About Commensurability of Diversity within and among Communities

Abstract

(1) Background: Is variation among the communities of a metacommunity higher than within the communities? Community ecologists and population geneticists often characterize the structure of metacommunities by partitioning variation (diversity) into the two following components using measures such as FST or GST and α- and β-diversity. The within-communities component is usually some average of (type, species, genetic) diversities within the communities, and the among-communities component is the additive or multiplicative complement of the overall diversity. Such an among-communities component lacks independent conceptual specification, a matter of long-standing dispute. Only if the two components are independently and commensurably specified can the central question of comparability be answered meaningfully. (2) Methods: A novel approach to overcoming this conceptual weakness identifies two principles of the partitioning of variation among communities (concentration and division) then relates these principles to the common notions of variation (diversity) within and among communities, distinguishes primary indicators to quantify the partitioning principles, transforms the indicators into conceptually independent measures (indices) of variation within and among communities, and by this attains their commensurability and thus comparability. The application of the methods to quantifying the effects of evolutionary mechanisms is outlined. (3) Results: Common approaches are corrected and extended. (a) Analyses of metacommunity/metapopulation structures that rely on apportionment or related indices and take its complement to be differentiation yield incomparable measures of variation within and among communities. (b) The common practice of partitioning the total diversity into additive or multiplicative components produces the inconsistent ranking of the two components. (c) Community concentration and division can result from elementary processes of adaptive differentiation and migration (gene flow) among communities, where the (commensurable) amounts of community concentration and division reflect the relative participation of these processes in metacommunity structuring and translate directly into the measures of diversity within and among communities. (d) The modelling of the contributions of the two partitioning principles to the metacommunity structure is restricted by the marginal distributions of types and community affiliation. (e) The model demonstrates the degree to which adaptational processes at the metacommunity level are mixtures of adaptational events within and among communities.