiters.  In the help under file formats, see List (Database) Format.

Error reading main matrix. Data read error

Q. I have had no success in importing a CSV file into PC-ORD.   I get the message "Error reading main matrix. Data read error." How can I correct the problem?

A. Check to be sure that you have included the header rows in your CSV file. Also, look at the text file "tempdat.tmp" in the application data folder.  This file contains info for the the last item at the time the import failed.  This file contains one data item per line.  You should be able to see the data for the row that failed or any other information out of place.

Graphs

Construct a dendrogram from TWINSPAN

Q. How do I construct a dendrogram (tree diagram) from the output of TWINSPAN?

A. It is possible to construct a dendrogram from the pattern of zeros and ones in the margins of the TWINSPAN table.  This pattern carries information on the series of divisions performed by TWINSPAN.  Observe the right-hand side of the table first.   The first column of zeros and ones shows the first division -- rows receiving a zero were separated from rows receiving ones.  Rows receiving the same digit are more similar to each other than rows in different groups.  Moving to the right, the next column shows the next two divisions.  Each of the preceding groups is again divided, as shown by the pattern of zeros and ones.  You can continue these sequential divisions until you reach the rightmost columns -- these groups were too small to divide further.  You can sketch in a traditional dendrogram to the right of the TWINSPAN table.  But it differs a little from the dendrogram you would get by cluster analysis, because in TWINSPAN the finest branches of the tree usually have more than one item on them.

View two graphs at once

Q. How can I view two graphs at once?

A. Yes. You can start two instances of PC-ORD, putting each in a window occupying half of your screen.  There is some potential for confusion if the two "sessions" are working from the same graph files.  Be sure to File | Save As | Graph and give the graph file a unique name for each before graphing.

Insert graphs into MS Word

Q. What is the best way to insert PC-ORD graphics into word documents?

A. Consider the following tips:

• Edit the ordination completely in PC-ORD -- do not attempt to re-edit the picture in Word.
• Use "save black & white" option (Graph | Options | Preferences) to avoid gray scales for figures destined for black-and-white reports and manuscripts.
• Drag joint plot labels into clear spaces for legibility.
• Edit title, axes, and legend in PC-ORD for clarity and informativeness
• When a figure is going to be reduced greatly in its final form, select larger font sizes and larger symbols in PC-ORD.
• Use options for Legend Symbol/Color to select easily distinguished symbols.
• Results may differ in sizing and other ways if you insert pictures from saved files vs. cut/paste using the clipboard. You may need to experiment with this.
• Resize the pictures in Word only by dragging the corners, not the sides, so that the proportions of the graphic are not altered.
• To include additional text, symbols, or graphics, do it on top of the imported pictures, not within them.  This avoids editing the picture with Word, which will usually force unwanted changes on the graphic.

Vertical axis becomes horizontal in MS Word

Q. When I insert a graphic into Word, the text in the vertical axis label becomes horizontal.  How do I fix this?

A.
1. Right click the graphic and select Edit Picture from the popup menu
2. Select the text box that you want vertical
3. From the menu select Format | Text Direction

Categories with text labels

Q. Can categories be given short text labels on ordination graphs, so that points are labeled with text indicating their category?

A. Yes, PC-ORD 7 allows text as data for categorical variables.  In versions 4 and 5 you can plot the row names from the second matrix, instead of getting those names from the graph file.  You can use this facility to assign ANY labels you wish, to be included in the ordination.  One application would be to give text names to groups, as you suggest.  First create a second matrix with row names that reflect group categories and open this matrix as the second matrix in PC-ORD.  Assuming you already have done the analysis and have a graph file, open the graph window. Select preferences in the menu and then select Labels From Second Matrix.

Groups with greater than 32 categories

Q. How can I overlay more than the 32 maximum categories on ordinations?

A. You can do this in two ways: 1) In the Graph | Preferences dialog, select Labels From Group Variable.  The values of your categorical (C) variable will then label the points. If you have more than 32 categories there will not, however, be a legend, but you can create one easily with your word processor by superimposing a text box containing a legend of your own design. 2) You can change the row names in your second matrix to reflect a group's categories and then select from Graph | Preferences | Labels From Second Matrix.  See Categories with text labels.

"Not a valid floating point value" error

Q. When I choose Overlay from Second Matrix or Joint Plot from the Graph menu I get the following error message and the program freezes: '2,0' or ',002' is not a valid floating point value?  What is the problem?

