Introduction on Canoco for Windows 4.5

Introduction on Canoco for Windows 4.5 Canoco for Windows is the next generation of CANOCO software, the most popular tool for constrained and unconstrained ordination in ecological applications. Canoco for Windows integrates ordination with regression and permutation methodology, so as to allow sound statistical modelling of ecological data. Canoco for Windows contains both linear and unimodal methods. Ordination with Canoco for Windows can provide insight into:

1. the structure of biological communities,

2. the relations between plant and animal communities and their environment,

3. the effects of a putative impact on the environment and/or its biological communities, and

4. the effects of treatments of complex ecological and ecotoxicological experiments on biological communities.

Ordination diagrams can be displayed on screen immediately after an ordination has been calculated. Canoco is unique in its capability to account for background variation specified by covariables and in its extensive facilities for permutation tests, including tests of interaction effects. These unique features make Canoco for Windows particularly effective in solving applied research problems.

Canoco has been designed for ecologists, but Canoco has also been used in toxicology, soil science, geology, public health research and market research, to name a few. About the authors

The Canoco for Windows package has been developed by Cajo J.F. ter Braak and Petr ?milauer.

Cajo J.F. ter Braak is a senior biometrician at the Biometris, Plant Research International BV, the Netherlands, with a specialization in multivariate methods for species-environment relationships. He is the inventor of canonical correspondence analysis, popularized (partial) redundancy analysis, and is co-author of the textbook Data Analysis in Community and Landscape Ecology. His inspiration for developing methods comes from collaboration with researchers from the DLO-Institute for Forestry and Nature Research and the DLO Winand Staring Centre for Integrated Land Soil and Water Research.

Petr ?milauer is a plant ecologist at the Faculty of Biological Sciences, University of South Bohemia, Ceske Budejovice, Czech Republic. He works at the interface of computer science, modelling, and ecology. He is the author of CanoDraw for Windows and of the Windows specific elements of Canoco for Windows.

References

? Jongman R. H. G., ter Braak, C. J. F. and van Tongeren, O. F. R., editors (1995). Data analysis in community and landscape ecology. Cambridge University Press, Cambridge.

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? ter Braak, C. J. F. (1986). Canonical correspondence analysis: a new eigenvector method for multivariate direct gradient analysis. Ecology, 67, 1167-1179. ter Braak, C. J. F. (1994). Canonical community ordination. Part I: Basic theory and linear methods. Ecoscience, 1, 127-140. ter Braak, C. J. F. (1996). Unimodal methods to relate species to environment. Centre

for Biometry Wageningen (DLO Agricultural Mathematics Group), Wageningen, the Netherlands, 266 pp.

? ter Braak, C. J. F. and Verdonschot, P. F. M. (1995). Canonical correspondence

analysis and related multivariate methods in aquatic ecology. Aquatic Sciences, 57, 255-289.

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? ter Braak, C. J. F. and Looman, C. W. N. (1994). Biplots in reduced-rank regression. Biometrical Journal, 36, 983-1003. ter Braak, C. J. F. and ?milauer, P. (2002). CANOCO Reference Manual and

CanoDraw for Windows User's Guide: Software for Canonical Community Ordination (version 4.5). Microcomputer Power (Ithaca NY, USA), 500 pp.

? van den Brink, P. J. and ter Braak, C. J. F. (1998). Multivariate analysis of stress in

experimental ecosystems by Principal Response Curves and similarity analysis. Aquatic Ecology, 32, 163-178.

Statistical methods in Canoco for Windows 4.5 Canoco for Windows 4.5 covers the following multivariate methods:

A. Unconstrained ordination methods -

methods to describe the structure in a single data set:

? principal components analysis (PCA), with various combinations of data standardization by rows and/or by columns (so supporting, among others, PCA on a covariance matrix and PCA on a correlation matrix). A special case is Aitchison's log-ratio PCA for compositional data

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? correspondence analysis (CA), also known as reciprocal averaging detrended correspondence analysis (DCA), often incorrectly named as DECORANA, after the original program implementing DCA principal coordinates analysis (PCO), a classical method of the metric multidimensional scaling

B. Canonical ordination methods -

methods to explain one data set by another data set (ordinations constrained by explanatory variables):

? redundancy analysis (RDA), also called reduced-rank regression, the canonical form of PCA. Special cases are simple and multiple regression, analysis of variance and the log-ratio form of reduced-rank regression

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? canonical correspondence analysis (CCA), the canonical form of CA detrended canonical correspondence analysis (DCCA), the canonical form of CCA canonical variate analysis (CVA), better known as Fisher linear discriminant analysis distance-based redundancy analysis (db-RDA), a constrained form of principal coordinates analysis (PCO)

C. Partial ordination methods -

methods to describe the structure in a data set after accounting for variation explained by a second data set (covariable data):

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? partial PCA partial CA partial DCA

D. Partial canonical ordination methods -

methods to explain one data set by another data set after accounting for variation by a third data set (covariable data):

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? partial RDA partial CCA partial DCCA partial CVA

For all the listed multivariate methods, you can have a supplementary data set with explanatory variables, that are projected a posteriori into the ordination space to facilitate the

interpretation of results.

The statistical significance of the explanatory variables in (partial) canonical methods can be determined by Monte Carlo permutation tests. Explanatory variables can be tested jointly (overall test) or separately after adjusting for other explanatory variables (partial tests). The problem of (auto-)correlation between samples can be overcome by using special permutation schemes. Canoco for Windows has built-in schemes for:

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? data from one or more equi-spaced time series, line transects, or rectangular grids of samples data originating from repeated measurement designs, Before-After-Control-Impact (BACI design) and data from nested and crossed designs with fixed and random factors

Other useful features include forward selection of explanatory variables, and ordination diagnostics on outliers and influential data points.

In addition, the plotting program CanoDraw for Windows contains both elementary and advanced methods for interpreting ordination diagrams. Elementary methods include:

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? plotting values of species or explanatory variables in the ordination diagram plotting diversity values in the ordination diagram plotting samples or species by group symbols

More advanced methods include:

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? fitting and plotting species response curves along ordination axes and contouring species or explanatory variables in the ordination diagram by:

o generalized linear modelling (e.g. Gaussian response curves/surfaces)

o loess smoothing

o generalized additive modelling (GAM)

The Canoco for Windows 4.5 Package The Canoco for Windows package consists of several software modules:

? to specify and calculate ordination analyses, and to view and plot the results. The Canoco for Windows module is truly interactive and utilizes the rich Microsoft Windows® user interface, with context-sensitive online help at each step

? ? to import spreadsheet data. to graph all basic types of ordination diagrams and to fully explore ordination results. CanoDraw is launched directly from the Canoco for Windows module.

? to run Canoco in batch for simulation studies and tailor-made applications. Also for users who want to stay with the CANOCO 3.1 textual user interface.

? ? to merge column-wise two or more data tables, to export data in TAB-separated format, or to remove rare species from data tables. to compute metric multidimensional scaling (= principal coordinates analysis, PCO) for specified dataset and to support calculation of distance-based RDA The Canoco for Windows packages comes with:

? revised 500 page Reference Manual (ter Braak and ?milauer, 2002) with a Getting started chapter, an in-depth, up-to-date explanation of the ordination methods and a completely new chapter (80 pages) describing many real-life applications of the Canoco program. Detailed documentation of CanoDraw for Windows is also part of this manual. An index is included to help you finding the information you need. ? new licenses of Canoco for Windows 4.5 come with the extended 266 page book Unimodal models to relate species to environment (ter Braak, 1996) with collected papers on ordination.

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a large set of files with real-life data sets and their analysis.