Polygenic and Multifactorial Inheritance

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CHAPTER 9 Polygenic and Multifactorial Inheritance

Many disorders demonstrate familial clustering that does not conform to any recognized pattern of Mendelian inheritance. Examples include several of the most common congenital malformations and many common acquired diseases (Box 9.1). These conditions show a definite familial tendency, but the incidence in close relatives of affected individuals is much lower than would be seen if these conditions were caused by mutations in single genes.

Because it is likely that many factors, both genetic and environmental, are involved in causing these disorders, they are generally referred to as showing multifactorial inheritance. The prevailing view until recently has been that in multifactorial inheritance, environmental factors interact with many genes to generate a normally distributed susceptibility. According to this theory, individuals are affected if they lie at the wrong end of the distribution curve. This concept of a normal distribution generated by many genes, known as polygenes, each acting in an additive fashion, is plausible for physiological characteristics such as height and possibly blood pressure. However, for disease states such as type 1 diabetes mellitus (T1DM), the genetic contribution involves many loci, some of which play a much more important role than others.

Sequencing of the human genome has shown that the 3 billion base pairs are 99.9% identical in every person. This also means that individuals are, on average, 0.1% different genetically from every other person on the planet. And within that 0.1% lies the mystery of why some people are more susceptible to a particular illness, or more likely to be healthy, than another member of the population. Our increased knowledge of genetic variation at the level of single nucleotide polymorphisms (SNPs), together with high throughput SNP genotyping platforms, has recently revolutionized our ability to identify disease susceptibility loci for many common diseases.

Polygenic Inheritance and the Normal Distribution

Before considering the impact of recent research in detail, it is necessary to outline briefly the scientific basis of what is known as polygenic or quantitative inheritance. This involves the inheritance and expression of a phenotype being determined by many genes at different loci, with each gene exerting a small additive effect. Additive implies that the effects of the genes are cumulative, i.e. no one gene is dominant or recessive to another.

Several human characteristics (Box 9.2) show a continuous distribution in the general population, which closely resembles a normal distribution. This takes the form of a symmetrical bell-shaped curve distributed evenly about a mean (Figure 9.1). The spread of the distribution about the mean is determined by the standard deviation. Approximately 68%, 95%, and 99.7% of observations fall within the mean plus or minus one, two, or three standard deviations, respectively.

Box 9.2

Human Characteristics that Show a Continuous Normal Distribution

Blood pressure

Dermatoglyphics (ridge count)

FIGURE 9.1 The normal (Gaussian) distribution.

It is possible to show that a phenotype with a normal distribution in the general population can be generated by polygenic inheritance involving the action of many genes at different loci, each of which exerts an equal additive effect. This can be illustrated by considering a trait such as height. If height were to be determined by two equally frequent alleles, a (tall) and b (short), at a single locus, then this would result in a discontinuous phenotype with three groups in a ratio of 1 (tall-aa) to 2 (average-ab/ba) to 1 (short-bb). If the same trait were to be determined by two alleles at each of two loci interacting in a simple additive way, this would lead to a phenotypic distribution of five groups in a ratio of 1 (4 tall genes) to 4 (3 tall + 1 short) to 6 (2 tall + 2 short) to 4 (1 tall + 3 short) to 1 (4 short). For a system with three loci each with two alleles the phenotypic ratio would be 1-6-15-20-15-6-1 (Figure 9.2).

FIGURE 9.2 Distribution of genotypes for a characteristic such as height with 1, 2, and 3 loci each with two alleles of equal frequency. The values for each genotype can be obtained from the binomial expansion (p + q)⁽²ⁿ⁾, where p = q = 1/2 and n equals the number of loci.

It can be seen that as the number of loci increases, the distribution increasingly comes to resemble a normal curve, thereby supporting the concept that characteristics such as height are determined by the additive effects of many genes at different loci. Further support for this concept comes from the study of familial correlations for characteristics such as height. Correlation is a statistical measure of the degree of resemblance or relationship between two parameters. First-degree relatives share, on average, 50% of their genes (Table 9.1). Therefore, if height is polygenic, the correlation between first-degree relatives should be 0.5. Several studies have shown that the sib–sib correlation for height is indeed close to 0.5.