A. The problem is the "," comma as a decimal point in the cutoff value. International handling of decimals in PC-ORD works for most countries, but not all.  The solution is to make sure the Cutoff r2 value has a "." and not a ",".   The easiest way to do that is change the international settings to English (United States).  From the Windows Start menu select Settings | Control Panel | Regional Settings.

Species areas curves by group

Q. My dataset consists of data from 6 regions.  I would like to run a species area curve for each of the six regions (overlayed).  Can PC-ORD run species areas curves by groups and how would you do it?

A. There is no built-in option for species area curves by groups.  Create a separate matrix for each region, then run spp-area curves for each.  Each time you run it, copy/paste the numerical output into a spreadsheet.  Use "text to columns" in Excel.  Then you can plot the selected columns on a single graph with Excel.

Ordination plot by group

Q. When I ran an ordination plot, I could not get the six groups to plot out as different symbols or colors.  Once I graph the ordination, the group button at the top is not on.  How do I fix this problem?

A. With the ordination graph menu up, go to Options | Preferences and make sure that either "Color code categories" or "symbol code categories" is turned on.  If that doesn't work, be sure that you have declared the variable in the second matrix as "C" for categorical.

Rotation of axes

Q. Does the new version permit rotation of PCA axes?

A. PC-ORD allows rotation of axes from ANY of the ordination methods.  Varimax rotation is, however, available only with NMS.

Edit and save graphics

Q. How can I edit and save graphic images of ordinations and overlays?

A. Graph an ordination. Then select File | Save Graph AsSave_Graph.  The graph is saved as a Windows metafile (*.wmf or *.emf).  You can also save it as a bitmap (*.bmp) or a jpeg (*.jpg) or a tiff (*.tif).  This file can then be inserted into many word processors and other programs where you can easily resize and edit it.  For high resolution bitmaps, see Resolution for Save and Copy.

Convert graphics to PDF

Q. Sometimes figures do not convert well to PDF.  The left axis label consistently ends up horizontal.  How can I fix this?

A. Two suggestions:

• Use the enhanced windows metafile format (*.emf) if you are not doing so already.
• Try Adobe Acrobat Distiller. Graphics are, in general, more reliably converted to a PDF by Distiller than by regular Adobe Acrobat.

3D graph label quality

Q. The labels on my 3D graphs are not crisp and have ragged edges.  Is there a solution?

A. This is a problem with Windows smoothing of fonts.

In Windows XP:

1. Select Start
2. Control Panel
3. Display
4. Appearance
5. Effects and uncheck Smooth edges of screen fonts
6. Click Apply and OK

In Windows Vista:

1. Select Start
2. Control Panel
3. Personalization
4. Window Color and Appearance
5. Click on Open classic appearance properties for more options
6. Click on Effects
7. Uncheck Use the following method to smooth edges of screen fonts
8. Click Apply and OK

In Windows 7:

1. Select Start
2. Control Panel
3. System and Security
4. System
5. Advanced system settings
6. Settings under Performance
7. (or Performance Information and Tools
8. Advanced tools
9. Adjust the appearance and performance of Windows)
10. Uncheck Smooth edges of screen fonts
11. Click Apply and OK

If Windows 7 Control Panel is Viewed by icons instead of Category then

1. Select Start
2. Control Panel
3. Performance Information and Tools
4. Advanced tools
5. Adjust the appearance and performance of Windows
6. Uncheck Smooth edges of screen fonts
7. Click Apply and OK

See also 3D graph label holes or rotation trails

3D graph label holes or rotation trails

Q. Labels that are behind my 3D graph show through and/or all labels leave trails when rotating the graph.  Is there a solution?

A. In the Graph | Preferences | Format tab check Hide labels that are behind graph.
Alternate solutions to try are:
Check Label one axis side so there are no labels behind the graph
Uncheck Adjustable labels, especially with a joint plot graph.

If you are Vista or Win 7 user and getting rotation trails, you need to take an additional step:

1. Right click on empty part of screen
2. Select Personalize
3. Select Window color and appearance
4. Select any of the Color schemes other than Windows Vista Standard or Windows Aero

Note, for Vista or 7 users, the problem only applies to what you see on the screen.   Labels will be properly hidden without the extra step of changing the screen appearance with Copy, Save, Print Preview, Print, and Save Animated GIF.

