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NTSYSpc Numerical Taxonomy and Multivariate

1. DCENTER Performs a double centering of a matrix of similarities or dissimilarities among the objects The resulting matrix can then be factored to perform a principal 4 Introduction coordinates analysis a method for displaying relationships among objects in terms of their positions along a set of axes based on a dissimilarity matrix EIGEN Computes eigenvector and eigenvalue matrices of a real symmetric similarity matrix This program can be used to perform a principal components or a principal coordinates analysis by extracting eigenvectors factors from a correlation or variance covariance matrix FOURIER Computes Fourier and elliptic Fourier transformations for both 2D and 3D curves FOURPLOT Plots outlines and estimated outlines produced by the FOURIER module MDSCALE Nonmetric and linear multidimensional scaling analysis This can be used as an alternative to principal components analysis MOD3D Plots a 3 way scatter diagram as a 3 D perspective view of a model with t objects at tops of wires attached to a base plane The view can be rotated interactively This program is often used to view the results of a principal compo nents or principal coordinates analysis MST Computes a minimum length spanning tree from a similarity or dissimilarity matrix This is useful for showing the nearest neighbors of objects based on their positions in a multidimensional space MULREG Performs various types of regression analyses Includ
2. NTSYSpc Numerical Taxonomy and M ultivariate Analysis System Version 2 1 User Guide F James Rohlf D epartment of Ecology and Evolution State U niversity of N ew Y ork Stony Brook NY 11794 5245 gt mu EXETER SOFTWARE 47 Route 25A Suite 2 Setauket N ew York 11733 2870 Information in this document is subject to change The software described in this document is furnished under a license agreement single user or site license The software may be used or copied only in accordance with the terms of the agreement Copyright 2000 by Applied Biostatistics Inc 10 Inwood Road Port Jefferson New York 11777 All rights reserved worldwide ISBN 0 925031 30 5 Current printing May 14 2004 Contents CO ep CU OND AAA eaten oh su suesavssaten asssuasay E A E E AA 1 LI Ateas OF APPIN CAN OM senescsiseitits delete muatide a austin riea laude atudee male aa aaa 1 1 2 Programimod les MN TS ESP odo os 3 1 3 How toget started using N TSY Dl is 6 LA What snew INVIAS 8 1 5 What was new in VESION 2 Dt dai 9 2 Modes OF ODA ON aaa 10 Z1 Interactive Modenan a a a ai 11 2 2 A AN 12 2 3 Both interactive and command Modes viii 14 3 Menus amp related W NdOWS ssssssssunsnununsnnnnnnnnnunnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn annuam annuam annuam nnnnnnnnnnnn annann annan 15 3A E E TAE wate teas T RA R 15 3 2 CUSCOMIZ AL MONCO DOM soria 15 3 3 Configuration options and lia Te eat 16 34 Output ISIC VU HIM OW s
3. Print preview which changes the plot to a preview of how it will look when printed Print to print the plot and Close to close the plot window The Edit menu allows one to copy the current plot to the Windows clipboard You can then paste it as a bitmap into a word processor or paint program The options menu allows you to save the current state of the plotting options to a graphic options file The plot Graphics options amp menu 29 options colors point and line options etc can later be restored by loading this file The Help menu leads to the standard Contents Topic search and A bout items 7 Typical applications Furnished below are some examples of typical applications of NTSYSpc For simplicity the required steps are shown as sequences of batch command statements This is a compact way to describe the sequence of modules and their parameters See the help file for more detailed technical information about each module N ote lines that begin with a quote character are treated as comment lines and are ignored by NTSY Spc 7 1 Cluster analysis Perhaps the most common use of NTSYSpc is for performing various types of agglomerative cluster analysis of some type of similarity or dissimilarity matrix The following is an example of a batch file that will standardize a data matrix compute distance coefficients among the columns of the standardized data matrix there are several other choices of coefficients cl
4. close ties to Some methods in the field of pattern recognition Within the field of systematic biology one can distinguish two different approaches to classification In phenetics one is concerned with the discovery and description of the patterns of biological diversity and forming classification based on overall similarity computed from multivariate data These methods are commonly used in morphometric studies In cladistics one is interested in inferring the evolutionary history of the organisms under study and using it as a basis for classification Specialized methods have been developed to take into account the assumption that the underlying model is of a branching evolutionary tree It is expected that the best biological explanation of the observed diversity of a set of organisms will come in terms of their evolutionary history The methods are intended to make the best estimates of the evolutionary tree given a set of descriptive data on a set of organisms The most commonly used methods are justified on the basis of the philosophical principle of parsimony that the shortest tree that can be fitted to a set of data should be the best estimate of the true tree but statistically more powerful methods based on the principle of maximum likelihood are increasing in popularity The neighbor joining method is also often used The methods furnished in NTSYSpc are largely associated with the field of phenetics However they are best interpreted as s
5. 6 2 09 F implemented see the Edit Se ee Ces so 18 17 21 menu 3 2 26 26 The NTedit help can 10 10 19 13 13 be consulted for additional information including ines R10 0 40 Ins various keyboard shortcuts Figure 5 2 Example of NTedit with the test nts file loaded in ASCII text mode 6 Graphics options amp menu The plots produced by NTSYSpc can be enhanced in many ways by taking advantage of the many options available Begin by clicking on a plot with the right mouse button or by selecting the Plot options item on the Options menu above the plot The options available depend upon the type of plot Figure 6 1 shows an example for the MXPLOT module All plots allow the user to specify a title and a subtitle and the fonts used to display them select the Titles tab There is also always a button labeled General select the Options tab that opens the general plot options dialog box described in the next section 6 1 General plot options The following options listed by group are available for all plots General Preserve axis aspect means to preserve the aspect of the x and y axes with respect to the original units of measurements This must be kept checked for the 3D and Tree plots For 2D scatter plots it should be checked when plotting the results of analyses such as 28 Graphics options amp menu principal components analysis where the relative lengths of the axes is importa
6. Study of Evolution meetings in Durham New Hampshire James Archie William H E Day Wayne Maddison Christopher Meacham F James Rohlf David Swofford and Joe Felsenstein were present The reason for the name is that the second and final session of the committee met at N ewick s restaurant in Dover NH Examples and a simple description of this format are available at http evolution genetics washington edu phylip newicktree html 5 NT edit The Ntedit program included with NTSYSpc is a data editor designed for use with NTSY Spc data files For each of the basic file formats rectangular symmetric diagonal tree and graph it displays an appropriate arrangement of the cells in the spreadsheet Using N Tedit ensures that the files are formatted correctly The program can be started in three ways 1 Click on the NTedit icon to start the program 2 Load this program from the File Edit file data file menu item or the edit speed button on N TSY Spc s toolbar 3 Usea DOS command window and type ntedit and the name of a file and then press the A_key to start the program Once the program is started you can either create a new file or load an existing file NTS format files can be loaded eather in a spreadsheet like grid Figure 5 1 or in a plain ASCII text editing Figure 5 2 view Excel files can only be displayed in the grid view and nexus files can only be displayed in the text view 26 NTedit
7. The changes to individual modules have been relatively minor since so much effort was spent simply converting the DOS program to a Windows program 2 Modes of operation There are two modes in which NTSYSpc can be used interactive and batch In interactive mode a module is selected from the main window by clicking on a button which causes a window showing the various parameters and options for that module to be displayed After this form is filled in click the Compute button to run the module and have the results appear as a new section in the Listing window You start batch mode by selecting the Run batch file item on the File menu or by using the convenient speed button on the toolbar The batch dialog box will let you select a file containing a sequence of NTSYSpc commands specify up to nine parameters and run the batch file The batch file contains commands that Call up various modules supply parameters and execute them automatically Batch files are Modes of operation 11 convenient for the processing of large data sets or for processing a large number of data sets perhaps from a simulation 2 1 Interactive mode The main program window displays a program bar with folders corresponding to sets of program modules See Figure 1 1 above Click on a folder to select a section This displays buttons corresponding to the modules available from that section To select a module click on the corresponding button The selec
