Additional file 2: Figure S1. Title: QQ plot for the maize panel, with kinship (GBLUP) (black diamond), the Gaussian kernel (gray filled circle), the K-kernel (orange square). Description: The C-kernel result is not plotted because it was equivalent to the GBLUP for that trait (as many clusters as individuals). Figure S2. Title: QQ plots for the rice panel, with kinship (GBLUP) (black diamond), the Gaussian kernel (gray filled circle), the K-kernel (orange square) and the C-kernel (blue triangle). Description: The rice dataset is in Table 1 and more details on the traits are available in Additional file 1 Table S1; for all kernels, the first four principal components of the markers design matrix were fitted as fixed effect. Figure S3. Title: Bootstrap of the C-kernel likelihood ratio test as a function of the number of markers in the maize panel for flowering time. Description: This figure presents additional results on C-kernel sensitivity to marker density.