See also 3D graph label quality

Add points/symbols for individual species

Q. How can I add in the points/symbols for individual species on the NMS or other ordination plots.

A. Two things need to happen to get points for species on ordinations:

1. 1. You need to have generated a graphcol.gph file, which should be visible in the window in the upper right. If you are using NMS, you get this automatically if you use autopilot. If you turn off autopilot, to get the graphcol.gph file you must be sure to check the box in NMS Setup | Ouptut options| Calculate scores for (species) by weighted averaging. A similar checkbox is available for other ordination methods. Note that if you save the graphcol.gph and graphrow.gph files, you don't need to rerun the analysis to do this, just open the saved files (File | Open | Graph Row File, Graph Col File.
   
   Sometimes even when you request the scores for species, they are not produced. This happens if one or more of your columns is empty (all zeros), such that the weighted averaging step fails.
   
   2. Graph | Options, preferences | Format tab | check Plot Points, Species (or whatever you called your columns).
   

3-D Plots Possible?

Q. Is it possible to generate 3-dimensional (XYZ) ordination diagrams in PC-ORD?

A. Yes. This feature was added in version 5.

Graphing freezes

Q. I am having problems using some graphics functions on the software, such as plotting 2D ordinations. Whenever I try this, the software freezes. What is wrong?

A. It is possible that your initialization file has become corrupt. You can reset this to all defaults and clear it by using the following steps:

1. Close PC-ORD.

2. In Windows Explorer, go to the Application Data Folder, something like C:\Users\xxxxxxxxxx\AppData\Roaming\MjM Software Design\PCORD 7.

3. Then rename pcord7.ini to something else like pcord7old.ini

4. Reopen PC-ORD and try again.

Then PC-ORD will recreate this initialization file the next time it runs and any bad graphics settings will be cleared. You will also lose previous graphics settings.

If you don’t see this file listed, then you might have your Windows Explorer set so that it isn't showing the file extensions and/or hidden files. You can turn these on and leave them on. Otherwise, Windows will hide many extensions and files. To do this, go to Windows | View, and check the boxes for "File name extensions" and "Hidden files".

Line weights – screen vs. print

Q. When displaying my results in figures, I've been showing two groups by using filled circles versus empty circles, but I'm finding the line weight of the empty circles is too fine to be clear. I can't find an option to edit the symbol line weight to make these empty symbols more clear. Can you point me in the right direction?

A. Line weights in open symbols (or any part of a graph, actually) will end up very thin if you save or print from a large screen. You can force thicker line weights by dragging the graph window smaller before printing or saving the graph. Compensate for the smaller window by increasing the resolution to 200% or 300%.

You can demonstrate this by saving the exact same graph two ways. First, with a maximized graph window save it at 100% resolution, File | Save Graph. as *.jpg. Now make the graph window half the size, but increase the resolution to 200% so it isn't excessively pixellated, then File | Save Graph. Now import the two files to Photoshop (or equivalent). Note the thicker line weights resulting from the smaller window. Of course the font sizes would need to be adjusted to accommodate this. Also note that the size of this effect will depend on the size and resolution of your monitor, and how much you shrink the window.

Some monitors have very high resolution and the effect will be quite pronounced.

CCA

How CCA in PC-ORD differs

Q. How does CCA in PC-ORD differ from that available in other statistical packages?

A. CCA is not yet available in major statistical software packages (do not confuse it with canonical correlation, an older eigenanalysis technique based on a linear response model).  CCA in PC-ORD does not have some of the options available in another implementation (such as inclusion of covariates and detrending), but we think you will be pleased with the spreadsheet data format, modern interface, integrated graphing, modest price, and our fully integrated set of data transformations and other multivariate tools.

CCA in PC-ORD is easier to use than CANOCO but doesn't have some of the options in CANOCO (e.g. inclusion of covariates).  On the other hand, CCA in PC-ORD is integrated into a relatively comprehensive package of community analysis, providing many more classes of analyses than CANOCO and including numerous nonparametric multivariate techniques.  Even so, PC-ORD is much less expensive than CANOCO, allows larger data sets, and a wider selection of graphical representations of community data (e.g. 3D ordination, cluster analysis, two-way clustering, species-area curves, successional vectors, etc.).

CCA: cannot solve weighted least squares

Q. When trying CCA I get the message "cannot solve weighted least squares, please check contents of matrices."  What should I check for?

A. CCA cannot solve the regression equation under several circumstances.  One common cause is when two or more variables are essentially identical or identical.  Another possibility is that the same variables are included in both the main and second matrices.

