Continuous traits

Mendel's laws are based on the transmission of dichotomous characteristics, yet many important human phenotypes such as height, weight, and blood pressure are continuously distributed. However, we are able to show that Mendelian principles can also be applied for these types of quantitative traits.

Let us first consider a phenotype measured on a continuous scale which results from the influence of a single gene with two alleles A 1 and A2 (see Fig 1). We can now describe the phenotypes of the three possible genotypes in terms of a quantitative value on the continuous scale. A 1A1 has a value of -a; A2A2 has a value of +a; and A1A2, the heterozygote, has a value of d. When d = 0, A1A2 lies exactly half way between A1A1 and A2A2, that is the genetic contribution is entirely additive. When d = -a, A2 is recessive to A1and when d = +a, A2 is dominant to A1.

Fig. 1 A phenotype, measured on a continuous scale, resulting from a single gene with two alleles A1 and A2.

At the simplest level, we assume that there are no dominance effects and that there is no mutation, selection, migration, or inbreeding in the population. If p is the frequency of allele A-,and q is the frequency of A2 in the population where p + q = 1 then the frequency of genotypes can be expressed as follows:

This is known as the Hardy-Weinberg equilibrium. If we now simplify further and state allelic frequencies where p = q = 0.5, then the phenotypic values of A1A1, A1A2, and A2A2 would be distributed in the population with relative frequencies of 1 : 2 : 1.

Now if we consider a trait which results from two genes each of which has two alleles of equal frequency and additive effect, there would be five possible phenotypic values with relative frequencies of 1 : 4 : 6 : 4 : 1. Overall as the number of genetic loci ( n) increases, the number of phenotypic values increases (2 n + 1) and the distribution of phenotypic values more closely approximates a normal distribution. It is thought that most quantitative or continuous traits result from the additive action of genes at many loci which is otherwise known as polygenic inheritance. Where familial transmission is explained by environmental factors as well as by multiple genes, we then call this a multifactorial mode of inheritance.

Complex disorders and irregular phenotypes Polygenic/multifactorial threshold models

Most common human psychiatric and medical disorders such as schizophrenia, diabetes, and heart disease do not show a Mendelian pattern of inheritance. Neither can they be considered as continuous traits in that people are described as being affected or unaffected. However, these conditions could be regarded as quasi-continuous in that those who are affected can be graded along a continuum of severity. It is possible to extend this to assume that there is an underlying liability to develop the disorder which is continuously distributed in the population. Those who pass a certain threshold manifest the condition. If the underlying liability to develop the disorder is inherited in a polygenic or multifactorial fashion, then we can assume that the distribution will be approximately normally distributed ( Fig..2).

The genetic liability of relatives of affected individuals will be increased and their liability distribution will be shifted to the right ( Fig 2). Thus, the proportion of relatives above the disease threshold will be greater compared with the general population. If we know the proportion of affected relatives of probands and the proportion of those affected in the general population, it is possible to calculate the correlation in liability between pairs of relatives using this type of model.

Fig. 2 A polygenic or multifactorial threshold model of disease transmission.

Single major locus model and atypical patterns of Mendelian inheritance

An alternative to a polygenic model of complex disease is a single major locus model. Single gene disorders do not always show typical Mendelian patterns of inheritance. For example familial transmission can be modified by variable expression and penetrance. Some conditions can show great variability in terms of clinical expression. For example neurofibromatosis, an autosomal dominant disorder can express itself as the full blown disorder or merely as a few cafe-au-lait spots. Penetrance is defined as the probability of manifesting the disorder given a particular genotype. For Mendelian disorders this is always 1 or 0, but irregular patterns of inheritance may occur because of incomplete penetrance where the probability of manifesting the disorder is greater than 0 but less than 1.

Finally, there are now molecular explanations for other types of unusual patterns of inheritance for single genes. Anticipation where disorders show a progressively earlier onset and greater severity with subsequent generations is now known to be explained by heritable unstable nucleotide repeat sequences (see later). Huntington's chorea and fragile X syndrome are examples of disorders caused by heritable unstable repeats. For some conditions such as the Angelman syndrome and the Prader-Willi syndrome, manifestation of the disorder depends on the parental origin of the gene. This is known as imprinting.

Other models

Alternative explanations of how complex conditions such as psychiatric disorders are inherited include mixed and oligogenic patterns of transmission. A mixed model includes a major gene and a polygenic/multifactorial contribution. However, for many of these disorders, genes of major effect may not exist. It may be that these irregular phenotypes are best explained by oligogenic models where the co-action or interaction of a small number of genes contributes to the disorder. These issues remain to be resolved by molecular genetic studies (see later).

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