Supplementary Table 1. The two-locus genetic-effect design matrix (SAB) for the G2A model presented in Appendix B. Here p1 and p2 are the frequencies of the A1 and A2 alleles respectively, and q1 and q2 are the frequencies of the B1 and B2 alleles respectively. See Table 1 in the main text for other details and a complete description of the Table structure.

Genotypic values / Coefficients
R / aA / dA / iA / aB / dB / iB / aa / ad / ai / da / dd / di / ia / id / ii
G1111 / 1 / 2p2 / / 0 / 2q2 / / 0 / 4p2q2 / / 0 / / / 0 / 0 / 0 / 0
G1211 / 1 / p2 – p1 / 2p1p2 / 1 / 2q2 / / 0 / 2(p2 – p1) q2 / / 0 / 4 p1p2q2 / / 0 / 2q2 / / 0
G2111 / 1 / p2 – p1 / 2p1p2 / −1 / 2q2 / / 0 / 2(p2 – p1) q2 / / 0 / 4 p1p2q2 / / 0 / –2q2 / / 0
G2211 / 1 / −2p1 / / 0 / 2q2 / / 0 / –4p1q2 / / 0 / / / 0 / 0 / 0 / 0
G1112 / 1 / 2p2 / / 0 / q2 – q1 / 2q1q2 / 1 / 2p2 (q2 – q1) / 4 p2q1q2 / 2p2 / / / / 0 / 0 / 0
G1212 / 1 / p2 – p1 / 2p1p2 / 1 / q2 – q1 / 2q1q2 / 1 / (p2 – p1) (q2 – q1) / / p2 – p1 / / 4p1p2q1q2 / 2p1p2 / q2 – q1 / 2q1q2 / 1
G2112 / 1 / p2 – p1 / 2p1p2 / −1 / q2 – q1 / 2q1q2 / 1 / (p2 – p1) (q2 – q1) / / p2 – p1 / / 4p1p2q1q2 / 2p1p2 / –(q2 – q1) / –2q1q2 / –1
G2212 / 1 / −2p1 / / 0 / q2 – q1 / 2q1q2 / 1 / –2p1 (q2 – q1) / –4p1q1q2 / –2p1 / / / / 0 / 0 / 0
G1121 / 1 / 2p2 / / 0 / q2 – q1 / 2q1q2 / −1 / 2p2 (q2 – q1) / 4p2q1q2 / –2p2 / / / / 0 / 0 / 0
G1221 / 1 / p2 – p1 / 2p1p2 / 1 / q2 – q1 / 2q1q2 / −1 / (p2 – p1) (q2– q1) / / –(p2 – p1) / / 4 p1p2q1q2 / –2p1p2 / q2 – q1 / 2q1q2 / –1
G2121 / 1 / p2 – p1 / 2p1p2 / −1 / q2 – q1 / 2q1q2 / −1 / (p2 – p1) (q2 – q1) / / –(p2 – p1) / / 4 p1p2q1q2 / –2p1p2 / –(q2 – q1) / –2q1q2 / 1
G2221 / 1 / −2p1 / / 0 / q2 – q1 / 2q1q2 / −1 / –2p1 (q2 – q1) / –4 p1q1q2 / 2p1 / / / / 0 / 0 / 0
G1122 / 1 / 2p2 / / 0 / −2q1 / / 0 / –4p2q1 / / 0 / / / 0 / 0 / 0 / 0
G1222 / 1 / p2 – p1 / 2p1p2 / 1 / −2q1 / / 0 / –2q1 (p2 – p1) / / 0 / –4 p1p2q1 / / 0 / –2q2 / / 0
G2122 / 1 / p2 – p1 / 2p1p2 / −1 / −2q1 / / 0 / –2q1 (p2 – p1) / / 0 / –4 p1p2q1 / / 0 / 2q2 / / 0
G2222 / 1 / −2p1 / / 0 / −2q1 / / 0 / 4pq / / 0 / / / 0 / 0 / 0 / 0

Supplementary Table 2. The inverse of the two-locus genetic-effect design matrix (i.e., ) shown in Supplementary Table 2. The inverse of the genetic-effect design matrix gives the unique solution to the two-locus vector of genetic effects, EAB, i.e., . Therefore, the resulting matrix gives the definition of the 16 terms in the two-locus vector of genetic effects. The columns of the matrix are, therefore, labeled with the corresponding genotypic value and the rows are labeled with the corresponding genetic effect. See Table 2 in the main text for other details.

Genetic effects / Genotypic values
G1111 / G1211 / G2111 / G2211 / G1112 / G1212 / G2112 / G2212 / G1121 / G1221 / G2121 / G2221 / G1122 / G1222 / G2122 / G2222
R / / / / / / / / / / / / / / / /
aA / / / / / / / / / / / / / / / /
dA / / / / / / / / / / / / / / / /
iA / 0 / / / 0 / 0 / / / 0 / 0 / / / 0 / 0 / / / 0
aB / / / / / / / / / / / / / / / /
dB / / / / / / / / / / / / / / / /
iB / 0 / 0 / 0 / 0 / / / / / / / / / 0 / 0 / 0 / 0
aa / / / / / / / / / / / / / / / /
ad / / / / / / / / / / / / / / / /
ai / 0 / 0 / 0 / 0 / / / / / / / / / 0 / 0 / 0 / 0
da / / / / / / / / / / / / / / / /
dd / / / / / / / / / / / / / / / /
di / 0 / 0 / 0 / 0 / / / / / / / / / 0 / 0 / 0 / 0
ia / 0 / / / 0 / 0 / / / 0 / 0 / / / 0 / 0 / / / 0
id / 0 / / / 0 / 0 / / / 0 / 0 / / / 0 / 0 / / / 0
ii / 0 / 0 / 0 / 0 / 0 / / / 0 / 0 / / / 0 / 0 / 0 / 0 / 0

Supplementary Table 3. Significance thresholds for QTL analysis. Given for each chromosome are the total number of markers analyze, the effective number of markers (Meff), calculated following Li and Ji (Li and Ji 2005) and the corresponding LPR Bonferroni threshold based on Meff. The table also includes the corresponding values for the whole genome.

Chrom. / # of markers / Meff / LPR
1 / 31 / 11 / 2.33
2 / 28 / 10 / 2.29
3 / 26 / 9 / 2.25
4 / 24 / 9 / 2.25
5 / 19 / 8 / 2.19
6 / 22 / 8 / 2.19
7 / 18 / 7 / 2.14
8 / 13 / 7 / 2.14
9 / 19 / 8 / 2.19
10 / 18 / 7 / 2.14
11 / 21 / 8 / 2.19
12 / 19 / 7 / 2.14
13 / 18 / 7 / 2.14
14 / 14 / 6 / 2.07
15 / 16 / 6 / 2.07
16 / 13 / 6 / 2.07
17 / 13 / 6 / 2.07
18 / 13 / 5 / 1.99
19 / 8 / 5 / 1.99
Genome / 353 / 133 / 3.41