Run times for PUMA and other available software for identical analyses.

For a typical simulated data set with 650 K markers, no pre-screening of markers and sample sizes, , of 1000, 2000 and 5000, we report run times for available software and PUMA performing the same analyses. For Lasso, we had Mendel and PUMA perform a search of tuning parameter space in order to return markers with nonzero coefficients. For NEG, we set HyperLasso to its default tuning parameter values and ran PUMA with the same values. For MCP, we set grpreg and PUMA to perform a search of tuning parameter space in order to return markers with nonzero coefficients, where was set to 30 as per Ayers and Cordell [32]. Analysis was performed on an 8 core Intel® Xeon® E5520 @ 2.27 GHz with 32 Gb memory. NA indicates the program crashed due to insufficient memory; we note that this is due to technical limitations of Mendel and R, in which grpreg runs.