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PLANT GENETIC RESOURCES

The Modified Location Model for Classifying Genetic Resources

II. Unrestricted Variance–Covariance Matrices

^a Facultad de Agronomía, Univ. de la República Oriental del Uruguay, Garzón 780, Montevideo, Uruguay
^b Maize Genetic Resources Unit, CIMMYT, Apdo. Postal 6-641, 06600 Mexico DF, México
^c National Seed Storage Laboratory, USDA-ARS, Fort Collins, CO 80523

* Corresponding author (j.crossa{at}cgiar.org)

When evaluating genetic resources and forming core subsets, gene bank accessions are classified into homogeneous and well-separated groups. The modified location model (MLM) is used in the context of a two-stage clustering strategy in which initial groups are first defined using a hierarchical clustering method (such as Ward) and then the MLM is applied to the groups that are formed (Ward-MLM). The MLM allows assuming correlations (between attributes) and variances (of the attributes) among subpopulations (SPs) to be equal (homogeneous, HOM) or different (heterogeneous, HET). The objectives of this study were (i) to compare the effect of assuming homogeneity with the effect of assuming heterogeneity of variance–covariance matrices on the classification of two simulated data sets using the Ward-MLM strategy; and (ii) to make the same type of comparison using data from maize (Zea mays L.) accessions from nine countries. When simulated HOM data were analyzed with the HOM model and the simulated HET data were analyzed with the HET model, some of the original SPs were represented in the resulting clusters but others changed and formed more separated groups. The HET model always formed the most compact and separated clusters, even for HOM data. Classification of 10 real data sets showed that the HET model produced more compact and well-separated groups than the HOM model. However, only the HOM model identified and grouped a small number of observations with very peculiar attributes. Although the HET model may suffice in most situations, the recommended strategy when classifying genetic resources would be to use both models.

Abbreviations: EM, expectation maximization • GM, Gaussian model • HET, heterogeneous • HOM, homogeneous • LM, location model • MLM, modified location model • SP, subpopulation

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