HUMAN GENETICS

for 1st YEAR STUDENTS


MULTIFACTORIAL INHERITANCE

IMPORTANCE

Multifactorial inheritance is responsible for the greatest number of individuals that will need special care or hospitalization because of genetic diseases. Up to 10% of newborn children will express a multifactorial disease at some time in their life. Atopic reactions, diabetes, cancer, spina bifida/anencephaly, pyloric stenosis, cleft lip, cleft palate, congenital hip dysplasia, club foot, and a host of other diseases all result from multifactorial inheritance. Some of these diseases occur more frequently in males. Others occur more frequently in females. Environmental factors as well as genetic factors are involved.

REGRESSION TO THE MEAN

Multifactorial inheritance was first studied by Galton, a close relative of Darwin and a contemporary of Mendel. Galton established the principle of what he termed "regression to mediocrity." Mendel studied discontinuous characters, green peas vs. yellow peas, tall vs. dwarf, etc. There was no overlap of phenotype in Mendel's studies. Characters fit into one of two classes. There was no blending in the heterozygote. On the other hand, Galton studied the inheritance of continuous characters, height in humans, intelligence in humans, etc. Galton noticed that extremely tall fathers tended to have sons shorter than themselves, and extremely short fathers tended to have sons taller than themselves. "Tallness" or "shortness" didn't breed true like they did in Mendel's pea experiments. The offspring seemed to regress to the median, or "mediocrity." Figure 12 shows the correlation between the father's height and the height of the son.

Galton's studies

Figure 12. A representation of GaltonŐs studies on the inheritance of height. If the sonŐs height were determined only by the fatherŐs height, the correlation should be that of the solid line. The dashed line is what is observed. Galton called this "regression to mediocrity."

If the son's height were completely determined by the father's height, the correlation would be as shown by the solid blue line. What is observed is shown by the dashed red line. The height of the father and the average height of the son are related, but the average height of the son always regresses toward the mean. That is understandable if there is no dominance. The son only gets half of his father's genes; the other half comes from his mother.

When comparing height differences between men and women, women are, on average, 3 inches shorter. A woman with a certain number of "tall" genes will be, on average, 3 inches shorter than a man with the same number. When that difference is taken into account, there is no selective bias in matings for tallness in human populations. It is true than men tend to marry women who are shorter than themselves, but that is a phenotypic difference, not a genotypic difference. Since the wives of taller than average men tend to represent the general population of women, they will not have, on the average, as many "tall" genes to pass on to their offspring as their husbands. Hence, the son will receive half of the father's "tall" genes, on average, and half of the mother's "tall" genes, on average, but his total genes for "tallness," on average, will be less than his father's. Shorter than average males have fewer "tall" genes than average, but they are still as tall as an average female, even though the average female has more "tall" genes. Their sons, on average, will be taller than their fathers because their mothers have, on average, more "tall" genes to give to their sons than their husbands have. On average, the son will have more "tall" genes than his father.

What holds true for height also holds true for other quantitative traits, such as intelligence. This is what worried Galton. He was a very intelligent member of British aristocracy who was interested in genetics as a way to maintain intelligence in his family. He was really the founder of the eugenics movement. His findings must have been very discouraging for him.

POLYGENIC INHERITANCE

For many years the argument raged between the "Mendelians" and the "Galtonians" as to which of the two paradigms was the correct one for human inheritance. There was no question that Mendelian inheritance was correct for some diseases, but these were rare, affecting only a small portion of the population. They were considered trivial by the Galtonians. On the other hand, the inheritance of quantitative traits could not be used to predict outcomes, only average estimates measured in large population studies. Mendelians considered the study of quantitative traits to be trivial because they had no predictive value. R. A. Fisher resolved the dispute by showing that the inheritance of quantitative traits can be reduced to Mendelian inheritance at many loci. Fisher's argument went as follows:

Consider the following: One locus for height, with three alleles. Allele h2 adds 2 inches to the average 68-inch height. Allele h0 neither adds nor subtracts from the average height of 68 inches. And allele h- subtracts 2 inches from the average height. Suppose h0 is twice as frequent as either h2 or h-. The Punnett square for the population would be as follows:

    FATHER'S GAMETES
    h2 2h0 h-
MOTHER'S

GAMETES
h2 h2,h2
72"
2(h2,h0)
70"
h2,h-
68"
2h0 2(h2,h0)
70"
4(h0,h0)
68"
2(h-,h0)
66"
h- h2,h-
68"
2(h-,h0)
66"
h-,h-
64"

When this is expressed in tabular form, it looks like the histogram in Figure 13.

Histogram I

Figure 13. The distribution of height in a population if it were determined by one locus with three alleles as described in the text.

