A complete enumeration and classification of two-locus disease models

There a re 512 two-locus, two-allele, two-phenotype, fully penetrant diseas e models. Using the permutation between two alleles, between two loci, and between being affected and unaffected, one model can be considered to be eq uivalent to another model under the corresponding permutation. These permut ations greatly reduce the number of two-locus models in the analysis of com plex diseases. This paper determines the number of nonredundant two-locus m odels (which can be 102, 100, 96, 51, 50, or 58, depending on which permuta tions are used, and depending on whether zero-locus and single-locus models are excluded). Whenever possible, these nonredundant two-locus models are classified by their property. Besides the familiar features of multiplicati ve models (logical AND), heterogeneity models (logical OR), and threshold m odels, new classifications are added or expanded: modifying-effect models, logical XOR models, interference and negative interference models (neither dominant nor recessive), conditionally dominant/recessive models, missing l ethal genotype models, and highly symmetric models. The following aspects o f two-locus models are studied: the marginal penetrance tables at both loci , the expected joint identity-by-descent (IBD) probabilities, and the corre lation between marginal IBD probabilities at the two loci. These studies ar e useful for linkage analyses using single-locus models while the underlyin g disease model is two-locus, and for correlation analyses using the linkag e signals at different locations obtained by a single-locus model, Copyrigh t (C) 2000 S. Karger AG, Basel.