8. a discussion with applications in analytical chemistry e Reyment 1991 gives an overview of the application of multivariate methods and features discussions of many data sets The supplement by Marcus gives SAS procedures for the computations of many of the multivariate analyses discussed in that book 2 Written by Joe Felsenstein University of Washington Introduction 3 e Romesburg 1984 gives detailed descriptions of many clustering methods e Sneath and Sokal 1973 may be consulted for a general introduction to the field of numerical taxonomy and for definitions of most of the jargon used in this manual Most examples are from biology but extensive references are given to applications in other fields The older version Sokal and Sneath 1963 is still a useful reference as it gives more complete listings of coefficients e Weir 1989 gives a short overview for DNA sequence data 1 2 Program modules in NTSYSpc Listed below are short descriptions of the computational modules included in NTSYSpc The acronyms under which they are listed are the codes used in batch command files Detailed technical descriptions of the modules including equations for the operations and the various coefficients are provided in the help file NTSYSpc is not limited to just the analyses mentioned below The modules can be used in different sequences to build many other types of analyses for example Gower s principal coordinates analysis can be carri
9. also enter the code as F8 4 asin FORTRAN but the NTSYSpc will always store the code with the f at the end The File overwrite code is used to determine what should happen when the program attempts to save a data file with the same name as an existing file Ask means that a window will pop up asking what should be done overwrite means that the existing file should be deleted and append means that the new file will be appended to the end of the existing file If you wish another editor can be substituted for the N Tedit program N ote the configuration parameters can also be changed through commands in a batch file Use CONFIG as if it were a module and use the batch codes given above to change the values of the parameters asthefollowing config LF 9 6f 3 4 Output Listing Window This window uses a notebook metaphor to display listing output from the computational modules Each time a module is run a new section is created with an index tab numbered in sequence and labeled by the name of the module An example is shown in Figure 3 1 A section can be examined by clicking an a tab and then moving the scrollbars Note that the entire window can be resized The File menu provides a number of important operations The entire notebook can be reloaded from a previous run saved to an ASCII file cleared i e deleted or printed Alternatively the currently displayed section of the notebook can be saved to an ASCII fil
10. beignored 7 5 Nonmetric multidimensional scaling This method is similar to PCOORDA in that it can be used to represent the relationships among a set of points in a low dimensional space The difference is that in non metric multidimensional scaling analysis the distances among the points in the final configuration need only have a monotone relationship to the distances implied by the original data matrix This relaxed constraint usually makes it possible to get a much better fit in fewer dimensions than is possiblein PCOORDA If possible one begins with the results of a PCOORDA as an initial configuration since this usually results in many fewer iterations being necessary in the MDSCALE module Use PCOORDA to obtain an initial configuration DCENTER O dist nts R dcent nts EIGEN O dcent nts N 2 R init nts non metric MDSCALE using initial solution MDSCALE O dist nts N 2 I init nts R final nts rotate result for ease in viewing SIMINT O final nts C varcov R vcv nts EIGEN O vcv nts N 2 R vect nts PROJ O final nts D row F vect nts R result nts plot the final rotated configuration MXPLOT O result nts When viewing the plot be sure to set the option Preserve axes aspect The Procrustes module can be used to compare the final configuration with another ordination such as the initial Pcoord solution 7 6 Burnaby s method for size adjustment The following batch file
11. example the height at which the set 1 3 2 joins the root is 4 3 and the height at which 4 5 joins is 1 3 The average of these two values is 2 8 which is smaller than the level at which 2 joined 1 3 The program constrains the average heights to be at least 0 0001 greater than the largest height within the sets being joined This preserves the topology indicated by the parentheses but shows the trees graphically as looking as if there was a multifurcation 4 3 Interface to other programs Since the matrix files have a simple format see the previous section they should be usable by other programs with very few changes needed Results from other programs should also be convertible into the format described above The largest problems are apt to be due to different conventions for furnishing labels and for reading symmetric matrices 4 4 Excel files NTSY Spc can read rectangular matrices from worksheet files compatible with Excel These files must have an extension of XLS The Excel program itself need not be present NTSYSpc will search the spreadsheet for the matrix parameter line by starting with the first row If only cell Al contains information then its search continues on to subsequent rows until a row is found with at least four non blank cells The information in the rows being Skipped over is taken as comments Once the matrix parameter line is found the cell in column A is interpreted as the matrix type code It must b
12. of any dimension e PROCPLOT 2D and 3D plot of the results of a Procrustes superimposition e FOURPLOT Plot outlines and estimated outlines from the FOURIER module e MULREG generalized multivariate multiple regression Can be used to perform simple bivariate regression multiple regression multivariate regression and generalized least squares regression as used for the comparative method e PLOT Plot one or more columns of a rectangular matrix against a selected column Points can be given different symbols and connected by lines Improved modules e CONSEN Input trees can be in the nexus file format Introduction 9 e COPH Input tree can be in the nexus format Path length additive distances and Phylogenetic covariances can be computed in addition to the usual ultrametric distances e CVA Can now compute canonical variates scores for individual observations e FOURIER Many changes were made to make this module more useful Linked to the new FOURPLOT module for direct viewing of the results e MOD3D Rewritten to provide interactive 3D rotation drag with the mouse and better axis labeling Different symbols can be given to different points 3D biplots can be produced e MXCOMP The Smouse Long Sokal 3way Mantel test has been added along with the additional plots it requires e MXPLOT Points can be given different symbols 2D biplots can be produced e NJOIN Completely rewritten to greatly increase it
13. of similar objects cluster analysis or in terms of a spatial arrangement along one or more coordinate axes ordination analysis or various types of multidimensional scaling analysis This User Guide assumes that the reader has some familiarity with the methods It does not contain much advice about which similarity coefficient or which clustering method should be used It does however give many hints about the use of the methods To keep the account general the neutral terms object or OTU for operational taxonomic unit are usually used to refer to the things specimens being analyzed and the terms variable or character are used to refer to the properties used to describe the objects under study Users may find the following general references helpful the complete references are given in the Bibliography Everitt and Dunn 1992 give a good concise introduction to both cluster analysis and multidimensional scaling analysis They furnish examples from biology Gnanadesikan 1977 describes many methods for detecting patterns in multidimensional data Applications are from many fields e Hartigan 1975 describes a large number of different clustering methods Examples with test data sets are from a great many fields e Jackson 1991 is an excellent mathematical text on multivariate analysis It is much more comprehensive than implied by its title A user s guide to principal components e Massart et al 1978 gives
14. of the data files It also describes the use of the special Be sure to check the README TXT file for any last minute notes or corrections to this User Guide The blue registration card should also be filled out and returned since this allows us to notify you of any problems that are discovered with this version of NTSYSpc It will also allow us to notify you of the availability of updates as new programs and features are added to NTSYSpc Your comments corrections and suggestions about the program are welcomed 1 4 What s new in version 2 1 Changes to the user interface e Thedesign of the user interface has been changed to make NT SY Spc easier to use The computational modules are now organized in folders in a bar along the left side of the main window e A customize option allows the user to place frequently used modules in a user defined folder e Excel data files can now be read directly by all appropriate N TSY Spc modules the less reliable DDE and OLE methods are no longer used e Nexus tree files can now be read and the NTS file format has been extended to allow trees with OTUs at different heights e Plot options choice of fonts colors etc can now be saved and reloaded in graphics options files The options are now organized in a convenient tabbed notebook display New modules e PROCRUSTES Procrustes superimposition of coordinates of 2D or 3D landmarks on specimens or superimpositions of multivariate ordinations
15. select niha Less jodas trend i Configuration under the Option menu on the main window This will display a window like those used for the various Figure3 1 Customization window D rag computational modules The entries here module names from the list at the right to the however are system parameters such as file User folder at the left formats directory names and other options The information you enter will be saved in the ntsys ini file in the same directory as the ntsys exe program The file also includes coded information about the position and size of various windows used by NTSYSpc Configuration parameters Data directory the directory to use as the D a for dats A append Editor to be called from the toolbar or the ed rr The File format code is used to write results to disk so they can be used as input to other modules The default format of e ensures these values are saved with maximum Menus amp related windows 17 precision This value should not be changed except possibly when working with very large matrices and you are low on disk space On the other hand the Listing format code will often be changed so that numerical information displayed in the Listing window has an appropriate level of precision for a given data set The default is 8 4f which means that floating point numbers should be displayed with four decimal places within a field eight characters wide You can