If a second locus, called the tall locus, or t, is also involved in height, with three alleles as above, one adding two inches, one neither adding nor subtracting from the phenotype, and one subtracting 2 inches, with the neutral allele occurring twice as frequently as the either of the others, the histogram becomes that of Figure 14.

Histogram II

Figure 14. The distribution of height in a population if were determined by two loci, each with three alleles as described in the text.

THE MULTIFACTORIAL MODEL

As more loci are included, this binomial distribution quickly approaches the Gaussian distribution, or the bell-shaped normal curve, observed with human quantitative traits. Three loci, each with three alleles, are enough to produce population frequencies indistinguishable from a normal curve. The multifactorial model is then:

  1. Several, but not an unlimited number, loci are involved in the expression of the trait.
  2. There is no dominance or recessivity at each of these loci.
  3. The loci act in concert in an additive fashion, each adding or detracting a small amount from the phenotype.
  4. The environment interacts with the genotype to produce the final phenotype.

As an example of 4. above, women are, on average, three inches shorter than men with the same genome. Environmental factors (hormones) affect the final phenotype.

Not all human traits that show a continuous distribution in the population are multifactorial traits. Any bimodal distribution is not controlled by multifactorial expression. It is more likely to be under the control of a single dominant/recessive gene with modifying environmental factors. Multifactorial traits all show a unimodal bell-shaped distribution.

CONCORDANCE

Twin studies, although limited by complicating factors, provide the best source for separating genetic contributions to the trait being studied from environmental influences. Monozygous (identical) twins have the same genome, but not the exact environmental factors, especially if they were raised apart. The concordance rate in monozygotic twins can be compared to the concordance rate in dizygotic (fraternal) twins to estimate the genetic component (heritability) of the trait. If the trait is truly 100% genetic, as it is for total fingerprint ridge count in humans, monozygotic twins will be 100% concordant while dizygotic twins, having, on average, only half their genes in common, will have a lower concordance rate. If the trait under study is 100% environmental, monozygotic twins and dizygotic twins will have the same concordance rate. The concordance rate for a disease is calculated as follows:

Concordance Rate = [Both Affected / (One Affected + Both Affected)] x 100

For quantitative traits, means and variances have to be substituted and the calculations are beyond the scope of this introductory course.

THRESHOLD MODEL OF DISEASE

If multifactorial traits are quantitative traits with continuous distribution, how can they control diseases, such as cleft lip or spina bifida? One either has the disease or doesn't. There is no intermediate. I'm glad you asked that question. Multifactorial diseases are best explained by the threshold model shown in Figure 15

Threshold Model

Figure 15. The threshold model for multifactorial traits. Below the threshold the trait is not expressed. Individuals above the threshold have the disease.

As the number of multifactorial genes for the trait increases, the liability for the disease increases. When it reaches a threshold, the liability is so great that abnormality, what we call disease, results. For example, consider the development of the cleft palate. Early in embryonic development the palatal arches are in a vertical position. Through embryonic and fetal development the head grows larger, making the arches farther apart, the tongue increases in size, making it more difficult to move, and the arches themselves are growing and turning horizontal. There is a critical stage in development by which the two arches must meet and fuse. Head growth, tongue growth, and palatal arch growth are all subject to many genetic and environmental factors. If the two arches start to grow in time, grow at the proper rate, and begin to move soon enough to the horizontal they will meet and fuse in spite of head size and tongue growth. The result is no cleft palate. They may fuse well ahead of the critical developmental stage or just barely make it in time, we have no way of telling. However, if they don't meet by the critical stage a cleft palate results. If they are close together at the critical stage, a small cleft will result, perhaps only a bifurcated uvula. If they are far apart, a more severe cleft will result. We call that critical difference in liability the threshold. Beyond the threshold, disease results. Below the threshold, normal development is observed. But the underlying liability is distributed as the normal curve shown in Figure 15.

DEGREE OF RELATIONSHIP AND GENES IN COMMON

Since one is not following a single locus with dominance or recessivity but is following several loci that act in concert, counseling for multifactorial inheritance diseases requires a different approach from that taken for Mendelian inheritance diseases. One has to calculate the number of genes in common. The easiest way to do that is to change the way we construct pedigrees. Instead of the familiar sibship method we use the pathway to common ancestor method. It is shown in Figure 16.

Pathway to common ancestor
method

Figure 16. Conversion of a standard pedigree to a path coefficient pedigree for determining the fraction of genes in common.

