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:

Reviews

• 1997 GENOMIC IMPRINTING IN MAMMALS
• 1999 Basics of gametic imprinting
• 2003 What good is genomic imprinting: the function of parent-specific gene expression
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Models

• 2001 Assessment of Parent-of-Origin Effects in Linkage Analysis of Quantitative Traits
• 2002 The Correlation Between Relatives on the Supposition of Genomic Imprinting
• 2002 Testing for Genetic Linkage in Families by a Variance-Components Approach in the Presence of Genomic Imprinting
• 2003 Genomic Imprinting and Linkage Test for Quantitative-Trait Loci in Extended Pedigrees
• 2006 Influence of Mom and Dad: Quantitative Genetic Models for Maternal Effects and Genomic Imprinting
• 2007 A statistical model for dissecting genomic imprinting through genetic mapping
• 2007 A simple method for detection of imprinting effects based on case–parents trios
• 2007 A random model for mapping imprinted quantitative trait loci in a structured pedigree: An implication for mapping canine hip dysplasia
• 2008 Maternal Effects as the Cause of Parent-of-Origin Effects That Mimic Genomic Imprinting

Applications

• 2003 Linkage analysis of adult height with parent-of-origin effects in the Framingham Heart Study
• 2004 Quantitative trait loci with parent-of-origin effects in chicken
• 2008 Genomic imprinting effects on adult body composition in mice

"Our [Their] results show that the effects of genomic imprinting are relatively small, with reciprocal heterozygotes differing by 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

• 1996 The evolution of genomic imprinting
• 1998 Genetic Conflicts, Multiple Paternity and the Evolution of Genomic Imprinting
• 2000 Population Genetics and Evolution of Genomic Imprinting
• 2001 The Evolution of X-Linked Genomic Imprinting
• 2004 The Effect of Genetic Conflict on Genomic Imprinting and Modification of Expression at a Sex-Linked Locus
• 2006 A Maternal–Offspring Coadaptation Theory for the Evolution of Genomic Imprinting
• 2006 A Chip off the Old Block: A Model for the Evolution of Genomic Imprinting via Selection for Parental Similarity
• 2006 Population Models of Genomic Imprinting. II. Maternal and Fertility Selection
• 2007 Sex-Specific Viability, Sex Linkage and Dominance in Genomic Imprinting