Measuring Differences of Trait Distributions Between Populations

Abstract

A measure of difference between populations for a trait should reflect not only the differences in the relative frequencies of the trait states but also the trait differences between the states. Common approaches to measuring differences between populations rely on distance, probability, or variance concepts. To overcome conceptual problems of these approaches, a new difference measure D is presented that is based on both frequency and trait differences. For two populations, D expresses the degree to which the frequency distribution of the trait states within one population must be transformed in order to make it match the distribution in the other population. This is done by shifting the relative frequency excesses of trait states to other trait states of deficient frequency, where shifts occur between as similar states as possible. D equals the minimum sum of the shifted frequencies weighted by the respective trait differences. Its bounds are functions of the difference measure d 0 , which considers only differences in relative frequency. The computer program DeltaS applies an algorithm from operations research to calculate D. The effect of including trait differences is demonstrated by the topological differences observed between D-and d 0 -dendrograms constructed from microsatellite allele frequencies in four riparian stands of black poplar (Populus nigra), where the trait difference between two alleles equals the difference in numbers of tandem repeats. D is applicable to all traits for which trait differences are measurable, and it is shown to have elementary linearity properties that considerably simplify its interpretation.

A rigorous comparison of sexual selection indexes via simulations of diverse mating systems

“…Consequently, we instead assessed proxy measures against the "distributional selection differential" d′, a measure that integrates both linear and nonlinear effects of selection on a trait distribution (Table 1; details in Supporting Information). Equivalent metrics have been used to quantify differences in trait distributions in other contexts (60,61).…”

Genetic diversity of Patellifolia patellaris from the Iberian Peninsula, a crop wild relative of cultivated beets

“…Thus, if we do not analyse the compositional differentiation at higher levels of genic integration, we miss information that may help explaining interactions between genotypes and selective forces (Gillet and Gregorius 2008). To this end, Gregorius et al (2003) developed the measure D of genetic distance between populations. So far, the measure D has only been used in forest tree population genetics (Gregorius and Kownatzki 2005;Gillet and Gregorius 2008) and, except for one single case (Frese et al 2013), not yet for the analysis of crop species and their wild allies.…”

Detecting differential viability selection between environments by analysis of compositional differentiation at different levels of genetic integration

“…Brought to you by | MIT Libraries Authenticated Download Date | 5/11/18 11:11 PM The genetic distance Δ between two demes additionally takes such structural differences between genetic types in the form of the above introduced genic differences into account (Gregorius et al, 2003;Gillet et al, 2004;Gillet and Gregorius, 2008). Δ equals the minimum "cost" of shifting genetic types in one of the demes to other genetic types in order to make the distribution of genetic types in this deme match the distribution in the other deme.…”

“…The measures of compositional differentiation δ SD and Δ SD , in contrast, directly measure the frequency differences between environments at any given level of genetic integration (Gregorius and Roberds, 1986;Gregorius et al, 2003;Gillet et al, 2004;Gillet and Gregorius, 2008). At still higher levels of genetic integration, multiple loci can be considered on the basis of measures of genic difference between multi-locus genotypes.…”