Hierarchical structure of genetic distances: Effects of matrix size, spatial distribution and correlation structure among gene frequencies

Geographic structure of genetic distances among local populations within species, based on allozyme data, has usually been evaluated by estimating genetic distances clustered with hierarchical algorithms, such as the unweighted pair-group method by arithmetic averages (UPGMA). The distortion produced in the clustering process is estimated by the cophenetic correlation coefficient. This hierarchical approach, however, can fail to produce an accurate representation of genetic distances among populations in a low dimensional space, especially when continuous (clinal) or reticulate patterns of variation exist. In the present study, we analyzed 50 genetic distance matrices from the literature, for animal taxa ranging from Platyhelminthes to Mammalia, in order to determine in which situations the UPGMA is useful to understand patterns of genetic variation among populations. The cophenetic correlation coefficients, derived from UPGMA based on three types of genetic distance coefficients, were correlated with other parameters of each matrix, including number of populations, loci, alleles, maximum geographic distance among populations, relative magnitude of the first eigenvalue of covariance matrix among alleles and logarithm of body size. Most cophenetic correlations were higher than 0.80, and the highest values appeared for Nei's and Rogers' genetic distances. The relationship between cophenetic correlation coefficients and the other parameters analyzed was defined by an "envelope space", forming triangles in which higher values of cophenetic correlations are found for higher values in the parameters, though low values do not necessarily correspond to high cophenetic correlations. We concluded that UPGMA is useful to describe genetic distances based on large distance matrices (both in terms of elevated number of populations or alleles), when dimensionality of the system is low (matrices with large first eigenvalues) or when local populations are separated by large geographical distances.