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PC-ORD for Windows 98, 00, ME, NT, XP, Vista, 7, 8, and 10
Multivariate Analysis of Ecological Data
Version 7

Order Online or Fax/Mail Order Form



Specifications

Advisor Wizard
Graphs
Ordinations
Groups

 

Import/Export File Formats
Data Modifications
Traits
Summaries
Distance Measures
Matrix Operations
Features Not Available in
Major Statistical Packages
General
System Operations
User-Written Add-In Tools
PC-ORD Interface
PC-ORD Graph Interface


Specifications

Advisor Wizard

Wizard Through a question and answer dialog, PC-ORD uses a decision tree to help you decide how to transform and analyze your data.  You can also use it as a self teaching tool.

Decision Tree for Community Analysis Poster now available.

Graphs
Publication-quality graphics can be printed, saved to file, or pasted into other applications.  Various kinds of overlays can be used, including varying symbol sizes, labels, vectors, grids, and joint plots.  Code groups in your data by colors or symbol types.

Graph Types


Graph Formatting

  • Reflect / rotate ordinations
  • Overlay side graph fit envelope
  • Confidence bands in species-area curves
  • PCA biplot vectors (calculate and graph distance-based biplot for species or other variables)
  • Save graphs as emf, wmf, bmp, jpeg, gif, and tiff
  • 32 symbol types or colors on a single graph
  • Set graphic resolution as dpi or % of view on screen for Save and Copy
  • Option to place tick marks inside, outside, or across axes
  • Quadrant-sensitive labeling of points in ordinations (smarter positioning of point labels)
  • Optional arrowheads and arrowhead sizes on biplots, joint plots, and successional vectors
  • Envelopes on side scatterplots with Gaussian kernel smoother


Ordinations

Bray-Curtis (Polar)
We offer numerous options and improvements beyond Bray and Curtis' original method, such as perpendicularized axes and variance-regression endpoint selection.

Canonical Correspondence Analysis (CCA)
CCA is unique among the ordination methods in PC-ORD in that the ordination of the main matrix (by reciprocal averaging) is constrained by a multiple regression on variables included in the second matrix.  In community ecology, this means that the ordination of samples and species is constrained by their relationships to environmental variables.  CCA is most likely to be useful when: (1) species responses are unimodal (hump-shaped), and (2) the important underlying environmental variables have been measured.

Detrended Correspondence Analysis (DCA, DECORANA)
DCA is an eigenanalysis ordination technique based on reciprocal averaging (RA; Hill 1973).  DCA is geared to ecological data sets and the terminology is based on samples and species.  DCA ordinates both species and samples simultaneously.

Non-metric Multidimensional Scaling (NMS)
Non-metric Multidimensional Scaling (NMS, MDS, NMDS, or NMMDS) is an ordination method that is well suited to data that are nonnormal or are on arbitrary, discontinuous, or otherwise questionable scales.  NMS is generally the best ordination method for community data.  Our auto-pilot feature makes it easy to use.  A Monte Carlo test of significance is included.
NMS Scree Plot graph example

NMS Scores
NMS Scores provides a prediction algorithm for non-metric multidimensional scaling (NMS).  This is not prediction in the sense of forecasting, but rather statistical prediction in the same way as using multiple regression to estimate a dependent variable.  NMS Scores calculates scores for new items based on prior ordinations.

Principal Components Analysis (PCA)
Principal Components Analysis is the basic eigenanalysis technique.  It maximizes the variance explained by each successive axis.  Although it has severe faults with many community data sets, it is probably the best technique to use when a data set approximates multivariate normality.  PCA is usually a poor method for community data, but it is the best method for many other kinds of multivariate data.  Broken-stick eigenvalues are provided to help you evaluate statistical significance.

Principal Coordinates Analysis (PCoA)
Principal Coordinates Analysis is an eigenanalysis technique similar to PCA, except that one extracts eigenvectors from a distance matrix among sample units (rows), rather than from a correlation or covariance matrix.  In PCoA one can use any square symmetrical distance matrix, including semi-metrics such as Sorensen distance, as well as metric distance measures such as Euclidean distance.

