MATHEMATICAL LIMITS OF MULTILOCUS MODELS - THE GENETIC TRANSMISSION OF BIPOLAR DISORDER

We describe a simple, graphical method for determining plausible modes of inheritance for complex traits and apply this to bipolar disorder. The constraints that allele frequencies and penetrances lie in the in terval 0-1 impose limits on recurrence risks, K-R, in relatives of an affected proband for a given population prevalence, K-p. We have inves tigated these limits for K-R in three classes of relatives (MZ co-twin , sibling, and parent/offspring) for the general single-locus model an d for two types of multilocus models: heterogeneity and multiplicative . In our models we have assumed Hardy-Weinberg equilibrium, an all-or- none trait, absence of nongenetic resemblance between relatives, and n egligible mutation at the disease loci. Although the true values of K- p and the K-R'S are only approximately known, observed population and family data for bipolar disorder are inconsistent with a single-locus model or with any heterogeneity model. In contrast, multiplicative mod els involving three or more loci are consistent with observed data and , thus, represent plausible models for the inheritance of bipolar diso rder. Studies to determine the genetic basis of most bipolar disorder should use methods capable of detecting interacting oligogenes.