16. shows an example of how the ORTH option of the PROJ program can be used for Burnaby s method to remove the effect of a vector from a data set The data are projected onto the hyperplane orthogonal to the specified vector In the example given below the first principal component axis is used as size Other vectors such as the isometric vector 1 1 1 could also be used compute VCV matrix from a data matrix simint o data nts c varcov r vcv nts d row compute first principal component eigen o vcv nts n 1 r pcl nts project data onto hyperplane normal to PCl proj o data nts f pcl nts pt orth r bproj nts The adjusted data matrix bpro3j nts can then be used for example to compute a distance matrix which is then clustered by SAHN The clusters should then not be influenced by variation in the original data set that was parallel to the first principal component which is often mostly due to size The first principal component points in the direction in which 34 Typical applications there is the most variation If the organisms sampled happen to be about the same size then this vector is apt to represent sexual differences polymorphisms etc In many cases it may be safer to use an a priori defined isometric vector as a size vector i e the vector 1 1 1 1 1 or to use the first principal component based only on a carefully selected subset of variables The adjusted data matrix could also be used as input
17. the same For legibility it is convenient to keep the lines short and use more than one line for each command if convenient The file TEST NTB on the distribution disk is an example of a NTSY Spc batch file To execute a file containing batch commands click on the batch speed button on the toolbar or else select the Run batch file item on the File menu of the main window This will bring up the batch mode dialog box as shown in Figure 2 3 Click on the Load button to bring up a file open dialog that allows you to specify which file to use The click on the Run button to execute the file While running this window will display the currently executing line If you change your mind you may click on the Cancel button and the run will be stopped at the next iteration or logical breakpoint in the currently executing module this might take a while for a large matrix The results will be sent automatically to the Listing window where they can be inspected when the computations are complete 14 Modes of operation It is also possible to prepare a batch file with replaceable parameters This allows batch files to be used with more than one data set If the codes 1 2 9 are found ina batch file they will be replaced by the values me of the corresponding replaceable parameter its eviernircanrz arestz NTE strings given in the parameter area of the Parameters batch mode window A maximum of 9 replaceable parame
18. 1 3 Listing window after running the Output module NTS For other types of on the TEST NTS datafile files click on the File of type window at the lower left and select Excel Nexus or All files Use this dialog to locate the TEST NTS filein C NTSYS or wherever you installed NTSYSpc and then click on the Open button Then click on the Compute button to run the Output module The results will be displayed in the Listing window every time you run a module a new section is added to the listing notebook An example is given in Figure 1 3 Press the key or use the Help menu items to open the help file You should note that the separate modules do not provide a complete analysis You will normally use a sequence of modules in order to carry out a complete analysis This structure makes NTSYSpc more flexible and useful in research applications Unless batch files are used this approach also helps one appreciate the various components making up a standard analysis See Chaper 7 for a number of examples N ext you should read Chapter 2 on M odes of operation to learn how to use NTSY Spc in both interactive and batch modes Note that This Style of type is used to indicate strings of characters that the user is expected to type into the computer such as file names 8 Introduction Chapter 4 on Preparation of input data files is of course essential reading as it describes the format
19. A 31 PCOORDA 32 phenetics 1 preference scaling 30 Principal components analysis 31 Principal coordinates analysis 32 repertory grid analysis 30 replaceable parameters 14 single link 5 singular value decomposition 5 size adjustment 33 Spatial autocorrelation analyses 35 thin plate spline 6 tree matrix 22 two block partial least squares 3 ultrametric 23 ultrametric values 3 UPGMA 5 XLS 23
20. In the grid mode you can enter or correct data in HICIERAS TERA IA NET any of the cells You can File Actions Options Help insert or delete rows and Row Labs Col Labs Ins row Del row ff Close columns within the table by dicking on the Matrix type Rectangular Comments Matrix f E ropriate menu choi appropriate menu choices No rows 5 No cols 10 Missing or the speed buttons on the tool bar You can also add or delete rows and columns from the end of the table by entering new values in the edit boxes displaying the current numbers of rows and columns To change the labels for the rows or Figure 5 1 Example of NTedit with the test nts file loaded in a columns given in the first 9rid view protected row or column of the data table click on the RowLabs or Col Labs buttons to unprotect these entries You can then type new information in these cells The new names must not have any blanks within them Click these buttons again to re protect these labels from accidental change To create a new file use the following steps 1 select New from the file menu 2 select the proper matrix type from the list you may receive a warning about the possible loss of data when you change matrix types 3 enter the correct numbers of rows and columns in the edit boxes labeled No rows and No cols note that the new values do not take effect until your cursor leaves the edit boxes an
21. Oe oe El In this case the L can be appended to either the number of rows the number of columns or to both But only one set of labels should be furnished If a symmetric matrix is 22 Preparation of input data files the output of some other program it may be stored as a full square matrix In that case you should code it as a rectangular matrix and use the SYMD or syms options of the TRAN SF program to convert it to the lower half matrix form required by NTSY Spc Tree matrices matrix types 5 and 6 are usually produced by programs rather than entered by a user The usual exception is when one wishes to enter an expected tree to compare with the observed results using the CONSEN program There are two styles in which a tree can be entered in NTSYSpc The format used internally in NTSY Spc is described at the end of the description of the SAHN program In addition you can describe a tree using nested parentheses as in the NEXUS format used for example in the program PAUP This option is only available for tree matrices based on dissimilarities matrix type code 5 While complete NEXUS files cannot be read the tree descriptions can be processed as long as the OTUS names are given as integer numbers corresponding to their position in a data matrix This format is provided to enable trees produced by other programs to be entered into NTSYSpc more easily One can also enter trees by hand using this notation but it becomes awkwar
22. See the examples in the next two sections Help This pulls down a submenu from which you can select Contents Topic search or About The contents item displays the table of contents for the help file Topic search brings up the Help topics dialog box in which you can search for various terms The about item displays the NTSYSpc about box showing copyright information version number and the registration number 3 2 Customization options 16 Menus amp related windows Because most analyses require one to run modules located in different folders you may find it convenient to make use of the User folder If you click on Customize under the Option menu the customization module will load see Figure 3 1 You can then drag module IERT names from the list at the right to the User Fie Options Hep folder on the left To remove a module from 5 cancel Fi close the eel folder Mentales on its name and eT ees select Remove module from the pop up N menu You can also rename a module Click Du on the OK button to closethis window Stan a dci e tps weig ts 33 C fi ti ti Output Labial a on igura ion op ions Cophenetic values E Fourier MST ei and file Fourier plot acia nog Procrustes Fr plot There are a number of aspects of how Procrustes plot Matri plot N TSY Spc operates that can be modified by a t sl user These are done from the ele Pirlo on modest Use i i t if S Configuration Window
23. a files Both the program and the documentation have greatly benefited over the years by the help of many of the users who have spotted many glitches in the program and the documentation Drs Dean Adams Leslie Marcus and Dennis Slice have made a number of important contributions NTSYSpc will continue to be developed New programs and features are planned so that the system can evolve to better meet your needs Your comments suggestions and criticisms are appreciated Port Jefferson New York F James Rohlf Introduction 1 1 Introduction 1 1 Areas of application NTSYSpc is a system of programs that is used to find and display structure in multivariate data For example one may wish to discover that a sample of data points suggests that the samples may have come from two or more distinct populations Of equal interest is the discovery that some subsets of variables are highly inter correlated The program was originally developed for use in biology in the context of the field of numerical taxonomy which explains why the name of the program is NTSY S for Numerical Taxonomy SY Stem But the programs have also been widely used in morphometrics ecology and in many other disciplines in the natural sciences engineering and the humanities The terms mathematical taxonomy and automatic classification have also been used to describe this field of application The techniques also represent a subset of multivariate data analysis and have
