Chapter 5
Unconstrained Ordination
5.1 Objectives
While cluster analysis looks for discontinuities in a dataset, ordination extracts the
main trends in the form of continuous axes. It is therefore particularly well adapted to
analyse data from natural ecological communities, which are generally structured in
gradients.
Practically, you will:
• learn how to choose among various ordination techniques (PCA, CA, MCA,
PCoA and NMDS), compute them using the correct options, and properly
interpret the ordination diagrams;
• apply these techniques to the Doubs River or the Oribatid mite data;
• overlay the result of a cluster analysis on an ordination diagram to improve the
interpretation of both analyses;
• interpret the structures revealed by the ordination of the species data using the
environmental variables from a second dataset;
• write your own PCA function.
5.2 Ordination Overview
5.2.1 Multidimensional Space
A multivariate data set can be viewed as a collection of sites positioned in a space
where each variable defines one dimension. There are thus as many dimensions as
variables. To reveal the structure of the data, it would be interesting to represent the
main trends in the form of scatter plots of the sites. Since ecological data generally
contain more than two variables, it is tedious and not very informative to draw the
objects in a series of scatter plots defined by all possible pairs of descriptors. For
© Springer International Publishing AG, part of Springer Nature 2018
D. Borcard et al., Numerical Ecology with R, Use R!,
https://doi.org/10.1007/978-3-319-71404-2_5
151
Unconstrained Ordination
5.1 Objectives
While cluster analysis looks for discontinuities in a dataset, ordination extracts the
main trends in the form of continuous axes. It is therefore particularly well adapted to
analyse data from natural ecological communities, which are generally structured in
gradients.
Practically, you will:
• learn how to choose among various ordination techniques (PCA, CA, MCA,
PCoA and NMDS), compute them using the correct options, and properly
interpret the ordination diagrams;
• apply these techniques to the Doubs River or the Oribatid mite data;
• overlay the result of a cluster analysis on an ordination diagram to improve the
interpretation of both analyses;
• interpret the structures revealed by the ordination of the species data using the
environmental variables from a second dataset;
• write your own PCA function.
5.2 Ordination Overview
5.2.1 Multidimensional Space
A multivariate data set can be viewed as a collection of sites positioned in a space
where each variable defines one dimension. There are thus as many dimensions as
variables. To reveal the structure of the data, it would be interesting to represent the
main trends in the form of scatter plots of the sites. Since ecological data generally
contain more than two variables, it is tedious and not very informative to draw the
objects in a series of scatter plots defined by all possible pairs of descriptors. For
© Springer International Publishing AG, part of Springer Nature 2018
D. Borcard et al., Numerical Ecology with R, Use R!,
https://doi.org/10.1007/978-3-319-71404-2_5
151