In many multivariate methods, one of the first steps is to calculate a matrix of similarities (resemblance measures) either between the samples (relevés) or between the species. Although this step is not explicitly done in all the methods, in fact each of the multivariate methods works (even if implicitly) with some resemblance measure. The linear ordination methods can be related to several variants of Euclidean distance, while the weighted-averaging ordination methods can be related to chi-square distances. There semblance functions are reviewed in many texts (e.g. Gower & Legendre 1986; Legendre & Legendre 1998; Ludwig & Reynolds 1988; Orloci 1978), so here we will introduce only the most important ones.

In this chapter, we will use the following notation: we have n samples (relevés), containing m species. Yik represents the abundance of the kth species (k = 1, 2, …,m) in the ith sample (i = 1, 2, …, n).

It is technically possible to transpose the data matrix (or exchange i and k in the formulae), thus any of the resemblance functions can be calculated equally well for rows or columns (i.e. for samples or species). Nevertheless, there are generally different kinds of resemblance functions suitable for expressing the (dis)similarity among samples, and those suitable for describing similarity among the species. This is because the species set is usually a fixed entity: if we study vascular plants, then all the vascular plants in any plot are recorded – or at least we believe we have recorded them. But the sample set is usually just a (random) selection, something which is not fixed.