24. ain menu Across the top of the main window is a menu bar see Figure 1 1 The various choices are described below File This pulls down a submenu from which you can select Edit data file View listing Printer setup Run batch file and Exit The edit menu item displays a file open dialog in which you can specify the name of the NTSYSpc file you wish to edit The separate program NTedit included with NTSYSpc is then run If the fileis a valid NTSY Spc file then it will be displayed in a spreadsheet like format If there are any errors in reading the file then an alternative ASCII editor Such as the Windows notepad or some other user selectable editor will be run The view listing item opens the Listing window see Section 3 4 The printer setup item opens the standard Windows printer setup dialog box The run batch file iten brings up the Batch mode dialog box so that a batch file can be run see Section 2 2 The exit item closes the program the program can also be closed by clicking on the Close speed button on the tool bar Options This pulls down a submenu from which you can select Configuration or Restore defaults The configuration item will display a parameter entry form for various program configuration options The restore defaults item will reset the configuration parameters back to their original states The Customize option will allow you to add or remove modules from the User folder
25. al programs were developed during the two week course It was quickly recognized that such a program on a personal microcomputer was of general interest both for use in student laboratories and for research computations The PC was easily able to handle most datasets NTSYSpc was originally written in FORTRAN for the IBM 360 50 mainframe computer at the University of Kansas in 1966 That version called NTSYS was developed with the help of Ron Bartcher who also converted it for use on a GE 635 computer in 1968 In 1969 John Kishpaugh and David Kirk helped with the conversion of NTSYS from the GE 635 back to an IBM 360 50 and then to the Univac 1100 computer system both at the State University of New York at Stony Brook In addition many others contributed to its development over the years But NTSYSpc is a new program written in Pascal Fortunately after all of the previous experience with conversions most of the computational routines in NTSYS were by now quite system independent and relatively easy to convert to another language At present NTSYSpc has moved beyond NTSYS and provides many operations not available in the version of NTSYS NTSYSpc has gone through many revisions and has become much easier to use The help files have been expanded and improved They contain the technical information that was once in the printed documentation Excel the NTedit program or any ASCII editor such as Notepad can be used for the preparation of dat
26. ates of the points as the primary input matrix and enter the name of the matrix giving the coordinates of the variables as the secondary input matrix The secondary matrix is plotted at the same scale and shown as vectors from the origin If the vectors are too short or too long one may use the TRAN SF program to scale them to a more convenient length 7 3 Principal components analysis Principal components analysis PCA is one of the most important methods of ordination analysis It constructs a new set of orthogonal coordinate axes such that the projection of points onto them have maximum variance in as few dimensions as possible While defined in terms of variances and covariances PCA is often applied to standardized data because the results are sensitive to the choices of units of measurement and the choice of units is often arbitrary The following batch file will standardize a data matrix by rows compute a matrix of correlations among the variables assumes rows extract 3 eigenvectors from the correlation matrix project the standardized data onto these eigenvectors and then make a 3 dimensional plot of the objects Various matrices are also output to files Standardize variables rows stand o data nts r sdata nts Compute correlations among variables rows simint o sdata nts c corr r corr nts d row Output the correlation matrix output o corr nts Extract first 3 PCA axes from correlation matrix eigen o corr nts n 3 r
27. d by a projection to eliminate the redundant dimensions A PCA of a covariance matrix for the aligned data and aPCA of acovariance matrix based on the partial warp scores will yield identical results except for the presence of zero eigenvalues when analyzing aligned data 7 8 Comparison of dis similarity matrices Often one wishes to test whether one set of relationships among a set of objects is independent of another For example one may wish to test whether the degree of morphological difference between samples is related to the geographical distances between the sampled populations see for example Sokal 1979 A simple way to do this is by the use of the Mantel test Mantel 1967 The test assumes that the two matrices have been obtained independently one cannot use it to test two matrices where one has been derived from the other The steps given below assume that one already has a matrix of geographical distance gdist nts Compute morphological dissimilarity matrix simint o data nts c dist r mdist nts d row Compare mdist with gdist 250 random permutations Typical applications 35 mxcomp x mdist nts y gdist nts np 250 The program can also be used to perform a 3 way Mantel test using the Smouse Long Sokal method This procedure performs a Mantel test two matrices that have been adjusted for the effects of regression on a third matrix It allows one to test for the relationship between two distance matrices when th
28. d for large trees since it is easy to miscount parentheses In this format nesting is indicated by parentheses branch lengths which are optional are given in the format value after each OTU name and right parenthesis and the end of the tree is indicated by a semicolon If branch lengths are not provided then NTSYSpc will generate arbitrary clustering levels consstent with the set relationships given in the tree N ote that one must either provide branch lengths for all branches or else for none of them A mixture will produce unpredictable results Example of a NEXUS style tree not using branch lengths NEXUS style input with OTU labels provided 5 S6 ZQ ABCODE 1 3 2 4 5 This implies a tree of the following topology 1 5 L Example of an input file using branch lengths Example using branch lengths but no OTU labels 5 ad Y MEME AMIA SES Y EE EAS SOL Ts CAT 54 5 OA 20 Os This tree has the same topology as in the previous example It should be noted as in the above example that the branch lengths may be inconsistent with the levels heights used to Preparation of input data files 23 describe an ultrametric tree In the above example the branch length for OTU 1 is 2 1 but the length for OTU 31s 2 5 The program will use the average 2 4 of these values An additional problem is that the raw average of heights of each interior node may not increase as one goes towards the root In the above
29. d may have a suffix letter to indicate the presence and location of row and column labels and possibly a floating point number They must be separated by at least one blank space e Thefirst number is a codefor the type of matrix 1 rectangular data matrix 2 symmetric dissimilarity matrix 3 symmetric similarity matrix 4 diagonal matrix 5 tree matrix for dissimilarity data 6 treematrix for similarity data 7 graph matrix for dissimilarity data and 8 graph matrix for similarity data e The second and third numbers are the numbers of rows and columns in the matrix If labels are to be furnished for either the rows or columns or both then a letter must be entered right after the number with no spaces in between An L is used to indicate the presence of a list of labels in a separate record placed before the data For example 25L means that there are 25 rows and labels are furnished in a separate record A lower case 1 can also be used but this is less desirable since it looks so similar to the number 1 The letter B is used to indicate that row labels are placed as the first item in each row and E indicates that the row labels are placed after the end of each row 20 Preparation of input data files e The fourth number is 0 if there are no missing data in the matrix If there are missing data then the fourth number should be a 1 followed by at least one blank and then the numerical code used to denote th
30. d then 4 start entering your data If there are missing data the identifying numerical code needs to be entered in the edit box labeled Missing Click on the Comments button if you wish to add comments to the matrix When you are done you can use the Check matrix item under the Edit menu to check that all data values are properly formatted numbers It also will check to make sure there are no empty cells This same check is made when to attempt to save the matrix to a disk file You will be given a chance to replace all the empty cells with whatever code you specified for missing data if that field is blank then zeroes will be used NTedit can also be used to view and make changes in existing files Changes have to be made with care as there is no undo feature A limitation of this mode is that the file must already be in a proper format If you try to load an NTS file that is not formatted properly you will receive an error message and N Tedit will try to load the file in ASCII text mode Preparation of input data files 27 More flexibility is provided when editing a HOENESS file in ASCII text mode File Edit Options Help see Figure 5 2 Text may 4 sample data matrix to test NTSY5 pe be freely moved around There are 5 characters rows and 10 OTUs column The columns are labelled No missing values and cut and pasted from 54010 0 other software An undo BCDEFGHIJ and redo feature is S49
31. e deleted or printed 18 Menus amp related windows The Edit menu provides commands to select all the text in the current section to cut selected text to the Windows clipboard to copy selected text to the clipboard and to paste in text from the clipboard These commands permit erre you to copy results into File Edit Options Help other software such as a There are 5 characters rows and 10 OTU wordprocessor They also The columns are labelled No missing val allow you to delete STAND input TEST NTS divide STD subts unwanted information SIMINI LAPU PORTA NIR coeff DIST dir mae type 2 size 5 by 5 ne none before printing or saving to N 10 a disk file Keeping such Mean X 5 5783 38x 98 9418 notebooks is a convenient Mean Y 1 0819 ssy 0 6887 way to verify which options were used to produce a Tests for association certain result The purpose Matrix correlation of reloading a notebook is normalized Mantel statistic to allow the appending of Approximate Mantel t test E new results so that a record A A cee es 5 of all the computations for a particular project can be kept together The file format is simply an ASCII file with the form feed character separating sections The Options menu allows you to change the font used both for the on screen display and for printing The indent item controls the size of the left margin when printing Figure 3 2 Example of the listing window after running the co
