The use of multiple thresholds in determining the mode of transmission of semi‐continuous traits *

A review of current textbooks of medical genetics (Goodman, 1970; Roberts, 1970) reveals that few, if any, of the common familial illnesses show simple Mendelian ratios. Many of these diseases may be considered semi-continuous traits, so that affected individuals manifest variable severity and normal individuals cannot be graded. Often either severe subforms or mild preclinical forms are defined, and the severity along with the presence or absence of the condition may be inherited in whole or in part. Use of these subforms as parameters in genetic models rather than their exclusion in favour of an all-or-none classification may help in the understanding of the genetic architecture of the trait. Several different modes of transmission have been proposed, including single-locus two-allele models with variable penetrance in one or all genotypes; multifactorial models in which many genes of small effect and environmental sources of variance play a role; and combinations of the two. Attempts to distinguish between the various modes of transmission have not been successful and Morton et al. (1971) has concluded that ‘it is exceedingly difficult, and may be practically impossible, to infer the genetic basis of traits which do not give regular Mendelian ratios. ’ To understand the nature of the variation with respect to disease status, it is helpful to postulate an underlying continuous variable, termed the liability by Falconer (1965), which is a linear scale representing the contribution of all genetic and environmental influences that make an individual more or less likely to manifest the disease. A threshold is defined so that individuals whose liability exceeds the threshold manifest the disease. More severely affected individuals are assumed to have a higher liability than less severely affected individuals. If a more severe subform of the disease is clinically distinguishable, a second threshold on the liability scale is defined; individuals with liabilities above this second threshold manifest the more severe subform. The positions of the two thresholds in relation to each other, and in relation to the mean liability of the population, are functions of the population prevalence of the two forms. The narrower form of the illness (less common) is entirely nested within the wider form (more common) and all individuals with the narrower form are counted as suffering the wider form as well. The population may thus be divided into three categories with respect to the trait: ‘unaffected’ (u), ‘wide but not narrow’ (w-n) and ‘narrow’ (n) . Examples of less common and more severe subforms of diseases which fulfil the above criteria are juvenile diabetes, malignant hypertension and catatonic schizophrenia. Mild pre-clinical syndromes when combined with the major forms of the diseases they represent include a greater proportion of the population than the disease alone, and are found in * This work was supported in part by U.S.P.H. S. grants MH-09247 and MH-13002. t Van Ameringen Fellow of the Foundations Fund for Research in Psychiatry. Current address: Department of Psychiatry, Washington University School of Medicine, 4940 Audubon Avenue, St Louis, Missouri 631 100, U.S.A. Address reprint requests to Dr Reich. 1 School of Wool and Pastoral Sciences, The University of New South Wales, Konsington, Australia.