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1. 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 Help menu leads to the standard Contents Topic search and A bout items Typical applications 23 T 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 information about each module Note 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 in file data compute distance coefficients among the columns of the standardized data matrix there are several other choices of coefficients cluster 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 out2. up to 16 letters or digits but no blanks They are separated by one or more blanks or by a comma i 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 i 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 dement 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 Preparation of input data files 17 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 th
3. 1992 give a good concise introduction to both cluster analysis and multidimensional scaling analysis They furnish examples from biology e 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 guideto principal components e Massart et al 1978 gives 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 e Romesburg 1984 gives detailed descriptions of many clustering methods 2 Written by Joe Felsenstein University of Washington Introduction 3 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 W
4. Only one matrix can be read from each spreadsheet 5 NTedit The Ntedit program induded with NTSYSpc is a data editor designed for use with NTSY Spc data files It recognizes actually requires valid NTSYSpc 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 NTedit ensures that the files are formatted correctly The program can be started in three ways 1 Click on the program icon to start the program and then use the File Open menu to load an existing data file or File New to begin a new file 2 Load this program from the File Edit data file menu of N TSY Spc 3 You can use a DOS command window and type ntedit and the name of a file and then press the key to start the program Once the program is started you can enter or correct data in any of the cells of the spreadsheet You can insert or delete rows and columns within the table by clicking on the appropriate menu choices 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 columns given in the first 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 name
5. See Chaper 7 for a number of examples N ext you should read Chapter 2 on M odes of operation to learn how to useNTSYSpc 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 Chapter 4 on Preparation of input data files is of course essential reading as it describes the format 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 Introduction are added to NTSYSpc Your comments corrections and IE BZTZALZU File Edit Options Help suggestions about the pro gram are welcomed A sample data matrix to test NTSYS pe There are 5 characters rows and 10 OTUs The columns are labelled No missing valu 1 4 What s new type 1 size 5 by 10 nc none in version 2 0 The entire user interface is new However much of the previous ways of using the program were preserved One still selects a module fills in a form and runs the module Some of the major differences are listed below e The entry forms have been simplified and all of the listi
6. Wiley and Sons New York 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 N ew York Gnanadesikan R 1977 M ethods for statistical data analysis of multivariate observations Wiley New York 311 pp Hartigan J A 1975 Clustering algorithms Wiley N ew York 351 pp Jackson J E 1991 A user s guideto principal components Wiley New York 569 pp 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 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 a new method for reconstructing phylogenetic trees Mol Biol Evol 4 406 425 Sneath P H A and R R Sokal 1973 Numerical Taxonomy Freeman San Francisco 573 pp 30 Bibliography 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 INDEX a
7. 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 esti mates 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 methods furnished in NTSYSpc are largely associated with the field of phenetics However they are best interpreted as simply methods for multivariate data analysis There are programs by others that are specialized for phylogenetic methods Some of the more well known ones are PAUP and PHYLIP2 However Saitou and Nei s 1987 neighbor joining method of phylogenetic tree esti mation is included in NTSY Spc 1 Written by David Swofford currently distributed by the Illinois Natural History Survey 2 Introduction The principal journal devoted to the general theory behind many of these techniques is the Journal 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 p
8. a message in an Error Window Click the OK EIGEN module The first button calls button to close this window so that you may MXPLOT to produce a 2D plot of the correct the problem and try again eigenvectors and the second calls M OD 3D fora 3D plot Figure 2 2 G raphic speed buttons for the To close the parameter entry window for a module you may either click the Close button or simply select another module from the NTSYSpc main window 2 2 Batch mode In batch mode NTSYSpc will attempt to directly execute a sequence of modules without displaying the parameter entry windows for each Commands are entered in an ASCII file which can be prepared with an editor such as Windows notepad or wordpad Figure 2 3 Batch mode window Click the although the latter has the annoying habit of Load button to select a batch file and then always placing the extension txt at the end of click the Run button a file name The following is a simple example standardize the rows of the data matrix stand o data r sdata compute distances among the OTUs Modes of operation 11 simint o sdata r dist now perform a UPGMA cluster analysis sahn o dist r tree Lines that begin with a quote characters either single or double are treated as comments Blank lines are ignored Each 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 l