Table 9.1 Degrees of Relationship

Relationship	Proportion of Genes Shared
First degree
Parents
Siblings
Children
Second degree
Uncles and aunts
Nephews and nieces
Grandparents
Grandchildren
Half-siblings
Third degree
First cousins
Great-grandparents
Great-grandchildren

In reality, human characteristics such as height and intelligence are also influenced by environment, and possibly also by genes that are not additive in that they exert a dominant effect. These factors probably account for the observed tendency of offspring to show what is known as regression to the mean. This is demonstrated by tall or intelligent parents (the two are not mutually exclusive!) having children whose average height or intelligence is slightly lower than the average or mid-parental value. Similarly, parents who are very short or of low intelligence tend to have children whose average height or intelligence is lower than the general population average, but higher than the average value of the parents. If a trait were to show true polygenic inheritance with no external influences, then the measurements in offspring would be distributed evenly around the mean of their parents’ values.

Multifactorial Inheritance—The Liability/Threshold Model

Efforts have been made to extend the polygenic theory for the inheritance of quantitative or continuous traits to try to account for discontinuous multifactorial disorders. According to the liability/threshold model, all of the factors which influence the development of a multifactorial disorder, whether genetic or environmental, can be considered as a single entity known as liability. The liabilities of all individuals in a population form a continuous variable, which has a normal distribution in both the general population and in relatives of affected individuals. However, the curves for these relatives will be shifted to the right, with the extent to which they are shifted being directly related to the closeness of their relationship to the affected index case (Figure 9.3).

FIGURE 9.3 Hypothetical liability curves in the general population and in relatives for a hereditary disorder in which the genetic predisposition is multifactorial.

To account for a discontinuous phenotype (i.e., affected or not affected) with an underlying continuous distribution, it is proposed that a threshold exists above which the abnormal phenotype is expressed. In the general population, the proportion beyond the threshold is the population incidence, and among relatives the proportion beyond the threshold is the familial incidence.

It is important to emphasize again that liability includes all factors that contribute to the cause of the condition. Looked at very simply, a deleterious liability can be viewed as consisting of a combination of several ‘bad’ genes and adverse environmental factors. Liability cannot be measured but the mean liability of a group can be determined from the incidence of the disease in that group using statistics of the normal distribution. The units of measurement are standard deviations and these can be used to estimate the correlation between relatives.

Consequences of the Liability/Threshold Model

Part of the attraction of this model, and it should be emphasized again that this is a hypothesis rather than a proven fact, is that it provides a simple explanation for the observed patterns of familial risks in conditions such as cleft lip/palate, pyloric stenosis, and spina bifida.

1 The incidence of the condition is greatest among relatives of the most severely affected patients, presumably because they are the most extreme deviants along the liability curve. For example, in cleft lip/palate the proportion of affected first-degree relatives (parents, siblings, and offspring) is 6% if the index patient has bilateral cleft lip and palate, but only 2% if the index patient has a unilateral cleft lip (Figure 9.4).

2 The risk is greatest among close relatives of the index case and decreases rapidly in more distant relatives. For example, in spina bifida the risks to first-, second,- and third-degree relatives of the index case are approximately 4%, 1%, and less than 0.5%, respectively.

3 If there is more than one affected close relative, then the risks for other relatives are increased. In spina bifida, if one sibling is affected the risk to the next sibling (if folic acid is not taken by the mother periconceptionally) is approximately 4%; if two siblings are affected, the risk to a subsequent sibling is approximately 10%.

4 If the condition is more common in individuals of one sex, then relatives of an affected individual of the less frequently affected sex will be at higher risk than relatives of an affected individual of the more frequently affected sex. This is illustrated by the condition pyloric stenosis. Pyloric stenosis shows a male to female ratio of 5 to 1. The proportions of affected offspring of male index patients are 5.5% for sons and 2.4% for daughters, whereas the risks to the offspring of female index patients are 19.4% for sons and 7.3% for daughters. The probable explanation for these different risks is that for a female to be affected, she has to lie at the extreme of the liability curve, so that her close relatives will also have a very high liability for developing the condition. Because males are more susceptible to developing the disorder, risks in male offspring are higher than in female offspring regardless of the sex of the affected parent.

5 The risk of recurrence for first-degree relatives (i.e., siblings and offspring) approximates to the square root of the general population incidence. Thus if the incidence is 1 in 1000, the sibling and offspring risk will equal approximately 1 in 32, or 3%.

FIGURE 9.4 Severe (A) and mild (B) forms of cleft lip/palate.

Heritability

Though it is not possible to assess an individual’s liability for a particular disorder, it is possible to estimate what proportion of the etiology can be ascribed to genetic factors as opposed to environmental factors. This is referred to as heritability, which can be defined as the proportion of the total phenotypic variance of a condition that is caused by additive genetic variance. In statistical terms, variance equals the square of the standard deviation. Heritability is often depicted using the symbol h² and is expressed either as a proportion of 1 or as a percentage.

Estimates of the heritability of a condition or trait provide an indication of the relative importance of genetic factors in its causation, so that the greater the value for the heritability the greater the role of genetic factors.

