We estimated the variance attributable to the X chromosome using the method we recently developed10. In brief, we estimated the GRM for the X-chromosome (AX) using the following equations A^jkM=∑iN(xijM−pi)(xikM−pi)pi(1−pi) for a male-male pair A^jkF=∑iN(xijF−2pi)(xikF−2pi)2pi(1−pi) for a female-female pair, and A^jkMF=∑iN(xijM−pi)(xikF−2pi)2pi(1−pi) for a male-female pair,where xijM and xijF are the number of copies of the reference allele for an X-chromosome SNP for a male and a female, respectively, pi is the frequency of the reference allele and N is the number of SNPs. Assuming the male-female genetic correlation to be 1, the X-linked phenotypic covariance is covX(yjM,ykM)=AjkMσX(M)2 for a male-male pair, covX(yjF,ykF)=AjkFσX(F)2 for a female-female pair, or covX(yjM,ykF)=AjkMFσX(M)σX(F) for a male-female pair25,40, where σX(M)2 and σX(F)2 are X-linked genetic variances for males and females, respectively. Assumptions about inactivity of the X-chromosome (dosage compensation) imposed a relationship between σX(M)2 and σX(F)2, which allow a single variance component σX(F)2 to account for the X-linked genetic variance for both sexes. Therefore, we can express the X-linked phenotypic covariances as covX(yjM,ykM)=d2AjkMσX(F)2, covX(yjF,ykF)=AjkFσX(F)2, and covX(yjM,ykF)=dAjkMFσX(F)2, where d is the lyonization coefficient, σX(M)=dσX(F), which takes 1