9. do IPS Gb4 An example of a data matrix with column labels and with row labels placed at the beginning of each row 1 4B 3L O el 2 03 rl duy 3 3 I2 Oy 2 4 18 Preparation of input data files r3 3 4 2 r4 2 1 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 L codeis valid A sample correlation matrix with labels 3 9L D Q ABCFE 4 1 3 0 4 1 Dus Ort Duo d ODO O O c LH JAU A OOF 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 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 TRANSF 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 NTSYSpc is described at the end of the description of the SAHN program In addition you can describe a tree using
10. 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 7 6 X Burnaby s method for size adjustment Thefollowing batch file 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 resultant adjusted data matrix ppro j 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
11. plotting the results of analyses such as principal components analysis where the relative lengths of the axes is important 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 M argin size Top bottom left and right margin sizes can be set Legend This group is not used at present but will be used to control how groups of points or lines are identified 6 2 Other options These depend upon the plot For MXPLOT and MOD3D there are pick lists for selecting the variables to be plotted There are also choices of whether the data points should be identified by sequential 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 In MOD3D the view options allow oneto rotate tilt and change the distance of the viewing position 6 3 Plot menu The File menu contains the following items Printer setup which allows you to select a printer paper size and orientation Print preview which changes the plot to a preview of how it will look when printed
12. principal component points in the direction in which 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 for a canonical variates analysis or for the computation of size free generalized distances see the CVA module 7 7 Comparison of 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 28 Typical applications 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 independentl y 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 mxcomp x mdist nts y gdist nt
13. 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 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 MXPLOT Plots 2 way scatter diagrams of rows or columns of a matrix NJOIN Computes Saitou and Nei s 1987 neighbor joining method trees as 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 NTSY Spc POOLVCV Computes a pooled within groups variance covariance matrix from two or more data matrices Can also perform a test for homogeneity 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 Th
14. Mean Y 1 0819 s8 0 6887 selected text to the Windows clipboard to Tests for association copy selected text to the dipboard and to paste in 2977 cried Mantel statistic Z text from the clipboard These commands permit Approximate Mantel t test t you to copy results into Prob random Z lt obs Z p other software such as a wordprocessor They also alow you to deee unwanted information before printing or saving to Figure 3 1 Example of the listing window after running the a disk file Keeping such commands in the test ntb batch file notebooks is a convenient Menus amp related windows 15 way to verify which options were used to produce a certain result The purpose of reloading a notebook is to allow the appending of new results so that a record 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 Theindent item controls the size of the left margin when printing TheHelp menu provides the standard contents topic search and about items 4 Preparation of input data files NTSY Spc data 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 inv
15. NTSYSpc Numerical Taxonomy and M ultivariate Analysis System Version 2 0 User Guide F James Rohlf D epartment of Ecology and Evolution State U niversity of N ew Y ork Stony Brook N Y 11794 5245 meee EXETER SOFTWARE 47 Route 25A Suite 2 Setauket New 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 1998 by Applied Biostatistics Inc 3 Heritage Lane Setauket New York 11733 All rights reserved worldwide ISBN 0 925031 28 3 Current printing July 8 1998 Contents Bs MMV CG ON TEE 1 Ms eh ees okapi Cati ON aa a uaa aust sasha A nessa hes US SRM taba ann aE 1 1 2 Program mod les in N T SY SDC ici d rief P EUER D Ade LR A ite 3 1 3 H ow to ge started using NTSYSpoC sssssssssee eene nennen enne nnn 5 1 4 What SQW ID VERSION 2 0 suia Dh n og D i chee ada de a dat OREL Etat 8 2 Modes OF operati Ohio ioco cios cis cud cid eEn uci Fade c Queue Clo aandaa Eee uUo Deu FOREN FOL nadadaan aiaa Ee wd ca 9 2 1 Interactive mode sinn dal o pr dm imb dba a dbi nb os 9 2 2 Batch Oe asse otto etel mutus cc utut rfe cuf x oett erae ae um urbi Pte Ek 11 2 3 Both interactive and command modes irritation eren eren eri eere raster aen ie 13 3 Menus amp related WIDndOWS ooscixckanciru cua aE a
16. SP 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 a series 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 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 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 4 Introduction 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 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
17. 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 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 the 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 1 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
18. ch dialog box will let you select a file containing a sequence of N TSY Spc 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 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 card file with tabs labeled corresponding to sets of programs see Figure 1 1 Modes of operation 9 Click on a tab to select a section This displays buttons corresponding to the modules available from that section Notice that as the mouse passes over a button additional information is displayed in the status area at the bottom of the window To select a module dick on the corresponding button The selected module will then display a parameter entry 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
