Canonical analysis of asymmetric matrices: two applications from a study of chalk grassland in the south of England

Abstract

Gower's (1977) method for the canonical analysis of asymmetric matrices (CAA) where the same entities index both the rows and the columns is described. This technique displays the indexing entities in a series of orthogonal planes of decreasing importance in such a way as to preserve the pattern of the asymmetry between them. The analysis is applied to a half-diallel experiment and to some leaf-overtopping data, both from a study of the control of relative abundance of perennials in chalk grassland. The results suggest a common source for the asymmetry in the very different interference and overtopping data, namely that of leaf height. It is concluded that relative abundance in the field may be determined, in part, by leaf height through aboveground interference between plants.