Schematic representation of variance attributable to maternal transmitted, maternal non-transmitted and paternal transmitted haplotypes in H-GCTA.

Schematic representation of variance attributable to maternal transmitted (), maternal non-transmitted () and paternal transmitted () haplotypes in H-GCTA – Z and W are the sets of causal variants with maternal and fetal effects, respectively. S1 (Black squares), S2 (orange circles) and S3 (purple triangles) are sets of causal variants with explicit maternal effects, joint-maternal-fetal effects and explicit fetal effects such that S1 ∈ Z, S2 = Z ∩ W and S3 ∈ W. and are causal effects through mother and fetus and and are reference allele frequencies of a causal variant in mother and fetus, respectively. Since each allele is a random draw from Bernoulli distribution, variance in terms of allele frequency is represented as and in mother and fetus, respectively. m1 affects the phenotype through maternal transmitted alleles in mother () and maternal transmitted alleles in fetus (). Likewise, and represent the maternal non-transmitted and paternal transmitted alleles. Therefore, allelic effects - , (in the absence of POEs) and is the covariance of two binomial random variables m1’ and m1” present in mother and fetus, respectively; where, ρ and <i>σ</i> represent correlation and standard deviation of respective alleles. For a causal variant with joint maternal-fetal effect, in a random mating population, therefore, and total phenotypic variance explained by m1, m2 and p1 is . (PDF)