May inclusion of trait differences in genetic cluster analysis alter our views?

Populations differ not only in the frequency distributions of their traits. Differences between the states of traits may also be of relevance. Examples are genetic traits based on DNA fragment length polymorphisms, such as microsatellites. The new measure (delta) of the difference between two populations considers both types of difference. (delta) quantifies the changes that must be made in the frequencies of the trait states in the one population in order to match the frequency distribution in the second population, under the requirement that trait states be shifted to the most similar trait state possible, in analogy to the transportation problem of operations research. The properties of (delta) as a model-free, descriptive measure are contrasted to measures of population difference that apply the "FST-principle" to trait differences. Its applicability in phylogenetic analysis is demonstrated using isoenzyme and microsatellite marker data.