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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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Shapes of two-locus models. Two-locus models. The model shapes for multiplicative and heterogeneous two-locus models.
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Figure 3: Shapes of two-locus models. Two-locus models. The model shapes for multiplicative and heterogeneous two-locus models.

Mentions: The penetrance factors are typically chosen from a recessive (0, 0, α), dominant (0, α, α) or additive (0, α/2, α) model. For an additive two-locus model with additive penetrance factors, the interaction coordinates δa, δb, IAA, IAD, IDA, IDD are all zero and the circuits all vanish. For all additive two-locus models IAA = IAD = IDA = IDD = 0, but δa and δb depend on the penetrance factors. The heterogeneous model is often viewed as an approximation to the additive model because if the same penetrance factors are used, the models give very similar penetrances. However, in terms of the type of interaction that can be modeled, the multiplicative and heterogeneous models are very similar. In Table 1, we list the values of the interaction coordinates for some common multiplicative models. If we consider the corresponding heterogeneous models, the single locus dominance terms, δa and δb, have the same value, as listed in the table, and the interaction terms, IAA, IAD, IDA, and IDD, all have the same absolute value but opposite signs. The shapes induced by these models are shown in Figure 3. Note that only 8 shapes can be induced and 6 of the 8 shapes are not generic models (they are subdivisions rather than triangulations of the 3 × 3 grid).


A complete classification of epistatic two-locus models.

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

Shapes of two-locus models. Two-locus models. The model shapes for multiplicative and heterogeneous two-locus models.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Shapes of two-locus models. Two-locus models. The model shapes for multiplicative and heterogeneous two-locus models.
Mentions: The penetrance factors are typically chosen from a recessive (0, 0, α), dominant (0, α, α) or additive (0, α/2, α) model. For an additive two-locus model with additive penetrance factors, the interaction coordinates δa, δb, IAA, IAD, IDA, IDD are all zero and the circuits all vanish. For all additive two-locus models IAA = IAD = IDA = IDD = 0, but δa and δb depend on the penetrance factors. The heterogeneous model is often viewed as an approximation to the additive model because if the same penetrance factors are used, the models give very similar penetrances. However, in terms of the type of interaction that can be modeled, the multiplicative and heterogeneous models are very similar. In Table 1, we list the values of the interaction coordinates for some common multiplicative models. If we consider the corresponding heterogeneous models, the single locus dominance terms, δa and δb, have the same value, as listed in the table, and the interaction terms, IAA, IAD, IDA, and IDD, all have the same absolute value but opposite signs. The shapes induced by these models are shown in Figure 3. Note that only 8 shapes can be induced and 6 of the 8 shapes are not generic models (they are subdivisions rather than triangulations of the 3 × 3 grid).

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