Genotypic values under genomic imprinting model

I came across paper by Spencer where he develops the quantitative genetic theory for a single loci with two alleles (A1 and A2) with genomic imprinting. Genomic imprinting is also known as parent-of-origin effect. If there is no imprinting, there are three possible genotypes A1/A1, A1/A2, and A2/A2 and therefore three different genotypic values. However, when imprinting is in place, the mean of genotypes depends on alleles and origin of alleles e.g. maternal imprinting means that alleles inherited from a father are more expressed. Spencer, as well as many others (see bellow), assumed that genomic imprinting changes the mean of heterozygotes. Additionally, heterozygotes need to be distinguished i.e. A1/A2 and A2/A1 are treated separately. He showed the following genotypes: A1/A1, A1/A2, A2/A1, and A2/A2. I was a bit surprised, since I excepted that there should also be some change in homozygotes.

If we assume that there is imprinting, then alleles have different effect when inherited from a particular parent. Naive approach would be to mark alleles as A1, A1+, A2, and A2+, where + means additional effect. However, this is actually a set of four alleles i.e. A1, A2, A3, and A4, from which we can construct 16 ordered genotypes. This is not OK. Let us mark alleles as A1f, A1m, A2f, and A2m, where f means father and m means mother. We can construct the following ordered genotypes: A1m/A1f, A1m/A2f, A2m/A1f, and A2m/A2f. Therefore, there are four possible ordered genotypes and it is clear that only four different genotypic values need to be defined by the model.

Here is a list of some papers on the genomic imprinting - I am sure I missed a bunch of important ones:

"Our [Their] results show that the effects of genomic imprinting are relatively small, with reciprocal heterozygotes differing by {approx}0.25 standard deviation units and the effects at each locus accounting for 1% to 4% of the phenotypic variance. We detected a variety of imprinting patterns, with paternal expression being the most common. These results indicate that genomic imprinting has small, but detectable, effects on the normal variation of complex traits in adults and is likely to be more common than usually thought."
Evolution of imprinting

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