This chapter introduces six more advanced techniques, which build on the foundations of constrained ordination methods and can be used with the Canoco software. Principal response curves (PRC) (Section 10.1, illustrated in Section 16.6) are useful when comparing the development of biotic communities in time under different conditions. Principal coordinates of neighbour matrices (PCNM, also known as dbMEM) technique (Section 10.2, illustrated in Chapter 19) allows us to study the spatial structure present in data and compare it with (separate it from) the effects of environment or experimental manipulation. Linear discriminant analysis (LDA, also known as CVA) is a traditional method of taxonomical studies, but it can be also useful in the field of population or community biology (Section 10.3, illustrated in Section 18.3). Section 10.4 demonstrates the hierarchical decomposition of community composition variation and Chapter 17 presents a case study using this method. Decomposition of the total biotic diversity into its alpha- and beta-diversity components using ordination methods is explained in Section 10.5 and illustrated with a practical example in Section 12.4. Finally, Section 10.6 briefly summarises how the community composition can be predicted for a given combination of environmental conditions.

Principal response curves (PRC)

When we experimentally manipulate whole communities, we often evaluate the effect of the experimental treatments over a longer period, because the response to disturbance or to nutrient addition has a strong temporal aspect. When we need to compare the community composition at sites differing in experimental treatment with the control (unmodified) sites at different sampling times, it is quite difficult to do so using an ordination diagram from a standard constrained ordination. The temporal trajectory of each site is usually not a straight line going through the ordination diagram, but rather a complex, wiggling path (see Figure 16–8 for an example). It is therefore difficult to evaluate the extent of differences among the individual time steps and – more importantly – among the individual treatments, across the time. Van den Brink and Ter Braak (1998, 1999) developed a new method called principal response curves (PRC), which focuses exactly on this aspect of the data.