[2]yj=μ+gj+ejandgj=∑i=1mzijui where gi is the total genetic effect of an individual j; m is the number of causal loci; ui is the scaled additive effect of the i-th causal variant; zij takes value of −2fi/2fi(1−fi),(1−2fi)/2fi(1−fi) or 2(1−fi)/2fi(1−fi) if the genotype of the j-th individual at locus i is qq, Qq or QQ, respectively, with fi the frequency of Q allele at locus i (alleles are arbitrarily called Q or q)20,29; E(zij)= 0 and var(zij)= 1. In matrix notation, y=μ1+ g+ e and g= Zu. We treat u as random effects and assume u∼N(0,Iσu2), with σu2 being the variance of causal effects; then gj∼N(0,σg2=mσu2), where σg2 is variance of total additive genetic effects, and the variance-covariance matrix of y (the vector of observations) can be expressed as
