Limits...
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.

Show MeSH

Related in: MedlinePlus

Subdivisions. 0/1 models. The subdivisions for the 50 Li and Reich 0/1 penetrance models.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC2289835&req=5

Figure 4: Subdivisions. 0/1 models. The subdivisions for the 50 Li and Reich 0/1 penetrance models.

Mentions: In [20] a classification of all two-locus disease models with 0/1 penetrance values is given. Although this classification is useful to generate data under various scenarios and to study general properties of two-locus models, it cannot be used to classify observed data. This class of models is much larger than the class of disease models discussed above, yet they only cover a small part of all two-locus models. The 50 models represent only 29 unique subdivisions, and only 10 out of those 29 are among the 69 model shapes, see Figure 4.


A complete classification of epistatic two-locus models.

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

Subdivisions. 0/1 models. The subdivisions for the 50 Li and Reich 0/1 penetrance models.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Subdivisions. 0/1 models. The subdivisions for the 50 Li and Reich 0/1 penetrance models.
Mentions: In [20] a classification of all two-locus disease models with 0/1 penetrance values is given. Although this classification is useful to generate data under various scenarios and to study general properties of two-locus models, it cannot be used to classify observed data. This class of models is much larger than the class of disease models discussed above, yet they only cover a small part of all two-locus models. The 50 models represent only 29 unique subdivisions, and only 10 out of those 29 are among the 69 model shapes, see Figure 4.

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