Assessing biological variation from the perspective of diversity

Particularly in ecological and evolutionary genetics, methods of discerning complex traits are improving at a considerable rate. As a consequence, the resolution of intrinsically qualitative traits such as species affiliation or genetic type is increasing to degrees that blur their distinction from continuously varying characteristics. The common notion of diversity, however, relies on distinct features such as the states of qualitative traits, and it aims to assess variation as a counting of these features or types. This situation brings up the question of whether and how the diversity perspective of variation can be broadened to cover higher levels of complexity without sacrificing its concept. The present paper suggests two approaches that refer to established criteria for measures of diversity and that complement each other. The partitions approach treats complexity through general measures of difference between trait states, and the relations approach rests on general binary relations that capture structural aspects of diversity. Both approaches are shown to consistently imply effective numbers of types even in cases where distinct types are not explicitly specified. Practically all of the common methods of measuring diversity can be classified into either of the two approaches, and new opportunities for analyses of the diversity of complex traits are provided. The latter analyses include those of diversity in subdivided collections. Other perspectives of variation (such as dispersion, variances, etc.) are discussed and analyzed for their distinction from the diversity perspective. In many cases, the distinction can be made apparent with the help of diversity portraits.