Table 1. Examples of 3 pairs of SNPs in 10 individuals (P1, …, P10) that illustrate theability of the maximum relationship R_ij, and maximum CCC_ij, i e {A,a}, j e {B, b}, to capture more meaningful and robust SNP correlations compared to PCC and r².

	Genotype of 10 individuals										|PCC|	r2	max Rij	max CCCij
	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10
SNP 1	Aa	AA	AA	AA	AA	AA	AA	AA	AA	AA	0.1	0.0	0.9	0.5
SNP 2	bb	Bb	bb	bb	bb	bb	bb	bb	bb	bb
SNP 3	Aa	Aa	AA	AA	AA	AA	AA	AA	AA	AA	0.7	0.5	0.9	0.6
SNP 4	bb	Bb	bb	bb	bb	bb	bb	bb	bb	bb
SNP 5	AA	AA	AA	AA	AA	aa	Aa	AA	aa	aa	0.3	0.0	0.5	0.7
SNP 6	bb	bb	bb	bb	bb	Bb	BB	Bb	BB	bb

Note: For the first two pairs of SNPs, P3-P10 are perfectly matched with ‘AA’|‘bb’genotypes. The only difference between the two examples is that for individual P2, SNP 1 is ‘AA’ and SNP 3 is ‘Aa’. While the PCC and r² values are highly sensitive to this small difference, CCC exhibits little sensitivity. In the third example, SNPs 5 and 6 are perfectly matched for P1-P5 in half of the individuals and uncorrelated in individuals P6-P10. PCC and r² were overwhelmed by the lack of correlation in P6-P10 and returned low values. In contrast, CCC looked over the heterogeneity and correctly captured a high correlation value CCC_Ab for the ‘Ab’ relationship in P1-P5. Note that the CCC value for ‘Ab’ is higher for this example than it is for the first two pairs of SNPs, despite the fact that had more ‘AA’|‘bb’ individuals. This is because CCC adjusts for chance pairing due to varying allelic frequencies. In the second pair, the allele frequency is 0.90 for ‘A’ of SNP 3 and 0.95 for ‘b’ of SNP 4, which gives an expected frequency of 0.73 (0.90*0.90*0.95*0.95) for ‘AA’|‘bb’ just by chance paring. Since the observed frequency of ‘AA’|‘bb’ of 0.8 is only slighter greater than expected by chance, the CCCAb value is lower. However, in the third pair, where the expected frequency for ‘AA’|‘bb’ is 0.21 and the observed frequency is 0.50, the CCC gives a high CCC_Ab value owing to the excess of ‘AA’|‘bb’ pairing than expected by chance.Thus, CCC is able to capture meaningful correlations more accurately than PCC or r².