Structural aspects of evenness and equalness

In ecology and evolution, measurement of uniformity or non-uniformity of variation aids in understanding adaptation and system stability. Despite the intricacy of problems addressed, a single concept and method of analysis prevails in the assessment of uniformity, namely evenness. Relevant entities of analysis, however, range from individuals, their genetic type or phenotype, pairs of these, to assemblages at various levels of organization. Entities, in turn, may be represented by frequencies/abundances, area occupied, pair differences, or diversity (of assemblages). The evenness concept views inequality in representation in terms of dominance of single entities (unevenness), but it does not cover the omnipresent phenomenon of differentness or heterogeneity as it appears in intermediate representations (unequalness). Here the concepts of evenness and equalness are expanded for application to more kinds of entities and their representations and related to common notions of equability and regularity. Beyond frequency distributions, a coherent approach to variability in similarity or difference of pairs of entities (pair differences) enables inclusion of facets of structure. Commensurability among all notions is then reached by specification of appropriate indicators and indices.