Recurrence risks for autosomal, epistatic two-locus systems: the effects of linkage disequilibrium

The properties of the recurrence risk functions for Mendelian models involving two loci with epistatic interaction are examined. The two loci, H (hypostatic) and E (epistatic), are arbitrarily linked and diallelic. The general parameters are the genotypic frequencies and recombination fraction; the particular arguments are the number of affected and unaffected offspring. Limiting properties of the models are first described. Then, the more detailed properties of the models such as the sensitivity of the recurrence risk to the number of affected offspring are examined. If linkage disequilibrium is present, ie, the determinant of the gametic matrix is not zero, the predicted recurrence risk may resemble that empirically found in certain heritable diseases not evidently Mendelian.