Although some continuously variable characters such as blood pressure or body mass index are of great importance in public health, medical geneticists are more concerned with dichotomous characters: the innumerable diseases and malformations that tend to run in families but do not show Mendelian pedigree patterns. DS Falconer provided a major conceptual tool in non-Mendelian genetics by extending polygenic theory to dichotomous or discontinuous characters (those that you either have or do not have).
The key concept is that even for a dichotomous character, there is an underlying continuously variable susceptibility. You may or may not have a cleft palate, but every embryo has a certain susceptibility to cleft palate. The susceptibility may be low or high; it is polygenic and follows a Gaussian distribution in the population. Together with the polygenic susceptibility, we postulate the existence of a threshold. Embryos whose susceptibility exceeds a critical threshold value develop cleft palate; those whose susceptibility is below the threshold, even if only just below, develop a normal palate. Stripped of mathematical subtlety, the model can be represented as in Figure 1. The threshold can be imagined as the neutral point of the balance. Changing the balance of factors tips the phenotype one way or the other.
Fig1. Multifactorial determination of a disease or malformation. The angels and devils can represent any combination of genetic and environmental factors. Adding an extra devil or removing an angel can tip the balance, without that particular factor being the cause of the disease in any general sense. (From an idea by the late Professor RSW Smithells.)
For cleft palate, a polygenic threshold model seems intuitively reasonable. All embryos start with a cleft palate. During early development the palatal shelves must become horizontal and fuse together. They must do this within a specific developmental window of time. Many different genetic and environmental factors influence embryonic development, so it seems reasonable that the genetic part of the susceptibility should be polygenic. Whether the palatal shelves meet and fuse with time to spare, or whether they only just manage to fuse in time, is unimportant—if they fuse, a normal palate forms; if they do not fuse, a cleft palate results. There is therefore a natural threshold superimposed on a continuously variable process.
Threshold theory helps us understand recurrence risks
Threshold theory helps explain how recurrence risks for non-Mendelian conditions vary in families. Affected people must have an unfortunate combination of high- susceptibility alleles. Their relatives who share genes with them will also, on average, have an increased susceptibility, with the divergence from the population mean depending on the proportion of shared genes. Thus, polygenic threshold characters tend to run in families (Figure 2). Moreover, in complete contrast to Mendelian conditions, the recurrence risk for polygenic conditions depends on the previous history. Parents who have had several affected children may have just been unlucky, but on average they will have more high-risk alleles than parents with only one affected child. The threshold is fixed, but the average susceptibility, and hence the recurrence risk, increases with an increasing number of previous affected children.
Fig2. A polygenic threshold model for dichotomous non-Mendelian characters. Liability to the condition is polygenic and Normally distributed (green curve). People whose liability is above a certain threshold value (the balance point in Figure 5.22) are affected. The distribution of liability among sibs of an affected person (purple curve) is shifted toward higher liability because they share genes with their affected sib. A greater proportion of them have liability exceeding the fixed threshold. As a result, the condition tends to run in families.
Thresholds may be sex-specific. Table 1 shows some old data that illustrate an example. Congenital pyloric stenosis is five times more common in boys than girls. It has a tendency to run in families. For parents who have had an affected baby, Table 1 shows that the recurrence risk is higher if the affected baby was a girl. Applying poly genic threshold theory, we can understand this. The threshold must be higher for girls than for boys. To be affected, a girl must on average have a higher liability than a boy. Relatives of an affected girl therefore have a higher average liability than relatives of an affected boy (Figure 3). The recurrence risk is correspondingly higher, although in each case a baby’s risk of being affected is five times higher if it is a boy because a less extreme liability is sufficient to cause a boy to be affected.
Table1. RECURRENCE RISKS FOR PYLORIC STENOSIS
Fig3. A polygenic dichotomous character with sex-specific thresholds. The figure shows a model that explains data such as those in Table 1. As in Figure 2, the general population displays a liability to this polygenic disease that is Normally distributed, with an average liability of A′ (green curve). Boys with a liability above the threshold value Tb manifest the condition; for girls to be affected, the liability must be above the female-specific threshold value Tg . Among siblings of affected boys, the liability (blue curve) is higher, with average A′′, and a greater proportion of these brothers and sisters have a liability that exceeds the respective threshold levels. Among siblings of affected girls, the liability is still higher (red curve, average liability A′′′), and an even greater proportion of these brothers and sisters will be affected because they have a liability that exceeds their sex-specific threshold levels.
All of this theory is not used by counselors to predict risks for people who consult them. Those predictions are based on empirical risks—risks defined by population surveys, like those in Table 1. For such purposes it is important to use data that are recent (unlike those in Table 1) and from the same population as the consultand. Different populations can have differing spectra of susceptibility factors, and environmental fac tors vary both between populations and over time. The value of the models discussed in this section is not to provide actual risk figures but to provide a mental framework that makes sense of the way non-Mendelian characters run in families, and how differing family histories and structures affect recurrence risks. Eventually geneticists want to know the specific genetic variants that contribute to liability. The ways of doing this are discussed in Chapter 18.