Heritability is estimated from the degree of resemblance between relatives expressed in the form of a correlation coefficient, which is calculated using statistics of the normal distribution. Alternatively, heritability can be calculated using data on the concordance rates in monozygotic and dizygotic twins. In practice, it is desirable to try to derive heritability estimates using different types of relatives and to measure the disease incidence in relatives reared together and living apart so as to try to disentangle the possible effects of common environmental factors. Estimates of heritability for some common diseases are given in Table 9.2.

Table 9.2 Estimates of Heritability of Various Disorders

Disorder	Frequency (%)	Heritability
Schizophrenia	1	85
Asthma	4	80
Cleft lip ± cleft palate	0.1	76
Pyloric stenosis	0.3	75
Ankylosing spondylitis	0.2	70
Club foot	0.1	68
Coronary artery disease	3	65
Hypertension (essential)	5	62
Congenital dislocation of the hip	0.1	60
Anencephaly and spina bifida	0.3	60
Peptic ulcer	4	37
Congenital heart disease	0.5	35

The degree of familial clustering shown by a multifactorial disorder can be estimated by measuring the ratio of the risk to siblings of affected individuals compared to the general population incidence. This ratio of sib risk to population incidence is known as λ_s. For example, in type 1 diabetes, where the UK population incidence is 0.4% and the risk to siblings is 6%, λ_s is 15. For type 2 diabetes in Europe, λ_s is estimated at a more modest 3.5 (35% sibling risk; 10% population risk).

Identifying Genes that Cause Multifactorial Disorders

Multifactorial disorders are common and make a major contribution to human morbidity and mortality (p. 8). It is therefore not surprising that vigorous efforts are being made to try to identify genes that contribute to their etiology. Several strategies have been used to search for disease susceptibility genes.

Linkage Analysis

Linkage analysis has proved extremely valuable in mapping single gene disorders by studying the co-segregation of genetic markers with the disease (p. 137). However, this approach is much more difficult in multifactorial disorders. This is because it is extremely difficult mathematically to develop strategies for detecting linkage of additive polygenes, each of which makes only a small contribution to the phenotype. In addition, many multifactorial diseases show a variable age of onset so that the genetic status of unaffected family members cannot be known with certainty.

Despite the limitations, a small number of susceptibility loci have been identified using modifications of the approaches used for mapping single gene loci. Examples are given in Chapter 15.

Affected Sibling-Pair Analysis

Standard linkage analysis requires information regarding the mode of inheritance, gene frequencies, and penetrance. For multifactorial disorders, this information is not usually available. A possible solution is to look for regions of the genome that are identical by descent in affected sibling pairs. If affected siblings inherit a particular allele more or less often than would be expected by chance, this indicates that the allele or its locus is involved in some way in causing the disease.

Consider a set of parents with alleles AB (father) and CD (mother) at a particular locus. The probability that any two of their children will have both alleles in common is 1 in 4 (Figure 9.5). The probability that they will have one allele in common is 1 in 2 and the probability that they will have no alleles in common equals 1 in 4. If siblings who are affected with a particular disease show deviation from this 1 : 2 : 1 ratio for a particular variant, this implies that there is a causal relationship between the locus and the disease.

FIGURE 9.5 The probability that siblings will have 2, 1, or 0 parental alleles in common. Significant deviation from the 1 : 2 : 1 ratio indicates that the locus is causally related to the disease.

Linkage Disequilibrium Mapping

After a chromosome region that appears to confer susceptibility has been identified, the next step is to reduce the genetic interval by fine mapping. The most powerful method uses linkage disequilibrium (LD) (p. 138) mapping to construct haplotypes by genotyping SNPs within the region. Historical crossover points reduce the genetic interval by defining LD ‘blocks’ (Figure 9.6). Candidate genes within the region are then sequenced to find DNA variants that can be tested for association with the disease.

FIGURE 9.6 The linkage disequilibrium (LD) structure of glucokinase. r² values between the 84 single nucleotide polymorphisms (SNPs) across a 116-kb region are presented. An r² value of 1 indicates that two SNPs are linked. There are two blocks of LD within the glucokinase gene (outlined in red).

Many genome-wide linkage scans (p. 76) have been performed for various disorders and although a number of loci have been mapped, the number of disease susceptibility genes identified by this approach is disappointingly small. One probable reason is the complex nature of multifactorial disease, with numerous genetic variants of modest effect interacting with each other and the environment. Most linkage studies are simply underpowered to detect these effects, and it was shown by Risch and Merikangas that an alternative approach, the association study, would be a more powerful way of finding genetic variants underlying complex diseases.