32. e a 1 The two cells to the right columns B and C must be the number of rows and the number of columns Note these must be integer numbers Do not try to append a code to indicate the presence of row or column labels as one does for an NTS file The cell in column D contains the code indicating whether or not there are any missing values Enter a zero or leave it blank if there are no missing values Otherwise enter the identifying numerical code in the cell in column E 24 Preparation of input data files The next row contains column labels beginning Ed Microsoft Excel test34c xls e Al File Edit View Insert Format Tools Data Window Help are left blank they will be A _ replaced with column O amp MW SQ E A lg o gt numbers Column A A3 Z contains the row labels If any cells are blank then will There are 3 rows and 4 columns be replaced by row 0 numbers Thus row and column labels are in their 1 3 natural position not as 2 3 records in front of the 3 3 matrix as in as in the L option for NTS files The Ready row and column labes should not contain any Figure 4 1 Example of a sample data file in Excel N ote that the blanks The matrix itself first two lines are actually text in cells Al and A2 begins in column B See Figure 4 1 for a simple example where the matrix starts in cell B5 This is a sample data matrix in Excel If empty cells are found within the matrix they ar
33. e assumed to also correspond to missing values Information in the spreadsheet in rows beyond the matrix is ignored and can be used to store other information Only one matrix can be read from each Excel file and the matrix should be in the first spreadsheet 1 6 Nexus files This format is supported by many programs concerned with estimating phylogenetic trees Within NTSYSpc the NJOIN module can save tree files in this format Trees in this format can be read by the COPH CONSEN and OUTPUT modules An example is given below The translate section is required It gives the labels for the OTUs There can be one or more tree commands in a file Each describes a tree using nested parentheses The length of each branch on the tree must be provided following the character The file is treated a single stream of characters with line breaks provided wherever convenient nexus begin trees 11 mosq extracted from Harbach amp Kitching 1998 translate 1 Anoph1 2 Toxol2 3 Wyeol3 4 Uran17 5 Culi21 6 Orth28 Preparation of input data files 25 7 Mans29 8 Psor32 9 Aede44 10 Culel01 11 Deinl26 tree 1 16 4 2 6 1 5 1 2 1 3 3 9 1 821 7 6 2 4 22 1021 11 23 21 3230 21 2 2 2 78 end The nexus file format is described in Maddison et al 1997 The method used for describing trees is called the Newick Standard and was adopted June 26 1986 by an informal committee meeting during the Society for the
34. e effects of a third matrix have been held constant While less efficient than a specialized program one can use the MXCOMP module to perform spatial autocorrelation analyses The geographical distance matrix is replaced with a series of matrices corresponding to different geographical distance classes In each matrix an entry is 1 if objects i and j are within the desired distance class and is 0 otherwise To make a distance correlogram one simply plots the resulting matrix correlations as a function of geographical distance The Mantel test can be used to determine which coefficients are statistically different from zero Bibliography 36 Bibliography Burnaby T P 1966 Growth invariant discriminant functions and generalized distances Biometrics 22 96 110 Darroch J N and J E Mosimann 1985 Canonical and principal components of shape Biometrika 72 241 252 Everitt B S and Dunn G 1992 Applied multivariate data analysis Oxford Univ Press New York 304 pp Gabriel K R 1968 The biplot graphical display of matrices with application to principal component analysis Biometrika 58 453 467 Gabriel K R 1971 The biplot graphical display of matrices with applicatin to principal componenet analysis Biometrika 58 453 467 Gabriel K 1981 Biplot display of multivariate matrices for inspection of data and diagnosis P 147 173 in Barnett V ed Interpreting Multivariate Data John Wiley and Sons New Y
35. e missing values 999 is a popular choice Row and column labels Labels must be furnished if a B E or L is placed after the numbers of rows or and L after the number of columns in the previous line Row labels can be placed in one of three locations as the first element at the beginning of each row B as the last element at the end of each row E or as a separate list of row labels in front of the matrix L The column labels if present always consist of a list of labels with the first label beginning on a new line Each label consists of strings of characters up to 16 letters or digits but no blanks They are separated by one or more blanks or by a comma e the are entered free format Examples are given below Matrix data lines The elements of the matrix are entered with rows in the input matrix corresponding to one or more lines in the input file i e matrices are always entered rowwise Symmetric matrices are entered as rows beginning with column 1 and ending with the diagonal elements e the lower half matrix with diagonals is entered rowwise If all the elements for a row do not fit on a single line then continue typing on as many new lines as needed It is important that the first element of a new row starts on a new line even if the previous line is mostly empty The elements themselves are free format Values must be separated by one or more blanks or a comma Missing values are indicated by the numerical code
36. ed out by using the SIMINT DCENTER and EIGEN modules Users experienced with earlier versions of NTSYSpc may wish to skip to Section 1 4 to see a summary of the new features CANPLS Performs canonical correlation and two block partial least squares analyses Used to study pattern of correlations between two sets of variables CONSENSUS Computes a consensus tree for two of two or more trees Such as multiple tied trees from SAHN or between two different methods Several consensus indices are also computed to measure the degree of agreement between trees COPH Produces a cophenetic value matrix matrix of ultrametric values from a tree matrix produced e g by the SAHN program Can also compute a matrix of path length distances from the results of the NJOIN program These matrices can be used by the MXCOMP program to measure the goodness of fit to the similarity or dissimilarity matrix on which they were based A phylogenetic covariance matrix can be computed to use in the MULREG module for comparative studies CORRESP Correspondence analysis This is a useful way to investigate the structure of 2 way contingency table CPCA Common principal components analysis Attempts to fit a single set of eigenvectors to aseries of variance covariance matrices CVA Performs a canonical vectors analysis a generalization of discriminant function analysis It can also be interpreted as a single classification multivariate analysis of variance MANOVA
37. ees Mol Biol Evol 4 406 425 Smouse P E J C Long and R R Sokal 1986 Multiple regression and correlation extensions of the M antel test of matrix correspondence Systematic Zoology 35 627 632 Sneath P H A and R R Sokal 1973 Numerical Taxonomy Freeman San Francisco 573 pp Sokal R R 1979 Testing statistical significance of geographic variation patterns Systematic Zool 28 227 231 Sokal R R and P H A Sneath 1963 Principles of Numerical Taxonomy Freeman San Francisco 359 pp Weir B S 1989 Building trees with DNA sequences Biometric Bulletin 6 4 21 23 38 Index INDEX association coefficients 5 axis aspect ratio 27 Batch mode 13 bimodel 30 biplot 30 Burnaby s method 33 canonical correlation 3 canonical vectors analysis 4 Cladistics 1 Cluster analysis 29 Common principal components analysis 3 Configuration window 16 consensus tree 3 cophenetic value matrix 3 Correspondence analysis 3 elliptic Fourier analysis 4 Excel 23 File formats 19 File overwrite code 17 Fourier analysis 4 homogeneity of covariance matrices 5 Installation 6 isometric vector 34 line limit 20 Mantel test 4 35 matrix comments 26 minimum length spanning tree 4 missing data code 20 26 multidimensional scaling 33 multidimensional scaling analysis 4 neighbor joining method 5 NEXUS format 22 Ordination analysis 30 Output Listing Window 17 PC
38. es simple bivariate regression multiple regression multivariate regression and generalized least squares regression to take into account non independence of observations MXCOMP Compares two symmetric matrices by computing their matrix correlation and then plotting a scatter diagram The statistics for a Mantel test are also computed It can be used to compute the goodness of fit of a cluster analysis to a dataset by comparing a cophenetic value matrix with a dissimilarity matrix It can also compare two matrices with the effects of a third matrix held constant the Smouse Long Sokal 3 way Mantel test MXPLOT Plots 2 way scatter diagrams of rows or columns of a matrix NJOIN Implements Saitou and Nei s 1987 neighbor joining method and Gascuel s 1997 unweighted neighbor joining method to produce estimated phylogenetic trees OUTPUT Formats matrices into pages for printing The files can also be read by most word processors This formatted output is also useful for checking to make sure that an input file has been prepared in the correct format for N TSY Spc PLOT Plot one or more columns of a matrix against a selected column Points can be connected by lines POOLVCV Computes a pooled within groups variance covariance matrix from two or more data matrices Can also perform a test for homogeneity Introduction 5 PROCPLOT Plots the results of the PROCRUSTES module PROCRUSTES Least squares Procrustes superimposition of the coo