Order of variables in correspondence analysis

Q. Concerns have be raised about results from correspondence analyses depending on order in which variables are entered - is this a problem?  If so, has it been fixed?

A. This was mainly a problem with DCA and TWINSPAN, less so with CCA.  The Windows version has implemented Oksanen and Minchin's (1997) "super strict" criteria for stability of CCA, DCA, and TWINSPAN.

Error message: delete empty rows

Q. I find an inexplicable error message with CCA using a monte carlo test.  I am told that I need to delete empty rows in my main matrix.  The rows specified are not empty. Indeed, none of the rows in the matrix are empty.  The problem occurs only when testing the hypothesis, "no structure in main matrix..."  What is wrong?

A. Probably you have many zeros in your main matrix.  This is common, but if the problem is extreme, then shuffling within columns of the main matrix will result in empty rows.  When this happens, the monte carlo procedure discards that particular randomization.  But if it happens many many times, eventually PC-ORD gives up and reports the error.  You may be able to solve the problem by deleting some rare species (for example those occurring in less than 5% of the sample units).  This problem can also occur with any randomization test involving shuffling elements within columns (species) of a community matrix (e.g. the monte carlo test in NMS)

Downweight in CCA

Q. To compare my DCA analysis with CCA, I would like to downweight the species data also in CCA.  Since this option is not available for CCA, how can I do it?

A. In PC-ORD you cannot downweight in CCA in exactly the same way as in DCA.  But you can downweight rare species prior to ANY analysis by appropriate adjustment of the data.  For example, a simple approach is to delete species that occur in fewer than 5% of the sample units.  Other transformations, such as the information function of ubiquity, downweight both very rare and very common species, maximizing the influence of species that occur in half of the sample units.

CCA error printing coefficients

Q. When checking the result file of CCA I found following message: "Error printing coefficients.  Possible multicollinearity problem" inside a table.  What does it mean and what should I do?

A. It means you have variables in your second matrix that are very strongly correlated with each other.  Check their correlations (use checkbox for "list correlation coefficients for second matrix"), then remove a redundant variable.  For example, if you have two variables, percent canopy cover and percent canopy open, one is a linear function of the other.  This can also arise with groups of related variables, for example %sand, %silt, and %clay in soil samples.  For most data sets, those three will add to 100%, so only two variables are providing new information.

Passive samples in CCA

Q. In a CCA ordination, is there a way to enter some samples passively so as to see where they fall out in a pre-existing ordination?

A. PC-ORD doesn't have an automatic way of doing this, but you can easily do it with a spreadsheet.  Plug in the values for the environmental variables into the multiple regression equation.  If you use the raw environmental variables, be sure to use the unstandardized regression coefficients.  If you express the environmental variables as standard deviates from the mean of the original data set, then you can use the standardized regression coefficients.

DCA or CCA with negative values for data

Q. Is it not possible to use DCA with negative values for my data?  I always get a warning that there are negative values found.

A. No, you should not run DCA or CCA on a main matrix with negative values.

NMS

NMS setup stability criterion value

Q. How low can I set the NMS stability criterion?  What is the consequence of making it smaller?

A. You can set the stability value as low as you want, down to zero.  The only cost is in computing time.  With a small to medium data set you should seek a stable solution by setting it very low (e.g. 0.0000001) and set the number of iterations very high (say 500).

NMS monte carlo shuffling error

Q. When I run NMS with a Monte Carlo test, the shuffling routine ends with a message: "Shuffling data resulted in undefined distances over 10,000 times.  Abandoning efforts to shuffle."  The results for the real data are ok, but I do not get results from the Monte Carlo test.  What should I do?

A. When the randomization routine creates one or more empty sample units, that particular shuffle is discarded.  If your matrix is very sparse (very many zero values), it is very difficult to almost impossible to obtain many shuffles of the data with no empty sample units.  NMS is basically giving up on the Monte Carlo test for your data.  Consider the following possibilities:

1. Can you aggregate your data and analyze it at a higher level?  If your sampling is hierarchical, the smallest units (say microplots within plots) are often empty.  By aggregating microplots up to the plot level, the density of zeros in the data becomes much lower.
2. Can you partition your data set into more homogenous pieces and analyzing them separately?  After removing empty columns from each submatrix, they should have a lower fraction of zeros than the whole matrix.
3. Can you discard rare species?  Discarding species that occur in fewer than 5% of the sample units will typically not change the results much.  If none of those is possible, then you're pretty much stuck without a randomization test.
   