19. cify the input file and other options for the selected module see Figure 1 2 A test v Compute f Close Help data set TEST NTS is supplied Mo comme ii cose SO you can try a few operations right away Click on the highlighted cell opposite Input Figure 1 2 Entry window for the Stand module 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 NTs If that is not true then click on the file type window at the lower left and select All files Use this dialog to locate the TEST NTS file in c NNTSYS or wherever you installed NTSYSpc and then click on the Open button Then dick 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 Page width Row order Column order Y ou should note that the separate modules do not provide a complete analysis Unlike many programs you do not just run one module 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
20. e 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 default row column direction options in most of the modules will be correct Since there is always the chance that there will be an error in the preparation 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 4 2 Examples of data 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 1 5 10L 0 ABCDEFGHIJ 8 7 S diss Qu T2 9 do WEL 3 5 6 3 3 7 TA Len 7 d Y II L3 E 9 S To Lr X 22 T3 10 18 22 8 7 17 18 26 24 18 Bu 6 cBz GEO GEO a ab
21. e 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 indude such commonly used clustering methods as UPGMA and single link The program can find alternative trees when there areties in the input matrix SIMGEND Computes matrices of genetic distance coefficients from gene frequency and DNA sequence data Introduction 5 SIMINT Computes various similarity or dissimilarity indices for interval measure continuous data eg correlation distance etc coefficients SIMQUAL Computes various association coefficients for qualitative data data with unordered states eg 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 principal 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 components of shape variation 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 Lo
22. easured in comparable units of measurement This might be appropriate for example for a matrix of log transformed variables in a morphometric study perhaps with means subtracted following Darroch and Mosimann 1985 7 4 Principal coordinates analysis PCOORDA PCOORDA can bethought of as a computational alternativeto 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 26 Typical applications The batch file given below performs the following operations the data matrix is standardized 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 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 t
23. eir 1989 gives a short overview for DNA sequence data 1 2 Program modules in NTSYSpc Listed below are short descriptions of the computational modules induded 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 sequence to build many other types of analyses for example Gower s principal coordinates analysis can be carried out by using the SIMINT DCENTER and EIGEN modules Users experienced with earlier versions of NTSY Spc 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 eg by the SAHN program This matrix can be used by the MXCOMP program to measure the goodness of fit of a cluster analysis to the similarity or dissimilarity matrix on which it was based CORRE
24. ence 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 a JK 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 25 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 then have maximum variance in as few dimensions as possible While defined in terms of variances and covariances PCA is usually applied to standardized data since the results are sensitive to the choices of
25. es 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 then 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 ZUAV One could set A 2U A and B V 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 Notethat the matrix A of singular values is the square root of the eigenvalue matrix obtained in a principal components analysis This type of decomposition of a data matrix is called preference scaling or repertory grid analysis in psychology and sociology One can equally well set A U and B2V A GH biplot of Gabriel and Odoroff 1986 One could also multiply both U and V by 495 an SQ biplot This latter choice would seem most appropriate in correspond
26. h lengths but no OTU labels 5 2 4 GCCODTZi 1 3 2 5 1 65 2 323 0 7 001205555420 5 30459 5 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 describe an ultrametric tree In the above example the branch length for OTU Lis 2 1 but the length for OTU 3is 2 5 The program will usethe 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 example the height at which the se 13 2 joins the root is 4 3 and the height at which 445 joins is 13 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 Provision is induded in the NTedit
27. h mode dialog box so that a batch file can be run see Section 2 2 The exit item doses the program the program can also be closed by clicking on the Close speed button on the tool bar Menus amp related windows 13 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 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 Configuration window and file There are a number of aspects of how NTSYSpc operates that can be modified by a user These are done from the Configuration Window select Configuration under the Option menu on the main window This will display a window like those used for the various computational modules The entries here however are system parameters such as file formats directory names and other options The information you enter will be saved in the ntsys ini file in the Windows directory The file also includes coded information ab
