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Version 3.1, described here, is obsolete. *For information on the currently shipping version, see our main page*

- a FORTRAN program for

*by Cajo J. F. ter Braak*

A common problem in community ecology and ecotoxicology is to discover how
a multitude of species respond to external factors such as environmental
variables, pollutants and management regime. Data are collected on species
composition and the external variables at a number of points in space and
time. Statistical methods available so far to analyze such data either assumed
linear relationships or were restricted to regression analysis of the response
of each species separately. To analyze the generally non-linear, non monotone
response of a community of species, one had to resort to the data-analytic
methods of ordination and cluster analysis - "indirect" methods
that are generally less powerful than the "direct" statistical
method of regression analysis. Five years ago, regression and ordination
were integrated into techniques of *multivariate* direct gradient analysis,
called canonical (or constrained) ordination. The use of canonical ordination
greatly improves he power to detect the specific effects one is interested
in. One of these techniques, canonical correspondence analysis, escapes
the assumption of linearity and is able to detect unimodal relationships
between species and external variables. The computer program CANOCO
is designed to make these techniques available to ecologists studying
community responses. CANOCO can carry out most of the
multivariate techniques described in Ter Braak (1987a) and Ter Braak and
Prentice (1988) using a general iterative ordination algorithm.

Researchers in other fields may find CANOCO useful as well, for example, to analyze percentage data/compositional data, nominal data or (dis)-similarity data in relation to external explanatory variables. Such use is explained in separate sections in the manual. CANOCO is particularly suited if the number of response variables is large compared to the number of objects.

Version 3.10 of CANOCO extends and enhances many of the features for version 2.1. Most importantly, the program is easier to use for the novice to ordination.

1.CANOCO is an extension of DECORANA (Hill, 1979). CANOCO formerly stood for canonical correspondence analysis (Ter Braak, 1986, 1987b) and included weighted averaging, reciprocal averaging/[multiple] correspondence analysis, detrended correspondence analysis and canonical correspondence analysis. The program has been extended to cover also principal components analysis (PCA) and the canonical form of PCA, called redundancy analysis (RDA). Redundancy analysis is also known under the names of reduced-rank regression (Davies and Tso, 1982) and PCA of y with respect to x (Robert and Escoufier, 1976). For these linear methods there are options for centering/standardization by species and by sites and for the method of scaling the species and site scores for use in the biplot. Principal coordinates analysis and canonical variates analysis are also available.

2.CANOCO can also carry out "partial" analyses in which the effects of particular environmental, spatial or temporal "covariables" are eliminated from the ordination. A partial analysis allows one to display the residual variation in the species data and to relate the residual variation to the variables one is specifically interested in. Partial canonical correspondence analysis is the appropriate technique for the analysis of permanent plot data or for the joint analysis of data from several locations.

3.CANOCO allows one to test statistically whether the species are related to supplied environmental variables. The test provided is a Monte Carlo permutation test (Manly, 1990). The effect of a particular environmental variable can be tested after elimination of possible effects of other (environmental) variables by specifying the latter as covariables. For the analysis of randomized-block experiments or data from several locations, there is an option to restrict the permutation to permutations among samples-within-blocks or samples-within-locations. Valid permutation methods are included for time series, line transect and rectangular grids and repeated measurement designs, e.g. the Before-After-Control-Impact design.

4.CANOCO can perform a forward selection of environmental variables in order to determine which variables best explain the species data. At each step, a Monte Carlo statistical test can be carried out to judge the significance of the selected variable.

CANOCO uses ASCII files as input. CANOCO can read species data, environmental variables and covariables that are either in free format or in Cornell condensed format or in full format. The solution file of the analysis cannot only be used for graphics programs, but also be used as input for subsequent analyses. This possibility allows one, for example, to use principal components extracted from environmental data as input for a later canonical analysis of species data.

The CANOCO solution file is standard input for the program
CANOPLOT that produces printed ordination diagrams or,
on MS-DOS computers, for CanoDraw^{TM}
that produces ordination diagrams, biplots and triplots on the screen and
on some of the most common hardcopy devices.

CANOCO can also supply:

* means, variances and correlations of environmental variables,

* eigenvalues and percentages of variance accounted for,

* diagnostics for the fit of species and samples in the ordination,

* canonical coefficients or regression coefficients of environmental variables with associated t-values,

* correlations of environmental variables with the ordination axes,

* centroids (weighted averages) of environmental variables in the ordination diagram. In particular, classes of nominal environmental variables are more naturally displayed by their centroid in the ordination diagram than by arrows. This option is also useful for displaying the results of a cluster analysis in an ordination diagram.

CANOCO allows interactive data analysis: results of an analysis can be displayed at the terminal and after inspection the analysis can be pursued. e.g.:

* by changing from an indirect gradient analysis to a direct gradient analysis,

* by dropping environmental variables or by turning them into covariables,

* by reading other environmental variables to be related to the current ordination axes or to be used in further canonical analyses,

* by extracting more than the default four ordination axes.

Ready-to-use versions are available for MS-DOS computers
and the Apple Macintosh. On an MS-DOS PC with 405 Kb
free memory, CANOCO 3.1 can analyze 500 samples, 500
species, 100 covariables and 58 environmental variables, but with some additional
limitations on the number of species occurrences and environmental and covariable
values (total data space 45000 reals) An 80x87 coprocessor is optional.
More demanding in terms of system requirements is CanoDraw^{TM}
LITE, which is included with the PC package. It has
the same system requirements as the CanoDraw^{TM}
program itself detailed elsewhere in this catalog. On a PC
with math coprocessor or on a standard Apple Macintosh, CANOCO
3.1 can analyze at most 1000 samples, 700 species, 75 environmental variables
and 100 covariables, (total data size <80000). The Macintosh version
supports the Macintosh user interface only in file launching from the Finder
and the standard open file dialog box from within the program. For use on
a PC or Macintosh, the source code is also available
at extra cost.

CANOCO has been successfully implemented on various mainframe computers. For implementation on VAXen or mainframes, the FORTRAN 77 source code of CANOCO can be supplied together with detailed compilation notes and a demonstration version of the program on a PC or Apple Macintosh diskette.

The one-time costs for single licenses, multiple licenses and Site licenses/LAN (local area network) are specified on the order form. Documentation (a manual and a booklet with relevant reprints) is sent with each license of the program. The Site license/LAN includes 10 copies of the documentation and permission to duplicate the program further for use at the site. The license based on the FORTRAN source code gives permission to install the Program on a single (main frame) processor. If the licensee is unable to install the program, a refund can be obtained after all the material has been returned. An Educational discount is also available to University shipping addresses.

Dr. Richard E. Furnas

Microcomputer Power Catalog

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