Relating measures of compositional differentiation among communities to conceptual models of migration and selection

•Communities may be differentiated for types and types for community membership.•Migration need not homogenize communities, but it does homogenize types for community membership.•Migration and selection do not have equivalent effects on differentiation.•Effective proportions of migration can be determined from conceptual models.

Selection and migration are the major deterministic forces that control adaptational processes of differentiation among communities. With the aim of distinguishing between their effects on metacommunity structure, compositional differentiation in metacommunities is viewed from dual perspectives: between communities for their distributions of the types (CDT, the common perspective) and between types for the distribution of their community membership (TDC). A measure of dispersion and four measures that fulfill the basic characteristics of differentiation (maximality for complete difference and minimality in the absence of differences) from both perspectives are introduced and compared. Conceptual modeling of selection and migration (the latter distinguished for its control by descent and type) yields relationships between the values of the measures that, when not fulfilled, lead to rejection of the model. Major results are: measures of dispersion that are not measures of differentiation cannot distinguish between the two perspectives; the commonly held view that type-independent migration homogenizes communities with respect to type distributions is invalid, though it does homogenize types for their community membership; after type-independent migration, differentiation among communities with respect to the source communities of their members bounds differentiation for any other trait; the effects of migration on CDT and TDC cannot always be realized by selection, and vice versa; effective proportions of migration can be obtained from measures of compositional differentiation and number of communities. The last result is based on the general concept of effective variables applied to conceptual models.