Structural type diversity: measuring structuredness of communities by type diversity

Recently, the notion of diversity, which is directed towards (effective) numbers of types (states of a trait such as species and genotypes), is increasingly used as an umbrella term akin to “variation”, thus including classical metrics of dispersion among others. This is probably due to the growing interest in functional aspects of variation which involve variable differences between types. Though the traditional notion of diversity does not cover these aspects, it shows up in many interpretations. To overcome this ambiguity, the traditional notion of diversity is extended in this paper to include variable differences with emphasis on their general significance as structuring features. For this purpose, structure is conceived to be captured by the representation of types via variable differences and abundances. Structural diversity then results from application of traditional measures of diversity to the relative structural representations of types in addition to their relative abundances. Since diversity as effective number of types alone provides no information about their mutual distinctness and the range covered by them, connections to measures of dispersion are indispensable. This is considered via two approaches that rely on dispersion characteristics and one approach that allows for an assessment of structural diversity for controlled levels of type distinctness. Effects of structure on dispersion and diversity are analyzed. The use of the approaches for discovering rarely considered characteristics of phylogenetic structure is demonstrated.