Reciprocal Averaging (RA) = Correspondence Analysis (CA)
Reciprocal averaging is also known as correspondence analysis (CA).  It is performed in PC-ORD by selecting options in program DCA adapted from the Cornell Ecology Program series.  Reciprocal averaging (RA) yields both normal and transpose ordinations automatically.  Like DCA, RA ordinates both species and samples simultaneously.

Redundancy Analysis (RDA)
Redundancy Analysis models a set of response variables as a function of a set of predictor variables, based on a linear model.  RDA thus applies to the same conceptual problem as canonical correspondence analysis (CCA).  RDA is, however, based on a linear model among response variables and between response variables and predictors.  CCA, on the other hand, implies a unimodal response to the predictors.

Weighted Averaging
The simplest yet often effective method of ordination is weighted averaging.  The essential operation is the same: a set of pre-assigned species weights (or weights for species groups) are used to calculate scores for sites (sample units).   The calculation is a weighted averaging for species or species groups actually present in a sample unit.  Weighted averaging used in Federal Manual and numerous ecological indices.

Fuzzy Set (FSO)
Fuzzy set ordination applies fuzzy set theory to direct gradient analysis in ecological ordination.  This ordination method requires the user to hypothesize the relationship between species communities and environmental variables or other predictors.   The predictors are most commonly environmental variables, but they can also be a secondary set of species communities, or any other quantitative data set with the same number of rows as the community matrix.  The community data are placed in the main matrix, and the secondary set is in the second matrix.  The resulting ordination is an ordination of sample units in species space.  Species can be superimposed on the ordination by a single weighted averaging step

Compare Scores (Compare Ordinations)
Evaluate the similarity of two ordinations, independent of any rotation, reflection, units for axis, and number of dimensions.  This is accomplished by evaluating the correlation between the interpoint distances of two ordinations. Squaring this correlation expresses the redundancy between two ordinations.  A formal test of the hypothesis of no relationship between the two ordinations is provided by a Mantel test.


Groups

Cluster Analysis
We offer eight fusion strategies and eight distance measures, for hierarchical, polythetic, agglomerative cluster analysis.  Results are given for each step in the analysis, along with a publication-quality final dendrogram.  Cluster Analysis graph example

Two-way Cluster Analysis
The purpose of our two-way clustering (also known as biclustering) is to graphically expose the relationship between cluster analyses and your individual data points.  The resulting graph makes it easy to see similarities and differences between rows in the same group, rows in different groups, columns in the same group, and columns in different groups.  You can see graphically how groups of rows and columns relate to each other.  Two-way clustering refers to doing a cluster analysis on both the rows and columns of your matrix, followed by graphing the two dendrograms simultaneously, adjacent to a representation of your main matrix.  Rows and columns of your main matrix are re-ordered to match the order of items in your dendrogram.
Two-way Cluster Analysis graph example

Group Linkage Methods
  • Nearest Neighbor
  • Farthest Neighbor
  • Median
  • Group Average
  • Centroid
  • Ward's Method
  • Flexible Beta
  • McQuitty's Method
Ward's is also know as Orloci's and Minimum Variance Method

Multi-Response Permutation Procedures (MRPP)
MRPP is a non-parametric procedure for testing the hypothesis of no difference between two or more groups of entities.  The groups must be a priori.  For example, one could compare species composition between burned and unburned plots to test the hypothesis of no treatment effect.  Discriminant analysis is a parametric procedure that can be used on the same general class of questions.  However, MRPP has the advantage of not requiring assumptions (such as multivariate normality and homogeneity of variances) that are seldom met with ecological community data.  Eight distance measures options are available.

Blocked Multi-Response Permutation Procedures (MRBP)
Randomized block experiments or paired-sample data can be analyzed with a variant of MRPP called MRBP or blocked MRPP. PC-ORD allows up to 1000 blocks and 100 groups.

Indicator Species Analysis
Dufrêne and Legendre’s (1997) method provides a simple, intuitive solution to the problem of evaluating species associated with groups of sample units.  It combines information on the concentration of species abundance in a particular group and the faithfulness of occurrence of a species in a particular group.  It produces indicator values for each species in each group.  These are tested for statistical significance using a Monte Carlo technique.

