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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

Example of epistasis. Example of epistasis in QTL data. The data is on chicken growth [24]. (a) The phenotypic means of the two-locus genotypes, (b) a wiggle plot of the data, where each line corresponds to a row in the table, (c) bar plot of the data, (d) the two-locus shape.
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Figure 1: Example of epistasis. Example of epistasis in QTL data. The data is on chicken growth [24]. (a) The phenotypic means of the two-locus genotypes, (b) a wiggle plot of the data, where each line corresponds to a row in the table, (c) bar plot of the data, (d) the two-locus shape.

Mentions: A visual representation of a two-locus model is given in Figure 1. The data comes from an example that will be discussed further later. The genotype values, relative to the value of aa/BB, are listed in Panel (a). Panel (b) shows the classical visualization of this table, where each line corresponds to one row in the table. In Panel (c) there is a bar-chart of the data, and the corresponding shape is shown in Panel (d). There is clearly epistatic interaction in the model in Figure 1, as the genotypes aa/bb, aa/Bb, Aa/bb, and AA/BB have much higher means than the remaining 5 genotypes. The shape shows the four planes of the upper convex hull of the heights. It includes a plane through the genotypes Aa/bb, aa/Bb, and AA/BB, which is given by the middle triangle in the picture, and three planes corresponding to the outer three triangles. Although the classical visualization in Panel (b) of Figure 1 contains complete information on the relative genotype values it is hard to grasp what types of interactions occur just by glancing at the figure. The bar-chart is a very good visual representation of the 9 values, however, any comparison between two different datasets based on bar-charts would be not only tedious, but hard to define. Some information is lost by considering only the shape of the model, but since it summarizes the epistasis that is present, the shape enables us to easily compare and classify different models.


A complete classification of epistatic two-locus models.

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

Example of epistasis. Example of epistasis in QTL data. The data is on chicken growth [24]. (a) The phenotypic means of the two-locus genotypes, (b) a wiggle plot of the data, where each line corresponds to a row in the table, (c) bar plot of the data, (d) the two-locus shape.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Example of epistasis. Example of epistasis in QTL data. The data is on chicken growth [24]. (a) The phenotypic means of the two-locus genotypes, (b) a wiggle plot of the data, where each line corresponds to a row in the table, (c) bar plot of the data, (d) the two-locus shape.
Mentions: A visual representation of a two-locus model is given in Figure 1. The data comes from an example that will be discussed further later. The genotype values, relative to the value of aa/BB, are listed in Panel (a). Panel (b) shows the classical visualization of this table, where each line corresponds to one row in the table. In Panel (c) there is a bar-chart of the data, and the corresponding shape is shown in Panel (d). There is clearly epistatic interaction in the model in Figure 1, as the genotypes aa/bb, aa/Bb, Aa/bb, and AA/BB have much higher means than the remaining 5 genotypes. The shape shows the four planes of the upper convex hull of the heights. It includes a plane through the genotypes Aa/bb, aa/Bb, and AA/BB, which is given by the middle triangle in the picture, and three planes corresponding to the outer three triangles. Although the classical visualization in Panel (b) of Figure 1 contains complete information on the relative genotype values it is hard to grasp what types of interactions occur just by glancing at the figure. The bar-chart is a very good visual representation of the 9 values, however, any comparison between two different datasets based on bar-charts would be not only tedious, but hard to define. Some information is lost by considering only the shape of the model, but since it summarizes the epistasis that is present, the shape enables us to easily compare and classify different models.

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