28. here 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 a 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 be ignored 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 Typical applications 27 DCENTER O dist nts R dcent nts EIGEN O dcent nts N 2 R init nts non metric MDSCALE using
29. ines 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 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 dick 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 b
30. isible binary codes that NTSYSpc will not 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 4 1 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 third may havea 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 code for the type of matrix 1 rectangular data matrix 2 symmetric dissimilarity matrix 3 symmetric similarity matrix 16 Preparation of input data files diagonal matrix 4 5 treematrix for dissimilarity data 6 tree matrix 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
31. n also be used to view and make changes in existing files A limitation of the program is that existing files must already be in a proper format If you try to load a file that is not formatted properly you will receive an error message and then an alternative editor the default is the Windows notepad program will be called to display the file The Alt Editor item under the Options menu allows you to select another editor Note you must select an editor capable of producing plain ASCII txt files TheNTedit help can be consulted for additional information 6 Graphics options amp menu The various plots produced by NTSYSpc can be enhanced in many ways by taking advantage of the many options available Begin by dicking 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 All plots allow the user to specify a title and a subtitle and the fonts used to display them There is also always a button labeled General that opens another dialog box described in the next section 22 Graphics options amp menu 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
32. n 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 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
33. names File names can optionally be preceded by a drive specification eg a test nts or a path specification eg d 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 dick 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 lists 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 ERAN the field there are two on Parameters Arguments examples in Figure 2 1 Click on the field to nputfile display a list of the Stand by rows x available choices Move the cursor or the mouse to Subtract option YBAR high light the desired Divide option stp option and then click with constant D 0DDOD the left mouse button Compute in Close Help Sometimes
34. 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 awkward 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 consistent with the set relationships given in the tree Note 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 N EXUS styletree not using branch lengths NEXUS style input with OTU labels provided 5 5L 2 0 Preparation of input data files 19 ABCDE 1 3 2 4 5 This implies a tree of the following topology 1 Geese 2 L 4 51 L Example of an input file using branch lengths Example using branc
35. ng results are saved to a Listing notebook window where you can save delete Or Figure 1 3 Listing window after running the Output module even edit the results on the TEST NTS data file You can also conveniently cut and paste them into other software such as word processors e Input file formats have not changed except that there is no longer a length restriction to the input lines They were limited to just 255 characters which seemed quite adequate just a few years ago Long file names are now recognized Upper and lower case letters are preserved as well as blank spaces within file names however batch files do not yet permit blanks within file names Long names permits much more descriptive identifiers often very important in more complicated analyses involving many files A new NTedit program replaces the previous NTEDITOR program The new program recognizes the various file formats and displays files in an appropriate spreadsheet like format Graphics have been greatly improved You can now call up the appropriate graphics modules directly from many of the computational modules so that you can for example immediately view a phenogram after using the SAHN module to perform a cluster analysis The entry forms for the graphics programs have also been simplified 8 Introduction since the graphic options are now available from option dialog boxes brought up by clicking on a plot with the right mouse button Yo
36. out the position and size of various windows used by NTSY Spc Configuration parameters Batch code Description FF File format code LF Listing format code LI Listing indent when printing DD Data directory the directory to use as the current directory for data files OW File overwrite code ask O overwrite and A append ED Editor to be called from the File Edit menu 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 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 also enter the code as F8 4 asin FORTRAN but the NTSY Spc 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 14 Menus amp related windows will pop up asking what should be done overwrite means that the exi
37. program for the reading of rectangular matrices from worksheet files compatible with Excel These files must have an extension of XLS In order import these files the Excel program itself must be present since NTSYSpc uses techniques called DDE and OLE to have Excel actually read the file and then pass the information to NTSYSpc NTSYSpc will search the spreadsheet for the matrix by starting with cell A1 That cell and the 3 cells to its right are taken as the matrix parameter line The first cell is the matrix type which must bea 1 The two cells to the right B1 and C1 must be the number of rows and then 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 Cell D1 contains the missing value code Leave it blank if there are no missing values The next row contains column labels beginning with cel B2 If left blank NTSYSpc will simply 20 Preparation of input data files number the columns The column beginning with cell A3 contains the row labels If blank then NTSY Spc will simply number the rows Thus row and column labels are in their natural position not as records in front of the matrix as in as in the L option The matrix itself begins in cell B3 If empty cals or labels are found within the matrix they are assumed to correspond to missing values Regions in the spreadsheet beyond the matrix are ignored and can be used to store other information