Blocked Indicator Species Analysis
Dufrêne and Legendre’s (1997) method for Indicator Species Analysis can be adapted to a randomized block experiment or a paired-sample design.  The data are pre-relativized by species within blocks (or pairs), such that the sum across groups equals one for each block.  If a species is absent from a block, the abundances are maintained at zero.  The relativization alters the relative abundance portion of the Indicator Value (IV) index to focus on within block differences.  Then the ISA is run as usual.  The randomization test differs from regular ISA in that instead of an unconstrained permutation of group identifiers, groups are randomly permuted within blocks.

Phi Coefficient for Indicator Species
Tichý and Chytrý's (2006) phi coefficient is a method for evaluating the indicator value (or diagnostic value) of a species with respect to a one-way grouping of sample units.   It applies only to presence-absence data.  If have quantitative data you choose this option in the Indicator Species Analysis Setup, then the data are automatically converted to presence-absence.  Any value greater than zero is transformed to 1, while values less than or equal to zero are transformed to zero.   Tichý and Chytrý's method corrects for unequal sample sizes among groups.   The adjusted phi coefficient also allows comparisons across studies with different sample sizes.

Mantel Test
The Mantel test evaluates the null hypothesis of no relationship between two dissimilarity (distance) or similarity matrices.  The Mantel test is an alternative to regressing distance matrices that circumvents the problem of partial dependence in these matrices.  Example applications are: evaluating the correspondence between two groups of organisms from the same set of sample units or comparing community structure before and after a disturbance.  Two methods are available in PC-ORD: Mantel’s asymptotic approximation and a randomization (Monte Carlo) method.

Partial Mantel Test
The partial Mantel test requires three matrices, the main matrix, a second matrix, and a control matrix.  The null hypothesis is of no relationship between the main and second matrices, after controlling for the relationship with the third (control) matrix.   If we call the main matrix Y, the second matrix X, and the control matrix C, then we seek the partial correlation between X and Y while controlling for C.

PerMANOVA
PerMANOVA performs distance-based multivariate analysis of variance, also known as nonparametric MANOVA or npMANOVA.  Hypothesis are evaluated with permutation tests, rather than by reference to an assumed distribution.  Options include one-way, factorial, nested, and blocked designs.

SumF
A simple but surprisingly effective method of comparing two or more groups of sample units is to calculate a univariate F statistic for each variable, sum those F statistics, then compare the resulting sum to the distribution of F statistics based on randomizing the data under the null hypothesis.  This is the core of the SumF method, as suggested by Edginton (1995).  Good performance of this method, as compared to distance-based methods, was found by Warton and Hudson (2004).  An advantage to this method is that by aggregating a simple, well-known test statistic, the F ratio, into a summary statistic across multiple variables, we simultaneously obtain information about differences between groups both across all variables and for individual variables.  Thus for the generic question, "Do communities differ between groups?", the SumF method allows us to report an answer for communities as a whole as well as for individual species.

TWINSPAN
TWINSPAN simultaneously classifies species and samples.  At its core, TWINSPAN is based on dividing a reciprocal averaging ordination space.  One of the most useful features of TWINSPAN is the final ordered two-way table.  Species names are arrayed along the left side of the table, while sample numbers are along the top.   The pattern of zeros and ones on the right and bottom sides define the dendrogram of the classifications of species and samples, respectively.  The interior of the table contains the abundance class of each species in each sample.  Abundance classes are defined by pseudospecies cut levels.



Import/Export File Formats

  • Excel (*.xls) and Excel 2007 (*.xlsx)
  • spreadsheet (*.wk1)
  • compact
  • database
  • Cornell condensed
  • comma-separated values (*.csv)


Data Modifications

Transformations Relativizations
  • power transformation
  • logarithmic
  • arcsine
  • arcsine squareroot
  • Beals smoothing
  • presence - absence
  • by totals
  • by proportion of maximum
  • rank
  • deviation from mean
  • binary with respect to median
  • ubiquity
  • deviation from mean
  • binary with respect to mean
  • info function of ubiquity
  • Hellinger


Traits

PC-ORD 7 provides ways to relate data on species traits (trait matrix) to community samples (main matrix) and environmental data (second matrix). While many of these operations can be done in the other PC-ORD menu items, the Traits menu provides several operations specific to this kind of data.

