The theory above works well if the markers are independent (that is have no LD), but in practice, and especially with the large genotype arrays that are beginning to be available, this is difficult to ensure. In extreme cases uncorrected LD will seriously distort the eigenvector/eigenvalue structure, making results difficult to interpret. Suppose, for example, that there is a large “block” [35,36] in which markers are in complete LD, and we have genotyped many markers in the block. A large eigenvector of our Wishart matrix X will tend to correlate with the genotype pattern in the block (all markers producing the same pattern). This will distort the eigenvector structure and also the distribution of eigenvalues.
