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

Abstract

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.<br>A estrutura geográfica das distâncias genéticas entre populações locais dentro das espécies, baseada em dados de aloenzimas, tem sido usualmente avaliada com algorítimos hierárquicos, como o método não ponderado por médias aritiméticas (UPGMA). A distorção produzida no processo de agrupamento é estimada por um coeficiente de correlação cofenética. Estas abordagens hierárquicas, entretanto, podem falhar em produzir uma representação acurada das distâncias genéticas entre populações em espaços de pequena dimensão, especialmente quando padrões contínuos (clinais) ou reticulares de variação existem. Neste trabalho, nós analisamos 50 matrizes de distância genética entre populações animais da literatura, variando de platelmintos a mamíferos, para avaliar em que situações o UPGMA é útil para entender os padrões de variação genética entre as populações. Os coeficientes de correlação cofenética, derivados do UPGMA baseados em três tipos de coeficientes de distância genética, foram correlacionados com outros parâmetros de cada matriz, incluind...

Geometric morphometrics of the wing as a tool for assigning genetic lineages and geographic origin to Melipona beecheii (Hymenoptera: Meliponini)

“…The first discriminant analysis, using the geographical origin of the colonies as labels, indicated that 13 Cartesian coordinates significantly contributed (α=0.05) to separation of the groups according to geographical origin (Wilk's dimensional representation of the calculated distances (Rodrigues and Diniz-Filho 1998). The discriminant functions and the aligned coordinates of the landmarks for each geographic population are listed in appendices I and II in the supplementary online material.…”

Hypothesis testing of genetic similarity based on RAPD data using Mantel tests and model matrices

“…In UPGMA clustering, the most commonly used measure of this distortion is the cophenetic correlation coefficient, which measures the correspondence between the original genetic distances among samples and the distances defined along the phenogram (Sneath and Sokal, 1973;Rodrigues and Diniz-Filho, 1998). A similar approach can be used to evaluate the results from ordination displays, although in this case there are also other specific measures of distortion, such as the accumulated explanatory power of the eigenvalues in PCORD or the "stress" value (S) in NMDS (Johnson and Wichern 1992).…”

“…Different microevolutionary processes acting at the populational level, especially those generating clinal or reticulated patterns of genetic variation across geographic space, always produce patterns of population differentiation that are difficult to represent in a few dimensions by clustering or ordination techniques (Lessa, 1990;Rodrigues and Diniz-Filho, 1998). Stochastic evolutionary processes at higher taxonomic levels, such as independent evolution by Brownian motion of quantitative characters or gene frequencies (Hansen and Martins, 1996;Diniz-Filho, 2000), generate a similar difficulty in representing genetic distances among species.…”

“…Despite these problems, in most cases the cophenetic correlations from UPGMA clustering of genetic distances, based on isozyme data from local populations, are elevated (Rodrigues and Diniz-Filho, 1998). However, using random amplified polymorphic DNA (RAPD) to assess genetic variability may be slightly more complicated compared to isozymes since the nature of the data may generate a large amount of random variation, especially at higher taxonomic levels .…”

“…Thus, despite the usefulness of RAPD in assessing patterns of genetic divergence among local populations (Swofford et al, 1996;Sunnucks, 2000;Russel et al, 2002), the clustering and ordination techniques commonly used may fail to accurately represent genetic distances, especially when dealing with Jaccard coefficients calculated among individuals. This problem can often be detected as a low cophenetic correlation coefficient, a low support of many clusters following bootstrapping of the genetic distances, and low relative eigenvalues of the ordination axes (see Lessa, 1990;Rodrigues and Diniz-Filho, 1998).…”