  • Traits | Categorical to Binary
    If, for a given variable, there are n unique categories (value labels), then n new binary (0/1) variables will be generated.  Each new variable will be designated as a Q variable with value 0 or 1.

  • Traits | Create Trait Combinations
    Create one new categorical variable by combining categories from two existing variables.  Each combination of categories from the two selected variables is taken as a new category in the new variable.  The resulting new variable is always categorical.  The existing variables are left intact, but you can easily remove them with Modify | Delete Columns.

    For example, say you had two categorical variables, one coding for native vs. non-native species, and one coding for annuals vs. perennials.  That might work well in the analyses, but what if species having a combinations of those, for example the non-native annuals, is particularly different ecologically from all remaining species?  You might, therefore, wish to create a new categorical variable with all four combinations of those trait categories: (1) native annuals, (2) native perennials, (3) non-native annuals, (4) non-native perennials.

  • Traits | Calculate SU x Traits Matrix
    Calculating a sample unit x trait matrix provides a flexible first step in analyzing the relationships between species traits and explanatory variables.  This matrix is obtained by multiplying a sample unit x species matrix by a species x trait matrix, but the content of the resulting matrix depends on whether and how traits are standardized and whether or not the multiplication is followed by a weighted averaging step (McCune 2015).  To maximize versatility of the SU x trait matrix, including comparability among traits, and usability with a wide range of distance measures, we recommend first standardizing traits by min-to-max, then calculating abundance-weighted trait averages in each sample unit.

  • Traits | Species Distances in Trait Space
    Species can be compared in their traits by calculating a distance matrix among species, starting with a species x trait matrix.  Mathematically this is the same as calculating a distance matrix among sample units in species space, except that in this case the objects are species and their attributes are traits, rather than objects being sample units and the attributes species.  The same distance measures are offered from the traits menu as for distances between sample units in species space.

  • Traits | Functional Diversity
    Functional diversity analyzes the combination of the sample unit x species matrix with a species x trait matrix.  Functional diversity measures attempt to describe the diversity of species functional traits represented in a sample unit, rather that simply species diversity.  For example, a plot containing three species, all having the same traits, are considered no more diverse than a single species.  Similarly, two species with very different functional traits contribute more functional diversity than two species that are similar in their functional traits.  For example, if we have two species in a plot and one is a weedy sun-loving pioneer plant species, and the other is a shade tolerant species with poor colonizing ability, that plot would have more functional diversity than two different species that were both shade tolerant poor colonizers.

  • Traits | Fourth Corner Analysis
    The methodological question of linking species traits to environmental variables, via the sample unit x species matrix, is called the fourth corner problem because of the arrangement of four basic matrices (see the traits x environment positions in Dray and Legendre (2008, Fig. 1a) and McCune and Grace (2002, Fig. 2.1).  Fourth Corner Analysis provides statistical tests of the strength of the links between these matrices.   For a detailed explanation of the theory and mathematics of fourth corner analysis see Legendre et al. (1997), Dray and Legendre (2008), Ter Braak et al, (2012), and Dray et al. (2014).

  • Fuzzy Set (FSO)
    Fuzzy set ordination applies fuzzy set theory to direct gradient analysis in ecological ordination.  This ordination method requires the user to hypothesize the relationship between species communities and environmental variables or other predictors.   The predictors are most commonly environmental variables, but they can also be a secondary set of species communities, or any other quantitative data set with the same number of rows as the community matrix.  The community data are placed in the main matrix, and the secondary set is in the second matrix.  The resulting ordination is an ordination of sample units in species space.  Species can be superimposed on the ordination by a single weighted averaging step


Summaries

Descriptive Statistics and Diversity Indices
Summarize attributes of your rows or columns (mean, standard deviation, sum, minimum, maximum, skewness, kurtosis), and measures of diversity: richness, equitability, Simpson index, and Shannon index).