38. put Standardize the variables stand o data nts r sdata nts Compute a distance matrix simint o sdata nts r dist nts c dist Doa 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 dicking 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 24 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 analyses 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 amp c among the points and of relationships usually correlation among the variabl
39. reakpoint 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 beinspected when the computations are complete 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 Load EAABNNTPCANT2 33TEST2 NTB the codes 1 2 9 are found in a Parameters batch file they will be replaced by the values of the corresponding replaceable parameter strings given in the parameter area of the v Run X Cancel batch mode window A maximum of 9 replaceable parameters can be specified An Figure 24 Batch mode window with the example is shown below test2 ntb file loaded and two replaceable stand o 1 nts r sdata nts parameters provided simint o sdata nts r dist nts sahn o dist nts cm 2 r tree nts 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 12 Modes of operation stand o mosgq 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 prog
40. ressing 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 cyde of computation it does not check constantly for a keypress since that would slow the program down Alternatively you can hold down the 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 belost 3 Menus amp related windows 3 1 Main 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 NTSY Spc file you wish to edit The separate program NTedit included with NTSYSpc is then run If the file is 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 berun The view listing item opens the Listing window see Section 3 3 The printer setup item opens the standard Windows printer setup dialog box The run batch file item brings up the Batc
41. ru cuE c ey fucus tn Qv c V un ONU Vo UR re SES Dey Ye SUR US QU SUR ON RV NK NR D ER 13 NER MIA EIC ATTI EDU CD OO D IR errr 13 3 2 Configuration window apdulle Mites eh ERR PES Perd ru PER DDR PE Per TERR ERU 14 3 3 Ou tp t Listing AM WOOW us eos ucr ter non de e etr D e ar decent ner net ned 15 4 Preparation of input data files nnns 16 d Ie TOLIalS o nA hac ASAP RARO ROM M MOM MM LA ec AD tee 16 ADT Kal eS OF data TI 86 Sousse need bono i occulte e SE eae lactate dedo 18 4 3 Interface to other DrogrdMS shi esten re e ERR dE EU Lee 20 E i 1 er 21 6 Graphics options amp Menu usorsceies sevi sen acbaser usb seas IuvkkeUnkuY cNUY cNUZ ENEE EYES GNE UNE SENA KAEEKR SK UY RES 22 5 1 General plot ODUONS su ef n ie a eed re drea eiie 23 5 2 Othier oDL ONS asumen vo droite o d bel P E n e e PH Fo EE A boa 23 6 3 Plot Men RET EET 23 PEE R10p E UID Da Ci 24 Job Custer analysis 15e beer a rendendo ies assu vd ates eiu eren dr 24 7 2 Ordination analyses and Di DIOES coute en Un UD RED uieiuaauees Unt on CUR toe Fr Rr E 25 7 3 Principal components anasby SiS 55 qaae I Er drei etae bt epi E m FO e Pet ei Fide Var C ies 26 1 4 Principal coordinates analysis PCOORDA ssseeeeennnnnn nennen nnns 27 7 5 Nonmenic multidimensional Scaling 3 52 9 9 039 293 93 9 3 NOI OR ORI ER Pea n ede deret MS 28 7 6 B rnaby s method for size adj USt TIED sri etr rrr erri rn e eri e ert 28 T Gomparison of Ma
42. s np 250 While less efficient than a specialized program one can use the above steps to perform spatial autocorrelation analyses The only modification needed to the above steps is to replace the geographical distance matrix in file gdist nts with a series of matrices corresponding to a desired geographical distance class In each matrix an entry is 1 if objects i and j are within the desired distance dass and is 0 otherwise To make a distance correlogram one simply plots the matrix correlations as a function of geographical distance The Mantel test can be used to determine which coefficients are statistically different from Zero Bibliography 29 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
43. s should 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 possibleloss 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 and then Preparation of input data files 21 4 start entering your data EEENTedit 1 0 ES If there are missing Ele Edit Options Help data the identifying Col Labs Ins row Del row Fi Close numerical code needs to be Mx type Rectangular M Comments entered in the edit box labeled Missing Click No rows No cols Missing si 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 Figure 5 1 Example of NTedit with the test nts file loaded 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 ca
44. ssociation coefficients 5 axis aspect ratio 23 Batch mode 11 bimodel 25 biplot 25 Burnaby s method 28 canonical correlation 3 canonical vectors analysis 4 Cladistics 1 Cluster analysis 24 Common principal components analysis 3 Configuration window 14 consensus tree 3 cophenetic value matrix 3 Correspondence analysis 3 elliptic Fourier analysis 4 Excel 20 File formats 16 File overwrite code 14 Fourier analysis 4 homogeneity of covariance matrices 5 Installation 6 isometric vector 29 line limit 18 Mantel test 4 29 matrix comments 22 minimum length spanning tree 4 missing data code 17 22 multidimensional scaling 28 multidimensional scaling analysis 4 neighbor joining method 4 NEXUS format 19 Ordination analysis 25 Output Listing Window 15 PCA 26 PCOORDA 27 Index 31 phenetics 1 preference scaling 25 Principal components analysis 26 Principal coordinates analysis 27 repertory grid analysis 25 replaceable parameters 12 single link 5 singular value decomposition 5 size adjustment 28 Spatial autocorrelation analyses 29 thin plate spline 5 tree matrix 19 two block partial least squares 3 ultrametric 20 ultrametric values 3 UPGMA 5 XLS 20