Association Studies

Association studies are undertaken by comparing the frequency of a particular variant in affected patients with its frequency in a carefully matched control group. This approach is often described as a case-control study. If the frequencies in the two groups differ significantly, this provides evidence for an association.

The polymorphic HLA histocompatibility complex on chromosome 6 (p. 200) has been frequently studied. One of the strongest known HLA associations is that between ankylosing spondylitis and the B27 allele. This is present in approximately 90% of all patients and in only 5% of controls. The strength of an association is indicated by the ratio of the odds of developing the disease in those with the antigen to the odds of developing the disease in those without the antigen (Table 9.3). This is known as the odds ratio and it gives an indication of how much more frequently the disease occurs in individuals with a specific marker than in those without that marker. For the HLA-ankylosing spondylitis association, the odds ratio is 171. However, for most markers associated with multifactorial disease, the frequency difference between cases and controls is small, giving rise to modest odds ratios (usually between 1.1 and 1.5).

Table 9.3 Calculation of Odds Ratio for a Disease Association

	Allele 1	Allele 2
Patients	A	b
Controls	C	d
Odds ratio	= ÷ =

If evidence for association is forthcoming, this suggests that the allele encoded by the marker is either directly involved in causing the disease (i.e., a susceptibility variant) or that the marker is in linkage disequilibrium with a closely linked susceptibility variant. When considering disease associations, it is important to remember that the identification of a susceptibility locus does not mean that the definitive disease gene has been identified. For example, although it is one of the strongest disease associations known, only 1% of all HLA B27 individuals develop ankylosing spondylitis, so that many other factors, genetic and/or environmental, must be involved in causing this condition.

Before 2006, association studies were carried out by first selecting a candidate gene or genomic region, which would either have plausible biological links to the disease of interest or be situated in a region of linkage. One or more genetic variants were selected from the gene or gene region and genotyped in cases and controls to test for association with the disease. Many studies showing evidence of association with candidate genes were published for a variety of diseases and traits. However, in numerous cases, these associations did not replicate in independent studies, leaving the validity of many of the initially reported associations unclear. The reasons for this inconsistency included (1) small sample sizes, (2) weak statistical support, and (3) the low prior probability of any of the few selected variants being genuinely associated with the disease. All of these features increased the chances of false-positive associations. An additional reason for false-positive associations is population stratification, in which the population contains subgroups of different ancestries and both the disease and the allele happen to be common within that subset. A famous example was reported in a study by Lander and Schork which showed, in a San Francisco population, that HLA-A1 is associated with the ability to eat with chopsticks. This association is simply explained by the fact that HLA-A1 is more common among Chinese than Europeans!

The candidate gene approach led to only a handful of widely replicated associations. Two important developments made it possible to move away from this approach, toward a genome-wide approach to association studies: the first was the development of microarray technology to genotype hundreds of thousands of SNPs in thousands of individuals quickly and at little cost; the second was the creation of a reference catalogue of SNPs and linkage disequilibrium, the International Haplotype Map (HapMap).

HapMap Project (www.hapmap.org)

Although it is estimated that there may be up to 10 million SNPs in the human genome, many SNPs are in linkage disequilibrium (p. 138) and therefore co-inherited. Regions of linked SNPs are known as haplotypes. The International HapMap project is identifying SNP frequencies and haplotypes in different populations (Table 9.4). By 2007, the project had genotyped more than 3 million SNPs in 270 samples from Europe, East Asia, and West Africa. It showed that most SNPs are strongly correlated to one or more others nearby. This means that by genotyping approximately 500,000 SNPs in most populations, we can capture information on the majority of common SNPs in the human genome (with minor allele frequency >5%). In African populations, the number needed is approximately 1 million SNPs because of lower overall linkage disequilibrium. Since 2007, genotype data have been added to the HapMap from seven other populations, whereas the original HapMap population samples have expanded. Together with high-throughput SNP genotyping, this valuable reference enabled a new generation of association studies, which could tackle the whole genome’s common SNP variation in just one experiment.

Table 9.4 Populations Studied in the International HapMap Project

Ancestry	Place of Residence	Number of Individuals Analysed
Yoruba	Ibadan, Nigeria	180*
Japanese	Tokyo, Japan	91
Han Chinese	Beijing, China	90
Northern and western European	Utah, USA	180*
Luhya	Webuye, Kenya	90
Maasai	Kinyawa, Kenya	180*
Tuscan	Italy	90
Gujarati Indian	Houston, Texas, USA	90
Metropolitan Chinese community	Denver, Colorado, USA	90
Mexican	Los Angeles, California, USA	90*
African	Southwestern USA	90*