39. for a canonical variates analysis or for the computation of size free generalized distances See the CVA module 7 7 Analysis of shape using landmark coordinates In recent years there has been many new developments in the field of geometric morphometrics The PROCRUSTES module has been included to provide these methods for studies using 2 or 3dimensional landmark coordinates The PROCRUSTES module will optimally superimpose specimens and then output the average consensus configuration as well as a transformed set of data in which each specimen has been optimally aligned to the consensus configuration and thus has the effects of variation in location orientation and size removed This matrix of aligned coordinates can then used as a matrix of shape variables for principal components analysis cluster analysis canonical variates analysis etc One has to be careful with some analyses because a covariance matrix based on these aligned data will be singular there will be 4 zero eigenvalues for 2D data and 7 for 3D data The CVA program in NTSYSpc can handle this if one changes the value for the Cutoff for roots parameter from zero to asmall number Such as 0 000000001 The TPSWTS module can be used to eliminate the singularity of the aligned data It transforms the aligned coordinates to a matrix of partial warp scores When the alpha parameter is set equal to zero the usual choice this operation can be viewed as a rotation followe
40. h an editor such as Windows notepad or wordpad although the latter has the annoying habit of always placing the extension txt at the end of a file name The following is a simple example ee ee ee EAS eee matrix stand o data r sdata lt Select batch file compute distances among the OTUs a simint o sdata r dist arameterts now perform a UPGMA cluster SS Sse analysis sahn o dist r tree Lines that begin with a quote characters Figure 2 3 Batch mode window Click the either single or double are treated as gad button to select a batch file and then comments Blank lines are ignored Each click the Run button command line begins with an asterisk followed by the name of the desired program It is followed by parameter value pairs that may take one or more lines lines that do not start with either an asterisk or a quote character are considered continuation lines Each parameter is a code for some program parameter Value gives the value of the parameter There must be an sign and no blanks between the parameter and its value Each such pair must be separated by at least one blank space The parameter is usually a one to three letter code they are given in the help topic for each module They can be typed in either upper or lower case The values can be file names numerical constants or option codes The values are identical to what would be specified in an entry form in interactive mode The defaults are also
41. imply methods for multivariate data analysis There are programs by others that are specialized for phylogenetic methods Some of the better known ones are PAUP and PHYLIP2 However Saitou and Nei s 1987 neighbor joining l Written by David Swofford currently distributed by the Illinois Natural History Survey 2 Introduction method of phylogenetic tree estimation is included in NTSYSpc NTSYSpc also contains specialized methods used in geometric morphometrics to study variation in shapes of objects The principal journal devoted to the general theory behind many of these techniques is the ournal of Classification It is published for the Classification Society of North America by Springer Verlag Theoretical papers are also published in many statistical journals Applications of these techniques are published in many scientific journals in the areas of application For example Systematic Biology formerly Systematic Zoology has published many theoretical and applied papers with special emphasis to applications in biological taxonomy Most users of these techniques begin with a data matrix that contains information about the properties features characters landmark or outline coordinates etc of a number objects individuals specimens quadrats OTUs etc NTSY Spc can then be used to compute various measures of similarity or dissimilarity between all pairs of objects and then summarize this information either in terms of nested sets
42. l axes and projections in a single step TPSWTS Computes projections of the 2D or 3D coordinates of objects onto the principal warps of a thin plate spline bending energy matrix This is done to enable a statistical analysis of the non affine and uniform components of shape variation 6 Introduction TRANSF Performs various linear and non linear transformations of the rows or columns of a matrix Can also be used to delete rows or columns read Lotus 1 2 3 files and alter the form of storage of some matrices matrix TREE Displays phenetic and phylogenetic trees e g from the SAHN or NJOIN modules Options are provided for scaling and scrolling through a tree interactively FRANTSYSpc 2 1 File Options Help Output amp transf Output Dcenter Fourier Standardization mo micinhts Version 2 1 Graphics Fiaure 1 1 NTSYSpc main window 1 3 Howto get started using NTSYSpc Installation of NTSYSpc is quite easy since a standard type of installation program is used Simply insert the disk and run its setup program The only decision you will have to make during installation is to select the name of the directory to be used A program group will be created on your startup menu There will be icons for NTSYSpc NTedit help files and the readme txt file NTSYSpc can be un installed e g in case you need to move NTSY Spc to another computer by using the standard Add Remove icon fro
43. ll show a summary of the input parameters you specified information about the input files and the results of the computations If you provided names for output files then these results are stored on disk and are available as input to other modules For some programs short cut graphics speed buttons will appear on the small toolbar at the bottom left of the parameter entry window Pass the mouse over the button to display the hint box describing the type of plot produced by each button For example Figure 2 2 shows the buttons available after running the EIGEN program Figure 2 1 D ialog window for the STAND module In case of an error such as entering the name of a non existent file for an input data matrix the program will beep and display a message in an Error Window Click the OK button to close this window so that you may L correct the problem and try again To close the parameter entry window for _ i Figure 2 2 G raphic speed buttons for the a module you may ether click the Close button or simply select another module from the N TSY Spc main window 2 2 EIGEN module The first button calls M XPLOT to produce a 2D plot of the eigenvectors and the second calls MOD3D for a 3D plot Batch mode Modes of operation 13 In batch mode NTSYSpc will attempt to drectly execute a sequence of modules without displaying the parameter entry windows for each Commands are entered in an ASCII file which can be prepared wit
44. m the Windows Control Panel When you run NTSYSpc the first time you will be asked to provide your name institution optional and a registration number Once the program is installed click on the NTSYSpc FRINTSYSpc Output File Options Help aloja Output amp transf Output Dcenter Fourier z Decimal places Standardization Page width na wainhka Clustering Row order Graphics Column order Ordination Similarity Figure 1 2 Entry form for the OUTPUT module Introduction 7 icon in the start menu to see what NTSYSpc looks like see MEE Figure 1 1 The NTSYSpc File Edit Options Help main window is divided into A sample data matrix to test NTSYS pe There are 5 characters rows and 10 OTUs The columns are labelled No missing valu type 1 size 5 by 10 nec none several regions At the left is a bar divided into folders with each containing buttons for several computational modules Click on a button such as Output to load the corresponding program module A form will be displayed in which you can specify the input file and other options for the selected module see Figure 1 2 A test data set TEST NTS iS supplied so you can try a few operations right away Click on the cell opposite Input file to bring up a file open dialog box Note that by default the dialog box assumes that data file names end with the file extension Figure
45. mmands in the test ntb batch file The Help menu provides the standard contents topic search and about items 4 Preparation of input data files NTSYSpc NTS files are ordinary ASCII files txt files not binary files A file for a data matrix may be prepared with an editor or any word processor that has a txt non document mode If you try to use a document file there may be invisible binary codes that NTSYSpc will not Preparation of input data files 19 know how to interpret Free format is used for the entries in the data matrices This means that at least one blank space or a comma is required between numbers The NTedit program included with NTSYSpc can be used to prepare data files and ensure that they are in the proper format In addition NTSYSpc can also read data matrices from Excel spreadsheets XLS files and trees from N exus format files 4 1 NTS file formats A matrix can contain 4 kinds of records The comment and label lines are optional Comments These optional lines are used to include notes with the data The first character in each line must be some type of quote character or The information on these lines will be copied onto comment lines in any matrices based on this input matrix In addition each subsequent program will add an additional comment line so that the sequence of steps leading to a given matrix can be determined M atrix parameter line This line contains 4 integer numbers The second and thir
46. nalyses When an original data matrix is available it is possible and usually desirable to make plots of both the variables and the points with respect to the same axes This is called a biplot This allows one to not only see the patterns trends etc among the points and of relationships usually correlation among the variables but also the relationships between the points and the variables at least to the extent that they can be summarized in a few dimensions Unfortunately there seems to be no strong consensus about how to scale the two ordinations relative to one another Gabriel 1968 1971 1981 defines a biplot of an nxp matrix Y as a simultaneous bivariate plot of the n points in each column of a matrix A and of the p variables in each column of matrix B where Y ABt it would be a bimodel if a 3 dimensional plot were made Matrices A and B can be expressed in terms of a singular value decomposition of matrix Y Y UAVt One could set A UA and B called aJK biplot by Gabriel and Odoroff 1986 In terms of principal components analysis this corresponds to computing normalized eigenvectors from the correlation or variance covariance matrix for the variables and then using the PROJ program to project the points onto these vectors The rows of A are plotted as points and the rows of B are plotted as vectors Note that the matrix A of singular values is the square root of the eigenvalue matrix obtained in a principal components anal
