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A complete classification of epistatic two-locus models.

Hallgrímsdóttir IB, Yuster DS - BMC Genet. (2008)

Bottom Line: Our approach is geometric and we show that there are 387 distinct types of two-locus models, which can be reduced to 69 when symmetry between loci and alleles is accounted for.The circuits provide information on epistasis beyond that contained in the additive x additive, additive x dominance, and dominance x dominance interaction terms.We discuss the connection between our classification and standard epistatic models and demonstrate its utility by analyzing a previously published dataset.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Statistics, University of Oxford, 1 South Parks Road, OX1 3TG, UK. ingileif@stats.ox.ac.uk

ABSTRACT

Background: The study of epistasis is of great importance in statistical genetics in fields such as linkage and association analysis and QTL mapping. In an effort to classify the types of epistasis in the case of two biallelic loci Li and Reich listed and described all models in the simplest case of 0/1 penetrance values. However, they left open the problem of finding a classification of two-locus models with continuous penetrance values.

Results: We provide a complete classification of biallelic two-locus models. In addition to solving the classification problem for dichotomous trait disease models, our results apply to any instance where real numbers are assigned to genotypes, and provide a complete framework for studying epistasis in QTL data. Our approach is geometric and we show that there are 387 distinct types of two-locus models, which can be reduced to 69 when symmetry between loci and alleles is accounted for. The model types are defined by 86 circuits, which are linear combinations of genotype values, each of which measures a fundamental unit of interaction.

Conclusion: The circuits provide information on epistasis beyond that contained in the additive x additive, additive x dominance, and dominance x dominance interaction terms. We discuss the connection between our classification and standard epistatic models and demonstrate its utility by analyzing a previously published dataset.

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Related in: MedlinePlus

Shapes of two-locus models. Epistastic models. The tables list the genotype values associated with four epistatic models and below each table is the shape induced by a model with purely add × add, add × dom, dom × add or dom × dom interaction.
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Figure 5: Shapes of two-locus models. Epistastic models. The tables list the genotype values associated with four epistatic models and below each table is the shape induced by a model with purely add × add, add × dom, dom × add or dom × dom interaction.

Mentions: In population genetics and in the study of quantitative traits, two-locus models are classified according to the type of epistatic effects. Four commonly studied patterns of epistasis are additive × additive, additive × dominance, dominance × additive and dominance × dominance. In an additive × additive model two double homozygotes, aa/bb and AA/BB, have higher phenotypic mean (or fitness) than expected, but the other two, aa/BB and AA/bb, have lower phenotypic mean than expected. A numeric representation of the four types is given in Figure 5 and the corresponding shapes are also shown. If these epistatic effects are added to a fully additive two-locus model, the resulting shape will be the one shown in Figure 5. However, the epistasis observed in real data is seldom purely of one type and although e.g. dominance × dominance epistasis is present in the data, the resulting shape can be different. If the dominance terms, δa and δb, are non-zero, the resulting shape will be the dominance × dominance shape, with the possible addition of one or both of the horizontal and vertical lines through the middle of the shape (depending on the magnitude of the dominance terms). A model with both additive × dominance and dominance × additive interaction can fall into one of three shapes. If either the additive × dominance or the dominance × additive interaction is much stronger than the other, the corresponding shape will dominate. If the magnitude of both types of interaction is similar, the resulting shape will be the shape shown in Figure 1 or any rotation thereof. Thus from the shape we can often infer what type of interaction is the strongest in the data.


A complete classification of epistatic two-locus models.

Hallgrímsdóttir IB, Yuster DS - BMC Genet. (2008)

Shapes of two-locus models. Epistastic models. The tables list the genotype values associated with four epistatic models and below each table is the shape induced by a model with purely add × add, add × dom, dom × add or dom × dom interaction.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2289835&req=5

Figure 5: Shapes of two-locus models. Epistastic models. The tables list the genotype values associated with four epistatic models and below each table is the shape induced by a model with purely add × add, add × dom, dom × add or dom × dom interaction.
Mentions: In population genetics and in the study of quantitative traits, two-locus models are classified according to the type of epistatic effects. Four commonly studied patterns of epistasis are additive × additive, additive × dominance, dominance × additive and dominance × dominance. In an additive × additive model two double homozygotes, aa/bb and AA/BB, have higher phenotypic mean (or fitness) than expected, but the other two, aa/BB and AA/bb, have lower phenotypic mean than expected. A numeric representation of the four types is given in Figure 5 and the corresponding shapes are also shown. If these epistatic effects are added to a fully additive two-locus model, the resulting shape will be the one shown in Figure 5. However, the epistasis observed in real data is seldom purely of one type and although e.g. dominance × dominance epistasis is present in the data, the resulting shape can be different. If the dominance terms, δa and δb, are non-zero, the resulting shape will be the dominance × dominance shape, with the possible addition of one or both of the horizontal and vertical lines through the middle of the shape (depending on the magnitude of the dominance terms). A model with both additive × dominance and dominance × additive interaction can fall into one of three shapes. If either the additive × dominance or the dominance × additive interaction is much stronger than the other, the corresponding shape will dominate. If the magnitude of both types of interaction is similar, the resulting shape will be the shape shown in Figure 1 or any rotation thereof. Thus from the shape we can often infer what type of interaction is the strongest in the data.

Bottom Line: Our approach is geometric and we show that there are 387 distinct types of two-locus models, which can be reduced to 69 when symmetry between loci and alleles is accounted for.The circuits provide information on epistasis beyond that contained in the additive x additive, additive x dominance, and dominance x dominance interaction terms.We discuss the connection between our classification and standard epistatic models and demonstrate its utility by analyzing a previously published dataset.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Statistics, University of Oxford, 1 South Parks Road, OX1 3TG, UK. ingileif@stats.ox.ac.uk

ABSTRACT

Background: The study of epistasis is of great importance in statistical genetics in fields such as linkage and association analysis and QTL mapping. In an effort to classify the types of epistasis in the case of two biallelic loci Li and Reich listed and described all models in the simplest case of 0/1 penetrance values. However, they left open the problem of finding a classification of two-locus models with continuous penetrance values.

Results: We provide a complete classification of biallelic two-locus models. In addition to solving the classification problem for dichotomous trait disease models, our results apply to any instance where real numbers are assigned to genotypes, and provide a complete framework for studying epistasis in QTL data. Our approach is geometric and we show that there are 387 distinct types of two-locus models, which can be reduced to 69 when symmetry between loci and alleles is accounted for. The model types are defined by 86 circuits, which are linear combinations of genotype values, each of which measures a fundamental unit of interaction.

Conclusion: The circuits provide information on epistasis beyond that contained in the additive x additive, additive x dominance, and dominance x dominance interaction terms. We discuss the connection between our classification and standard epistatic models and demonstrate its utility by analyzing a previously published dataset.

Show MeSH
Related in: MedlinePlus