45. sting 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 NTedit program Note 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 as the following config LF 9 6f 3 3 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 on a tab and then moving the scrollbars Note that the entire window can beresized 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 pime notebook can be saved to an File Edit Options Help ASCII file deleted or There are 5 characters rows and 10 OTU printed The columns are labelled No missing val STAND input TEST NTS divide STD subts The Edit menu SIMINT input SDATA NTS coeff DIST dir provides commands to type 2 size 5 by 5 nc none select all the text in the N i0 current section to cut Mean X 5 5783 s8x 98 9418 i
46. th C65 ovoteri b Do Dd X bae ad bebe ba a rane ol aan 29 Bibliography oxuecuidxenid viii dO RO UE QUU IN DOC EUR UL BD OR RUE I E RU RN 30 Preface NTSYSpc was developed originally for use by students in a seminar course Taxonomia n merica em microcomputadores held in September 1985 at the Esta 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 actual 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 ableto handle most datasets NTSYSpc was developed originally as a mainframe system of programs NTSYS It was written in FORTRAN for an IBM 360 50 computer at the University of Kansas in 1966 It 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 i
47. there is a blank entry signifying that this option is to be ignored The selected code will then be entered into the Figure 2 1 Dialog window for the STAND module form 10 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 to indicate for example whether the program should operate on the rows of the input matrix or whether additional information 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 key The Listing window will be opened to a new section and it will 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 In case of an error Such as entering the E Fj name of a non existent file for an input data matrix the program will beep and display
48. ts development over the years But NTSYSpc is a new program Fortunately after all of the previous experience with conversions most of the computational routines in NTSYS were by now quite system independent and easy to convert to another language such as Pascal At present N TSY Spc has moved beyond NTSYS and provides many operations not available in the mainframe version of NTSYS NTSYSpc has gone through many revisions and has become much easier to use especially now that it is a Windows program The help files have been improved and contain much of the technical information that was once in the printed documentation Thereis also a special soreadsheet like editing program NTEDIT for the preparation of data files Both the program and the documentation have greatly benefited over the years by the help of many of the users especially Drs Richard Jensen and Leslie Marcus who have spotted many glitches in the program and the documentation Dr Dennis Slice has also made a number of important contributions Dean Adams and other graduate students have also been very helpful NTSYSpc will continue to be developed N ew programs and features are planned so that the system can evolve to better meet your needs Your comments suggestions and criticisms are appreciated Setauket N ew 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 i
49. tus 1 2 3 files and alter the form of storage of some matrices matrix TREE Displays a tree eg from a cluster analysis as a phenogram Options are provided for scaling and scrolling through a tree interactively 1 3 How to 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 NTSY Spc NTedit help files and the readme txt file A convenient program is also included to EMBS PISTES allow you to un install NTSYSpc eg in case you need to move i3 e NTSYSpc to another computer When you run NTSYSpc the first Graphics time you will be asked to General provide your name institution optional and a registration number Dcenter Stand Fourier TPSwts Transf Clustering Ordination Similarity Fiqure 1 1 NTSYSpc main window 6 Introduction Once the program is installed click on the NTSYSpc r mmwm ATX icon in the start menu to see what NTSYSpc looks like see Figure Parameters Arguments 11 Click on a button such as Input file Output on this main window Field width to bring up a program module Decimal places such as the Output program A form will be displayed in which you can spe
50. u 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 To do this the program now requires that the start of each command line begins with an asterisk e Theinformation 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 These 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 The changes to individual modules have been relatively minor since so much effort was spent simply converting the DOS program to a Windows program Future updates will emphasize adding new computational methods and options 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 dick 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 bat
51. ublished in many scientific journals in the areas of application For example Systematic Biology was called 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 etc of a number objects individuals specimens quadrats OTUs etc NTSYSpc 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 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 t does not contain much advice about which similarity coefficient or which dustering 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 e Everitt and Dunn
52. units of measurement and this is arbitrary in most studies 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 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 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 m
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