47. nt One will usually not want it checked when plotting raw data Center controls whether the plot is centered in the window Frame Optionally a line can be drawn around the outside of the plot to frame it Options are available to control its size and color Background color The background color in the different regions of a plot can be set individually Margin size Top bottom left and right margin sizes can be set Legend This group is not used at present but Pa M atrix plot options Ea will be used to control how groups of points or Titles Variables Points Secondary points Options lines are identified Points 6 2 Other ID code fi symbol Labels None Font options These depend upon the plot For MXPLOT II i and MOD3D there are Show vectors Lines pick lists for selecting the variables to be plotted select the Variables tab There are also choices of whether the aata poimi should be Figure 6 1 Example of graphic options window from the identified by sequential MXPLOT module numbers or labeled using the labels in the input data There are also options to control the various attributes of the points and lines making up a plot There are special dialog boxes to allow you to select colors plotting symbols fonts etc 6 3 Plot menu The File menu contains the following items Printer setup which allows you to select a printer paper size and orientation
48. of a data matrix it is strongly suggested that you use the NTedit program and that you first try the OUTPUT module to display your input data matrix It can be printed out for convenience in proofing If there are major problems in the file format you may need to load the matrix into N Tedit in text mode 4 2 Examples of NTS files An example of a data matrix file with 3 comment lines and labels for the columns but not the rows is given below This set of test data is furnished on the distribution disks for NTSYSpc and is used for many of the examples given in this manual A sample data matrix to test NTSYSpc There are 5 characters rows and 10 OTUs columns The columns are labeled No missing values Y 5 TOLO A BoC DE E 6 4 LE J 8 7 9 13 6 2 9 7 11 6 5 6 S 3 7 10 5 7 5 7 LL P3 oda 9 S ds SET a 22 3 LO Teo Za 8 E EE Ie 26o 24 T8 11 6 12 10 10 19 gt Uo we A An example of a data matrix with column labels and with row labels placed at the beginning of each row 1 4B 3L 0 cl c2 3 EL Gpo By v4 EL As Al PSr S37 4 2 r4 2 Tiy 2 An example of a symmetrical correlation matrix file note that elements past the diagonal of a symmetric matrix must not be entered Labels can only be placed in a list in front of the data i e only the 1 code is valid A sample correlation matrix with labels 3 DL 5 Y ABCEFE 1 Osa Gad Ud AL Ob cU o 04 1 Oa T
49. ork Gabriel K and Odoroff C L 1986 Illustrations of model diagnosis by means of three dimensional biplots Pp 257 274 in Wegman E J and DePriest D J eds Statistical image processing and graphics Marcel Dekker New York Gascuel O 1997 Concerning the NJ algorithm and its unweighted version UNJ Pp 149 170 in B Mirkin F R McM orris F S Roberts and A Rzhetsky eds M athematical hierarchies and biology DIMACS series in discrete mathematics and theoretical computer science Vol American M athematical Society Providence R I Gnanadesikan R 1977 M ethods for statistical data analysis of multivariate observations Wiley New York 311 pp Hartigan J A 1975 Clustering algorithms Wiley New York 351 pp Jackson J E 1991 A user s guide to principal components Wiley New York 569 pp Maddison D R D L Swofford and W P Maddison 1997 NEXUS an extendible file format for systematic information Systematic Biology 46 590 621 Mantel N A 1967 The detection of disease clustering and a generalized regression approach Cancer Res 27 209 220 Reyment R A 1991 Multidimensional paleobiology Pergamon Press New York 377 pp Bibliography 37 Romesburg H C 1984 Cluster analysis for researchers Lifetime Learning Publications Belmont California 334 pp Saitou N and M Nei 1987 The neighbor joining method anew method for reconstructing phylogenetic tr
50. provided on the matrix parameter line They cannot be simple left blank they can however be indicated by a if a missing value code is provided on the matrix parameter line The lines can be very long the theoretical limit is 2 GB but it will be easier to work with them with most editors if you use shorter lines 80 characters or fewer Blank lines are ignored More than one matrix can be stored in a single file The records for a second matrix starting with the optional comment lines simply follow after those for the first Most program modules in NTSYSpc will perform the selected set of operations on each of the matrices in an input file The results for the second and subsequent matrices are simply appended to the files produced by processing the first matrix For some programs it is necessary to put more than one matrix in a single file in order to perform a certain computation It is required by programs such as CPCA CVA and POOLVCV It is also necessary in order to compute the majority rule consensus tree for more than two trees Note if you prepare the original data matrix so that the rows correspond to the characters variables and the columns correspond to the objects being classified OTUs data points etc then you will find that many of the default row column direction options will be correct Preparation of input data files 21 Because there is always the chance that there will be an error in the preparation
51. rdinates of points in two or more objects Computes the average configuration of points and aligns all objects to the average PROJ Projects a set of objects onto one or more vectors or onto a space orthogonal to a set of vectors In principal components analysis one will project standardized data onto the eigenvectors of the correlation matrix in order to see the best in a least squares sense low dimensional view of a data set The orthogonal projection option can be used to implement Burnaby s 1966 method for size adjustment SAHN Performs the sequential agglomerative hierarchical and nested clustering methods as defined by Sneath and Sokal 1973 These include such commonly used clustering methods as UPGMA and singlelink The program can find alternative trees when there are ties in the input matrix SIMGEND Computes matrices of genetic distance coefficients from gene frequency and DNA sequence data SIMINT Computes various similarity or dissimilarity indices for interval measure continuous data e g correlation distance etc coefficients SIMQUAL Computes various association coefficients for qualitative data data with unordered states e g simple matching Jaccard phi etc coefficients STAND Performs a linear transformation of a data matrix so as to eliminate the effects of different scales of measurement SVD Computes a singular value decomposition of a rectangular data matrix It allows you to compute principa
52. s soeed Large datasets more than 500 OTUs can now be processed Results can be saved in nexus format or as an extended NTS tree format that allows for unequal heights of the OTUs in the tree An option has been added for unweighted neighbor joining trees e OUTPUT Supports Excel files and the new tree formats e POOLVC Allows missing values in data when computing the mean and covariance matrices e TPSWTS For convenience it now includes the Procrustes superimposition step It also now provides an estimate of the uniform component for 3D data e TREE Can now plot trees with unequal heights of the OTUs N Tedit e Can now directly read rectangular matrices from Excel files the DDE and OLE methods are no longer used e A new text mode display allows NTedit to be used to edit any ASCII file including NTSYSpc batch command files Files sizes up to 16MB with line lengths up to 32K can be edited Standard cut copy paste and other text editing commands are supported e Thecurrent matrix or file being edited can now be printed from within the editor 1 5 What was new in version 2 0 The old DOS program was converted to Windows There were of course major changes in the user interface was new but the way in which the program was used was preserved Some of the major changes are listed below 10 Introduction e The entry forms have been smplified and the listing results are saved to a Listing notebook window where you can
53. save delete or edit the results You can also cut and paste them into other software e Input file formats there is no longer a length restriction to the input lines they were limited to just 255 characters Long names permit more descriptive identifiers often very important in more complicated analyses involving many files e A new NTedit program replaces the previous NTEDITOR program The new program recognizes the various file formats and displays files in a soreadsheet like grid e Graphics Can now call up the appropriate graphics modules directly from many of the computational modules The entry forms for the graphics programs have also been simplified since the graphic options are now available from option dialog boxes brought up by clicking on a plot with the right mouse button You can now control the colors fonts line widths etc of most aspects of the plots e Batch files have been changed to allow both longer lines and the ability to have continuation lines for a command The program now requires that the start of each command begin with an e The information in the previous User M anual has been divided into this User Guide and the very extensive help file The help file contains the detailed technical descriptions of each computational module Sections can be printed from the help file if you want the information in a printed form This User Guide contains only general information about how to use the program