NMS 3-D solution

Q. I am trying to run a 3-D NMS with autopilot off.  It runs fine, but only two axes are written into the graph file.  Can you tell me how I can force a 3-D solution in NMS and see all three axes in the graph?

A. It sounds like you are requesting a 3-D solution but PC-ORD is deciding a 2-D solution is better, based on the built-in criteria for selecting the "best" solution.   You can prevent this by unchecking the box "Step down in dimensionality" and specifying a 3-D solution.  Then, if you request, for example, 100 runs with the real data, it will choose the best 3-D solution from those runs.

Different solutions with NMS

Q. Every time I run NMS, 2D graphs come out differently, and I cannot figure out how to get the same result repeatedly.

A. NMS differs fundamentally from other ordination techniques in a number of ways (see McCune & Grace (2002), chapter 16). One important difference is that NMS is typically run from random starting configurations. This means that the results will vary across different runs. Usually the variation is small, even though sometimes at first glance it appears big. For example, axis 2 in one run may be nearly identical to axis 1 in another run. Or an axis in one run may be essentially a mirror image of an axis from another run. You can also get different solutions that are essentially the same, but one is a rotation of the other. For other fundamental differences from other ordination techniques, please see upper right of p. 131 in McCune & Grace (2002).

Significance of correlations with ordination axes

Q. Does PC-ORD provide p-values for the significance of correlations between scores on ordination axes and other variables, such as 1) correlations between community ordinations and environmental data and 2) correlations between ordinations and individual species? Or, can the significance of the correlation be determined using tables with significance levels for r?

A. PC-ORD does not provide p-values for these correlations. It is important to understand the reason why not. Please see the first column on p. 107 in the book, Analysis of Ecological Communities.

This section starts out, "These correlations should primarily be used for descriptive purposes. It is both desirable and possible to resist the temptation to assign a p-value for the null hypothesis of no relationship between ordination scores and some other variable..."

The remedy for this -- how to describe its importance -- lies in the _effect size_ rather than the p value. Please see the middle paragraph in that column. A short excerpt: "...set your own standards for how small an effect size, as indicated by the r-value or rank correlation coefficient, you are willing to interpret. In almost all cases, this threshold will be more conservative than one determined by the p-value..."

If you don't like this logic, or an editor or reviewer insists on a p-value, you can look up and report p values (see end of that paragraph), but that makes you vulnerable to the arguments presented earlier.

TWINSPAN

Construct a dendrogram from TWINSPAN

Q. How do I construct a dendrogram (tree diagram) from the output of TWINSPAN?

A. It is possible to construct a dendrogram from the pattern of zeros and ones in the margins of the TWINSPAN table.  See the example in McCune and Grace (2002).  The pattern or zeros and ones carries information on the series of divisions performed by TWINSPAN.  Observe the right-hand side of the table first.   The first column of zeros and ones shows the first division -- rows receiving a zero were separated from rows receiving ones.  Rows receiving the same digit are more similar to each other than rows in different groups.  Moving to the right, the next column shows the next two divisions.  Each of the preceding groups is again divided, as shown by the pattern of zeros and ones.  You can continue these sequential divisions until you reach the rightmost columns -- these groups were too small to divide further.  You can sketch in a traditional dendrogram to the right of the TWINSPAN table.  But it differs a little from the dendrogram you would get by cluster analysis, because in TWINSPAN the finest branches of the tree usually have more than one item on them.

Enhancements of TWINSPAN

Q. I would like to see dendrograms produced by TWINSPAN as well as other enhancements to the program. Will TWINSPAN be improved in PC-ORD?

A. We decided not to spend much time trying to upgrade Twinspan, other than expanding its memory capabilities, because of serious, fundamental flaws with the concepts behind the method and the resulting poor performance of Twinspan with heterogeneous data sets (see for example van Groenewoud 1992, Belbin, L. and C. McDonald. 1993).  The problem is how well the underlying structure of the data is represented by the two-way table produced by Twinspan.  Have you tried two-way cluster analysis?  Or simple cluster analysis?  If you are not familiar with cluster analysis, we recommend using the following options: Ward's method of linkage and Euclidean distance.  If you get groups of sample units that are acceptable, then save the classification as a new variable (see option under cluster analysis), then run Indicator Species Analysis to tell you which species are most strongly separated among the groups.  Or use two-way clustering to get a graphical representation of how groups of sample units and species are related.