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METHODS 1994-1996


H.J.B. Birks

Niklas E. Indrevær


Cecilie Rygh

Botanical Institute, University of Bergen

Allégaten 41, N-5007 Bergen



The development of canonical correspondence analysis (CCA) by Cajo ter Braak in the mid 1980's and
its implementation in his computer program CANOCO (along with other constrained ordination
methods such as redundancy analysis (RDA), detrended canonical correspondence analysis and hybrid
methods) have revolutionised quantitative community ecology and related subjects such as limnology
as well as many applied ecological topics such as the study of ecological impacts and the analysis of
monitoring data. Besides these direct gradient analysis techniques, CANOCO also permits 'partial'
analysis where the effects of external 'nuisance' variables are removed statistically, the statistical
testing of the relationship between response variables (usually species) and external predictor variables
by means of several different types of Monte Carlo permutation tests, the reconstruction ('calibration')
of environmental variables (e.g. lake-water pH) from biological data (e.g. fossil diatoms), the statistical
analysis of multivariate data from field experiments, etc.

Our initial bibliography (Birks et al. 1994, 1996) attempted to list all the publications about canonical
correspondence analysis and its linear relative redundancy analysis that had been published since Cajo
ter Braak's original paper on CCA in 1986. That bibliography covered the period 1986 to 1993 and
contained 378 entries listed alphabetically by first author. This bibliography primarily covers the period
1994 - 1996 and contains 402 entries published during that period. It also contains 23 entries published
between 1985 and 1993 that were missed in our initial bibliography.

As in our earlier bibliography, each entry is numbered and is indexed in terms of 137 topics that serve
as index entries for the bibliography, grouped into 3 main categories. These are (1) Methods used (e.g.
canonical correspondence analysis, redundancy analysis, hybrid analysis, Monte Carlo permutation
tests), (2) Subject (e.g. algology, ecology, limnology, marine biology, palaeolimnology,) and (3)
organisms studied (e.g. birds, diatoms, fungi, zooplankton). In addition, the various topics that each
publication covers are shown in brackets after each reference. This bibliography and our previous
bibliography lists a total of 804 publications.

Since Cajo ter Braak first published about CCA in 1986 and brought redundancy analysis
(=constrained principal components analysis) to people's attention, CCA, RDA, and their close
relatives have been used in very many different subjects, not only in community ecology and
biogeography, but also in the study of ecological dynamics, ecological impacts, ecological
management, analysis of field experimental data, conservation, limnology, palaeoecology,
microbiology, ornithology, palaeolimnology, ecotoxicology, marine biology, and morphology. CCA
and related techniques are also now being used in topics such as agriculture, horticulture, landscape
ecology, monitoring , and public health. Geographically the authors of the 804 publications show a not
unexpected concentration on the Netherlands, followed by Norway, Sweden, Great Britain, Finland,
Canada, and the USA and with an increasing number of publications from scientists in South America
and Africa, and in Spain, Portugal, Switzerland and Germany. There are still very few publications
from Australia, not surprising perhaps given the disparaging comments of Austin et al. (1994) about
CCA that "the ecological assumptions although explicit are unrealistic. Adoption of the method in
Australia should not be undertaken without extensive evaluation" and that "there is an urgent need for
the method to be more thoroughly tested, particularly the implications of the regression procedure". As
judged by the 804 publications listed in our two bibliographies, many scientists working with a wide
range of response variables (ranging from algae, bacteria, chironomids, etc. to cancer types and
whiskies!) have found CCA, RDA and related techniques to be useful tools in analysing their complex
multivariate data, in testing specific hypotheses, and in furthering their understanding of the ecology of
the organisms under study.

Since our initial bibliography, the most obvious developments have been the increased use of RDA, the
greater use of Monte Carlo permutation tests and variance partitioning, the use of partial CCA and
RDA, the incorporation of spatial or temporal constraints in constrained ordinations, the testing of
specific hypotheses, and the use of CCA or RDA to analyse field experimental data.

We are very grateful to the staff of the Bergen University Library for helping us obtain many
publications not available locally, to colleagues who have informed us of additional references, and to
Cajo ter Braak and Petr Smilauer for their continuing advice, help and encouragement.


A copy of this bibliography will eventually be available on the World Wide Web.

We would naturally be most grateful for to readers who draw our attention to any errors or omissions.

Bergen, August 1998

H.J.B. Birks
Niklas E. Indrevær
Cecilie Rygh


Austin, M.P., Meyers, J.A. & Doherty, M.D. (1994) Predictive models for landscape patterns and
processes, Sub-project 2, Modelling of landscape patterns and processes using biological data.
of Wildlife and Ecology, Commonwealth Scientific and Industrial Research Organisation, Canberra, 44

Birks, H.J.B., Peglar, S.M., & Austin, H.A. (1994) An annotated bibliography of canonical
correspondence analysis and related constrained ordination methods 1986-1993
. Botanical Institute,
University of Bergen, Bergen, 59 pp. (Available on the World Wide Web at

Birks, H.J.B., Peglar, S.M. & Austin. H.A. (1996) An annotated bibliography of canonical correspondence
analysis and related constrained ordination methods 1986-1993. Abstracta Botanica 20, 17-36.

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