Abstract
Theoretical advantages of nonparametric logarithm of odds to map polygenic diseases are supported by tests of the beta model that depends on a single logistic parameter and is the only model under which paternal and maternal transmissions to sibs of specified phenotypes are independent. Although it does not precisely describe recurrence risks in monozygous twins, the beta model has greater power to detect family resemblance or linkage than the more general delta model which describes the probability of 0, 1, or 2 alleles identical by descent (ibd) with two parameters. Available data on ibd in sibs are consistent with the beta model, but not with the equally parsimonious but less powerful gamma model that assumes a fixed probability of 1/2 for 1 allele ibd. Additivity of loci on the liability scale is not disproven. A simple equivalence extends the beta model to multipoint analysis.