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Gregorius H.-R.,Institute For Populations Und Okologische Genetik
Diversity | Year: 2010

Generally speaking, the term differentiation refers to differences between collections for the distribution of specified traits of their members, while diversity deals with (effective) numbers of trait states (types). Counting numbers of types implies discrete traits such as alleles and genotypes in population genetics or species and taxa in ecology. Comparisons between the concepts of differentiation and diversity therefore primarily refer to discrete traits. Diversity is related to differentiation through the idea that the total diversity of a subdivided collection should be composed of the diversity within the subcollections and a complement called "diversity between subcollections". The idea goes back to the perception that the mixing of differentiated collections increases diversity. Several existing concepts of "diversity between subcollections" are based on this idea. Among them, β-diversity and fixation (inadvertently called differentiation) are the most prominent in ecology and in population genetics, respectively. The pertaining measures are shown to quantify the effect of differentiation in terms of diversity components, though from a dual perspective: the classical perspective of differentiation between collections for their type compositions, and the reverse perspective of differentiation between types for their collection affiliations. A series of measures of diversity-oriented differentiation is presented that consider this dual perspective at two levels of diversity partitioning: the overall type or subcollection diversity and the joint type-subcollection diversity. It turns out that, in contrast with common notions, the measures of fixation (such as F ST or G ST) refer to the perspective of type rather than subcollection differentiation. This unexpected observation strongly suggests that the popular interpretations of fixation measures must be reconsidered. © 2010 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. Source


Gregorius H.-R.,Institute For Populations Und Okologische Genetik | Kownatzki D.,University of Hamburg | Holtken A.M.,University of Hamburg
Perspectives in Plant Ecology, Evolution and Systematics | Year: 2011

The spatial distribution of wild cherry is characterized by a mixture of scattered and clumped occurrences. In addition, the mating relations of the species are determined by its capacity for clonal reproduction in combination with its self-incompatibility system and by insect pollination. Common paternity analyses basically take the spatial distances between mates into account, but fail to incorporate structural factors in addition to distance such as the patchiness of individuals. We determined mating relations via mating preferences (proportion of matings realized within a group divided by the proportion of potential matings within that group) in various sizes and forms of clusters. The results did not support the common view that mating frequencies more or less steadily decline with increasing spatial distance between mating partners. In fact, mating took place preferentially among members of intermediate sized clusters. However, preference patterns varied distinctly among individual seed trees depending on the shape of neighboring tree clusters and (possibly) attractiveness to pollinators. Distinct preferences for stand-external pollen parents were observed for seed trees located at the border of the higher density area of the stand with stand-external matings generally exceeding stand-internal matings. © 2011 Perspectives in Plant Ecology, Evolution and Systematics. Source


Gregorius H.-R.,Institute For Populations Und Okologische Genetik
Ecological Modelling | Year: 2012

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. © 2011 Elsevier B.V. Source


Gregorius H.-R.,Institute For Populations Und Okologische Genetik | Gregorius H.-R.,University of Gottingen
Theoretical Ecology | Year: 2014

The notion that trait variation is partitioned among communities essentially rests on the supposition that the total variation in the metacommunity exceeds the variation within the communities due to differences between their trait distributions (the partitioning principle). Two elementary perspectives of partitioning can be distinguished: apportionment (members of the same community tend to hold the same trait state) and differentiation (members of different communities tend to hold different trait states). While the apportionment perspective reaches its extreme when each community is monomorphic (fixation), the differentiation perspective does so if communities share no trait states. Even though both perspectives can be shown to be involved in the analysis of community dynamics, their assessment is still almost completely limited to the apportionment perspective (chiefly G ST and its relatives). To overcome this limitation, methods of quantifying both partitioning perspectives are developed for qualitatively and quantitatively varying traits, where variation is represented by the differences in type resulting from sampling two individuals. It is shown that the validity of the partitioning principle and the design of corresponding measures crucially depend on proper specification of the modes of sampling and specification of differences between types that follow a concavity principle. This approach allows comparison between measures of apportionment and measures of differentiation. Such comparisons enable conclusions about the share that random (drift) and directional (selection, migration) processes have in the partitioning of variation among communities. One of the more far-reaching conclusions is that effects of forces apportioning variation outperform the effects of forces of differentiation, if the average similarity within communities exceeds the average difference between them. © 2014 Springer Science+Business Media Dordrecht. Source


Gregorius H.-R.,University of Gottingen | Gregorius H.-R.,Institute For Populations Und Okologische Genetik
Acta Biotheoretica | Year: 2011

Because of their elementary significance in almost all fields of science, measures of association between two variables or traits are abundant and multiform. One aspect of association that is of considerable interest, especially in population genetics and ecology, seems to be widely ignored. This aspect concerns association between complex traits that show variable and arbitrarily defined state differences. Among such traits are genetic characters controlled by many and potentially polyploid loci, species characteristics, and environmental variables, all of which may be mutually and asymmetrically associated. A concept of directed association of one trait with another is developed here that relies solely on difference measures between the states of a trait. Associations are considered at three levels: between individual states of two variables, between an individual state of one variable and the totality of the other variable, and between two variables. Relations to known concepts of association are identified. In particular, measures at the latter two levels turn out to be interpretable as measures of differentiation. Examples are given for areas of application (search for functional relationships, distribution of variation over populations, genomic associations, spatiogenetic structure). © 2011 The Author(s). Source

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