DAPC

Discriminant Analysis of Principal Components (DAPC) is a multivariate method used to identify and describe genetic structure in populations. It combines data reduction by principal components analysis with discriminant analysis to emphasize variation between predefined groups, while minimizing variation within groups. DAPC is implemented in the R package adegenet and is commonly used in population genetics and conservation biology to summarize genetic differentiation and to assign individuals to groups.

The method begins with a dimensionality reduction step in which a subset of principal components is retained from the multilocus genotype data. A subsequent discriminant analysis is then performed on those retained PCs to derive linear discriminants that maximize between-group separation while minimizing within-group dispersion. The resulting discriminant functions provide a low-dimensional representation of the data that highlights the differences among groups. The approach can be used with predefined group memberships or with groups inferred by clustering methods such as find.clusters. In adegenet, functions such as xvalDapc help determine an appropriate number of PCs to retain, balancing bias and variance.

DAPC is primarily descriptive and supervised. It excels at visualizing and quantifying genetic structure, identifying diagnostic alleles, and performing assignment tests. However, its results depend on the quality and definition of the groups; inappropriate grouping can bias interpretations. The method does not model population history in a probabilistic framework, and the choice of how many PCs to retain can influence conclusions.

Originating from work by Jombart and colleagues in 2008, DAPC has become a standard tool in population genetics for exploring structure, monitoring genetic diversity, and supporting conservation management decisions.