While we can think of potential applications for linear discriminant analysis (LDA) in ecology (such as finding differences in habitat conditions among a priori recognized community types), its real use is quite infrequent. This is probably caused by the fact that many problems that seem to be a good fit for discriminant analysis produce weak rather than convincing results. A good example of this might be an attempt to use discriminant analysis for the selection of plant species indicating a particular community type. The discriminant analysis then attempts to separate the community types using a linear combination of species abundances. However, because the species occurrences are often strongly correlated and each of them alone provides little information, it is usually impossible to single out few such diagnostic species, even if the species composition differs strongly among the distinguished types. We will therefore use an example from a numerical taxonomy here, in the hope that the topic will be easily understood by ecologists and that they can apply the hints provided to their own problems.

Data

The sample data were taken from a taxonomic study of several species of Melampyrum, hemiparasitic plants from the Scrophulariaceae family. Eighty plant specimens were measured, selected from four taxonomic groups: M. bohemicum from Czech localities, M. bohemicum from Austrian localities, hybrid populations of M. bohemicum × M. nemorosum, and M. nemorosum. Each group was represented by 20 specimens, originating usually from several local populations. You will be looking for the plant vegetative and flower-related characteristics, which would allow the four taxonomic groups to be distinguished.