. 2009 Mar 12;364(1520):1107–1115. doi: 10.1098/rstb.2008.0238

Table 4.

An example of an interaction between the maternal and zygotic genotypes. (The locus expressed in offspring has two alleles, A₁ and A₂, with frequencies p₁ and p₂ while the maternal genotype is defined by a second locus that has two alleles, B₁ and B₂, with frequencies x₁ and x₂. The cells show the expected offspring (zygotic) phenotypes and the frequencies (in parentheses) of the nine maternal–offspring genotype combinations. The locus shows an additive-by-additive interaction effect, where the additive maternal effect depends on the offspring genotype and vice versa. The A₁ allele has a+a effect on the offspring phenotype while the A₂ allele has a−a effect. The column labelled ${\bar{z}}_{maternal}$ gives the mean phenotypes of offspring produced by the three maternal genotypes at the B locus while ${\bar{z}}_{offspring}$ gives the mean phenotypes of the three offspring genotypes at the A locus.)

		offspring genotype

		A₁A₁	A₂A₁	A₂A₂	${\bar{z}}_{maternal}$
maternal genotype	B₁B₁	+a ( $p_{1}^{2} x_{1}^{2}$ )	0 ( $2 p_{1} p_{2} x_{1}^{2}$ )	−a ( $p_{2}^{2} x_{1}^{2}$ )	+a(p₁ − p₂)
	B₁B₂	0 ( $p_{1}^{2} 2 x_{1} x_{2}$ )	0 ( $2 p_{1} p_{2} 2 x_{1} x_{2}$ )	0 ( $p_{2}^{2} 2 x_{1} x_{2}$ )	0
	B₂B₂	−a ( $p_{1}^{2} x_{2}^{2}$ )	0 ( $2 p_{1} p_{2} x_{2}^{2}$ )	+a ( $p_{2}^{2} x_{2}^{2}$ )	−a(p₁ − p₂)
${\bar{z}}_{offspring}$		+a(x₁−x₂)	0	−a(x₁−x₂)