54. ser tect ll ls da 17 4 Preparation of input data Ti iii AAA AAA 18 Al NES Ona raro 19 4 2 EXAmples OFNT S ALS serra dt 21 4 3 Interfaceto other A A O O 23 44 A Y 23 LO Neus TUS tarada 24 Si IN Ted iia ias 25 6 Graphics options amp Menu iS 27 Gel General plot OD EIONS ut ao as 27 A OPONGA tae net OO 28 Oar A e RC A 28 iv 7 Typical apphica onsS iii 29 TL CIU a io 29 7 2 Ordination analyses and biplots ad a 30 7 3 Principal components analysis sss sssssssssssissssiesresiesresirsrenitsreninstenintninatnninatnnntnnanannnnnatannn a as 31 7 4 Principal coordinates analysis PCOORDA anan 32 7 5 Nonmeric multidimensional SCAlING aa mie oR 33 7 6 Burnaby s method for size adjustment ee eessessssseesesesssssesssesssssssssssessssssssssssssssssssssasssesssesasasaees 33 Tab COMPArFISOM OMA CS Aa 34 o o AAA O A cvansted duadauistdanstas cutuads chansiestsadausceansidhcubuadSachansieiteadassicaaievans 36 Preface NTSYSpc was developed originally for use by students in a seminar course Taxonomia n merica em microcomputadores held in September 1985 at the Estac o Agron mica Nacional Oeiras Portugal Many of the programs were written on a portable computer as worked each evening on the balcony of a hotel in Estoril trying to develop the programs needed by the students for the next day s lab projects The beautiful surroundings and enthusiastic students seemed to have helped Most of the design and many of the actu
55. sts Many of the programs require one to select one of several choices for a field such as a method of standardization or a clustering method They are indicated by the small upside down triangle at the right end of the field there are two examples in Figure 2 1 Click on the field to display a list of the available choices Move the cursor or the mouse to high light the desired option and then click with the left mouse button Sometimes there is a blank entry signifying that this option is to be ignored The selected code will then be entered into the form Modes of operation Checkboxes Press the space bar or click with the mouse to alternate between checked for yes and unchecked for no states These are used FRANTSYSpc Stand File Options Help Compute Output amp transf Parameters Output Input file Stand by rows Output file Subtract option to indicate for example whether the program should operate on the Dcenter Fourier Standardization ES rows of the input Clustering matrix or whether Graphics Divide option iti Ordination additional information Constant Similarity should be included in the output listing Once the fields have been filled in correctly click the Compute button to run the program since the Compute button has the focus initially you can also just press the A key The Listing window will be opened to a new section and it wi
56. tandardized by variables rows a matrix of distances between the objects is computed the distance matrix is double centered the double centered matrix is then factored and a plot is made showing the objects in a 3 dimensional space standardize data if in different units stand o data nts r sdata nts Compute distances among objects simint o sdata nts r dist nts Double center the distance matrix dcenter o dist nts r dcent nts eigenvectors correspond to projections of objects eigen o dcent nts n 3 r proj nts output o proj nts Display gt Note that direction is col mod3d o proj nts d col PCOORDA can also be viewed as a distinct ordination method since it can also be applied to various types of similarity and dissimilarity matrices or even to experimentally determined proximity matrices where there is no original data matrix The computational steps would then be as follows Double center the matrix dcenter o dist nts r dcent nts Extract eigenvectors eigen o dcent nts n 3 r proj nts Output eigenvectors projections output o proj nts Display Note that direction is col mod3d o proj nts d col Of course an arbitrary dissimilarity matrix may not be very compatible with a Euclidean metric In such cases many of the eigenvalues may be negative In performing such an analysis one hopes that such negative eigenvalues are small and can
57. ted module will then display a parameter entry form at the right side of the main program window such as that for the STAND program shown in Figure 2 1 To run a program you must enter the required information in the Entry Window you need to at least specify the name of an input file To fill in the entry form select the desired locations in the form using a mouse and enter the appropriate information the method of entering the information depends on the type of field The default choices if there are any will have already been entered into the form Input or output matrix names names are any valid Windows file names including long names File names can optionally be preceded by a drive specification e g a test nts or a path specification eg c data test nts If the name contains either a colon or a backslash character then the name is used as is Otherwise the name will be appended to the current data directory The program will remember the drive and directory from previous runs so that you do not have to enter it every time if all the files are in the same directory It is easiest to simply double click on the cell to bring up a file open dialog box where you can select the file visually Numerical constants Often numerical constants make sense only within certain limits NTSYSpc will not permit you to enter an out of range value Decimal points should not be typed when integer numbers are expected by the program Pick li
58. ters can be specified An rr Cancel example is shown below Y Ran stand o l nts r sdata nts simint o sdata nts r dist nts sahn o dist nts cm 2 r tree nts Figure 2 4 Batch mode window with the test2 ntb file loaded and two replaceable parameters provided If the first replaceable parameter is mosq and the second is single as in Figure 2 4 then this batch file will be interpreted as if it were as follows stand o mosq nts r sdata nts simint o sdata nts r dist nts sahn o dist nts cm single r tree nts 2 3 Both interactive and command modes During execution the programs echo the input parameters and the comment information furnished with the input matrices to the Listing window In addition a progress bar and a status panel given an indication of how computations are progressing within each module Press the Cancel button if you need to stop the execution of programs that take a long time to complete The program should stop once it completes its next iteration or cycle of computation it does not check constantly for a keypress since that would slow the program down Alternatively you can hold down the Gp keys to bring up the Windows Close Program dialog box Select NTSYSpc and then click on the End task button The program should then stop abruptly but any information that was in the listing window will be lost Menus amp related windows 15 3 Menus amp related windows 3 1 M
59. uster the distance matrix using the singlelink clustering method there are other choices such as UPGMA compute a cophenetic value ultrametric matrix compute the cophenetic correlation as a measure of goodness of fit and then plot the results in the form of aphenogram The distance matrix is also displayed Standardize the variables stand o data nts r sdata nts Compute a distance matrix simint o sdata nts r dist nts c dist Do a single link cluster analysis of the distance matrix sahn o dist nts r tree nts cm single Display phenogram tree o tree nts Compute cophenetic values coph o tree nts r coph nts Compute the cophenetic correlation mxcomp x coph nts y dist nts When working interactively one can view the tree from within the SAHN module by clicking on the plot speed button Note that the Mantel test results displayed by the MXCOMP module should be ignored since the two matrices being compared are not independently derived 30 Typical applications 7 2 Ordination analyses and biplots In ordination analyses the goal is to position points along coordinate axes in a low dimensional space rather than to form sets of points as in cluster analysis There are many different methods depending upon the criteria used to define what is meant by the best low dimensional representation of the relationships among the points Several programs in NTSY Spc can be used to perform these a
60. vect nts val val nts Output principal component axes output o vect nts Project objects onto PCA axes proj o sdata nts d col f vect nts r proj nts Output projections output o proj nts Display 3D plot of projection of objects mod3d o proj nts Display 3D plot of variables defining the PCA axes mod3d o vect nts d col p n p n The last two plots together comprise a three dimensional biplot a bimodel for these data An alternative procedure would be to not standardize the data and to use a variance covariance matrix rather than a correlation matrix in the above steps In such a case the largest weights are given to those variables with the largest variances This implies that the variables were measured in comparable units of measurement This might be appropriate for example for a matrix of log transformed variables in a conventional non geometric 32 Typical applications morphometric study perhaps with means subtracted following Darroch and Mosimann 1985 7 4 Principal coordinates analysis PCOORDA PCOORDA can be thought of as a computational alternative to PCA The steps shown below will give results identical to PCA Oneimportant consideration is that when there are many fewer points than variables computation time may be much less than for the usual PCA The batch file given below performs the following operations the data matrix is s
61. ysis This type of decomposition of a data matrix is called preference scaling or repertory grid analysisin psychology and sociology One can equally well set A U and B VA GH biplot of Gabriel and Odoroff 1986 One could also multiply both U and V by A05 an SQ biplot This latter choice would seem most appropriate in correspondence analysis where both the rows and columns can be interpreted as variables The matrix A could also be apportioned in any other way to U and V as long as their product yields Y A problem with aJK biplot is that the vectors for the variables are of unit length and thus are not in the same scale as the vectors for the points Since the vectors for the variables are dimensionless a plot of them does not indicate how well the variance of each variable is explained by the number of dimensions used For this reason one can deviate from a true biplot and multiply both U and V by A As a consequence one cannot visually estimate an element say y of the original data matrix as simply the inner product of row i of A and row j of B one must compute the projection of row i of A onto row j of B One compares the relationships between the ordinations of the points and of the variables by examining the angles between them Jackson 1991 indicates that this alternative is popular among French practitioners Typical applications 31 The MXPLOT module can be used to make a biplot Enter the name of the matrix giving the coordin

NTSYSpc Numerical Taxonomy and Multivariate

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