*3.7. Regularization Method*

Alternatively, we also conducted regularization methods, such as LASSO, to identify candidate regions associated with the seed aspect ratio (Figure 6) [71]. The regularization method was performed using an entire dataset at a time and could select several putative markers most likely related to the trait based on the value of selection probability, whereas the ECMLM analysis only tested one marker at a time. As a result, one SNP locus (AX-177640219 on Araip.B08) was identified as being most likely related to the seed aspect ratio based on the selection probability at the permuted threshold 0.894, and was also found to be highly significantly associated in the GAPIT analysis (Figure 6). When loosening the strict threshold to 0.506, a total of six SNPs were additionally identified, AX-177640938 on chromosome Araip.B08, AX-147218661 on Aradu.A03, AX-147251864 on Araip.B06, AX-176802342 on Araip.B04, AX-176791478 on Aradu.A02, and AX-176800768 on Aradu.A01, which presented significant associations with ECMLM results indicating that the regions flanked with these markers might be candidate regions for possible determination of seed shape in peanuts. Therefore, the use of both methods to conduct association studies is beneficial in (1) boosting confidence in the case where common markers are identified and (2) to maximize the possibility of finding new significant markers associated with a trait of interest.

**Figure 6.** Manhattan plot of a genome-wide association analysis by the least absolute and shrinkage selection operator (LASSO).