Outlier Analysis
Detect multivariate outliers.  These are frequent in ecological data and they often exert undue influence over the results of multivariate analyses.

Species-area Curves
Species-area curves are constructed by randomly subsampling a data set.   Species-area curves are frequently used during study design to help determine sample sizes.  Species-area Curves graph example

Species Lists
Easily produce species lists from your spreadsheets, based on a species file.   This file associates your species acronyms with full species names, as they will appear in your lists.  Request a species list for each sample unit, or for your combined sample units.  You can include key summary statistics, such as frequency and abundance of each species.

Write Distance Matrix
Although many analyses in PC-ORD calculate a distance matrix and offer to write the distance matrix to the result file, these have limited formats and options.   Consider Write Distance Matrix if you wish to use your distance matrix in other software, save it for further analysis, or simply calculate a distance matrix with no other analysis.

Shuffle
Randomly reassign values in columns to new positions in the same column.  The resulting data set has the same column totals, matrix total, and number of elements containing zeros, but it effectively randomizes the data set.  Why shuffle your data?   Explore how multivariate methods can appear to detect pattern from nonsense.   Generate null models for comparison with your unshuffled data.



Distance Measures
  • Sorensen (Bray-Curtis)
  • Relative Sorensen
  • Jaccard
  • Euclidean (Pythagorean)
  • Relative Euclidean
  • Correlation
  • Chi-squared
  • Squared Euclidean
  • Morisita-Horn
  • Gower
  • Gower ignore 0,0


Matrix Operations
  • transpose
  • switch with secondary matrix
  • multiply by secondary matrix
  • delete columns or rows
  • delete rows or columns with < N non-zero values
  • delete rows filtered by matrix variable
  • multiply or add a constant
  • append matrix
  • augment matrix
  • random sample
  • stratified random sample
 

Features Not Available in Major Statistical Packages

  • CCA
  • NMS Autopilot mode (NMDS)
  • NMS Predictive-mode (NMDS)
  • PerMANOVA
  • Indicator species analysis (Dufrêne & Legendre)
  • DCA (DECORANA)
  • TWINSPAN
  • Two-way cluster analysis (biclustering)
  • MRPP
  • Blocked MRPP
  • Species-area curves
  • Diversity indices
  • Species lists
  • Mantel test
  • Various rotation methods
  • 3-D ordination graphics
  • Publication-quality dendrograms
  • Ordination overlay methods:
    Quantitative, grid, joint plot, biplot, and
    succesional vector, all with symbol and color coding
  • Bray-Curtis (Polar) ordination
  • City-block distance measures
  • Tree data summaries
  • Species ordinations for NMS, BC, PCA
  • Beals smoothing
  • Species list broken down by groups
  • Permutation-based MANOVA (PerMANOVA) with one-way, factorial, nested, and blocked designs
  • Current Profile to display most important summary features of your data set
  • Smoothed univariate frequency distributions calculated with density estimation techniques
  • Species associations based on 2 x 2 contingency tables
  • Advisor Wizard: Helps you to decide how to analyze your data, based on a decision tree.
  • Simultaneous adjustment of main and second matrices (for example, simultaneous deletion of rows from both matrices)
  • Filter rows by criterion variable in main or second matrix
  • Randomization tests for PCA
  • Cluster analysis from distance matrix directly
  • Mantel test based on rank correlation or rank-transformed distance matrix
  • Write distance matrix to spreadsheet or text file; full matrix or pairwise list
  • Save NMS scores to text file, spreadsheet, or result file
  • Option to break down row and column summaries by a variable in the second matrix.
  • Allow direct modifications of second matrix
  • Add scores to second matrix
  • Append matrices (append rows and match columns)
  • Terminology tailored to ecology

General

System Requirements
  • Operating System: Windows 98, NT, ME, 2000, XP, Vista, 7, 8, and 10
  • 80486 or higher CPU (including Pentium 4, Athlon, Celeron, etc.)
  • 8 MB RAM (more RAM means ability to analyze larger data sets)
  • 16 MB of available hard disk space
  • Guidelines for Network Installation of PC-ORD

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