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 under the hypothesis of equal X-linked genetic variance for both sexes, takes 12 under the hypothesis of no dosage compensation (both X-chromosomes are active for females) and takes 2 under the hypothesis of full dosage compensation (complete inactivity of one X-chromosome for females) (Supplementary Note). In the analysis of MLM, we took the lyonization coefficient into the account by parameterizing the raw Ax matrix, i.e. AXP=d2AX for male pairs, AXP=AX for female pairs and AXP=dAX for male-female pairs. We estimated σX(F)2 under the three hypotheses by fitting the parameterized GRM for the X-chromosome ( AXP) conditional on the GRM estimated from all autosomal SNPs in an MLM y=Xβ+gX+gG+ε, where gX is a vector of X-linked genetic effects with var(gX)=AXPσX(F)2.