In Figure 16, Pedigree A represents the standard method of pedigree construction. Pedigree B represents the pathway system of pedigree construction. It is much easier to see how genes flow from generation to generation in Pedigree B. In Figure 16, II-2 and II-3 are brother and sister. They have two common ancestors, I-1 and I-2. To determine the fraction of genes II-2 and II-3 have in common one simply counts all of the pathways and their connecting lines through the common ancestors. There is one line from II-2 to I-1, and a line from I-1 to II-3. That is one pathway with two lines of descent. There is another line from II-2 to I-2, and a line from I-2 to II-3. That is a second pathway with two lines of descent. These are the only pathways from II-2 to II-3. The fraction 1/2 is then raised to the power of the number of lines of descent and summed for each possible pathway, (1/2)2 for the pathway through I-1, and (1/2)2 for the pathway through I-2, making a total of 1/2. Brothers and sisters have, on average, 1/2 of their genes in common.

A parent and offspring, say I-1 and II-2 also have 1/2 of their genes in common. There is only one pathway between them and only one line in that pathway, (1/2)1.

Other relationships follow in the same manner. In Figure 16, III-1 and III-3 are first cousins. There are two pathways connecting the two individuals, one through I-1 and the other through I-2, each with four lines. Their fraction of genes in common is then (1/2)4 + (1/2)4 or 1/8. First cousins have 1/8 of their genes in common. A grandparent and grandchild have 1/4 of their genes in common. There is a single pathway with two lines of descent. III-1 and IV-1 are first cousins once removed. Again there are two pathways, one through I-1 and the other through I-2, each with 5 lines, (1/2)5 + (1/2)5 or 1/16 of their genes in common.

The degree of relationship is often used rather than the fraction of genes in common. The degree of relationship is simply the power to which (1/2) is raised to reach the fraction of genes in common. First degree relatives have (1/2) of their genes in common. Second degree relatives have 1/4, (1/2)2, of their genes in common, etc.

Calculations for first
degree relatives

Figure 17. Method of calculating the recurrence risk of a multifactorial trait to first degree relatives.

If one returns to the normal curve for liability shown in Figure 15, one can now see where various relatives of affected lie in relationship to the threshold. Figure 17 shows these calculations for first degree relatives. The mean of affected can be calculated by dividing the affected rate by 2 and plotting that area under the normal curve. If a multifactorial disease affects 1/2000 offspring of normal x normal matings, then the mean of affected is an area of 1/4000. The number of standard deviations this area is from the mean can be found in statistical tables. Since first degree relatives have 1/2 their genes in common with their affected relative, first degree relatives of affected will be 1/2 of the way between the mean for affected and the population mean. This can also be calculated. A new normal curve with the same variance is then plotted using the mean for first degree relatives. The threshold does not move, so the overlap of the threshold will give the probability of recurrence to first degree relatives of affected. This is shown in Figure 18. Don't worry, you won't be asked to do this on an examination. This was done solely for the purpose of demonstrating the method for calculating the recurrence risk to relatives of affected. In practice you will simply look up the disease in the proper atlas and find the recurrence risks listed.

Probability of recurrence

Figure 18. Recurrence risk to first degree relatives of affected individuals.

TWO THRESHOLD DISEASES

In many multifactorial diseases the two sexes have different probabilities of being affected. For example, pyloric stenosis occurs in about 1/200 newborn males but only in about 1/1000 newborn females. This means that there is a double threshold, one for females and one for males, with the female threshold farther from the mean than that for the male. However, since it takes more deleterious genes to create an affected female, she has more genes to pass on to the next generation. Her male offspring are at a relative high risk of being affected when compared to the population risk.

SEVERITY OF DISEASE AND RECURRENCE RISK

Unlike Mendelian traits with variable expressivity, where the recurrence risk is the same no matter how severely the individual is affected, multifactorial traits have a higher recurrence risk if the relative is more severely affected. In multifactorial traits, the more severely affected the individual, the more genes he/she has to transmit, and the higher the recurrence risk.

MULTIPLE AFFECTED OFFSPRING AND RECURRENCE RISK

Another difference is the presence of multiple affected individuals within a sibship. In Mendelian traits the number of affected in a family did not change the recurrence risks. But multiple affected children does change the recurrence risk for multifactorial traits. The presence of one affected child means the parents probably are midway between the mean for affected and the mean of the normal population, but the presence of a second affected child means they probably are closer to the threshold, and hence, have a higher recurrence risk should they choose to have another child.

CONSANGUINITY

Consanguinity also increases the probability of an affected child for a multifactorial trait, but only slightly when compared to rare autosomal recessive diseases. First cousin matings may increase the risk for two normal individuals to have a child with a multifactorial disease by about two fold when compared to the risk for unrelated individuals.

HALLMARKS OF MULTIFACTORIAL INHERITANCE

In summary, the hallmarks for multifactorial inheritance are:

  1. Most affected children have normal parents. This is true of diseases and quantitative traits. Most geniuses come from normal parents, most mentally challenged come from normal parents.
  2. Recurrence risk increases with the number of affected children in a family.
  3. Recurrence risk increases with severity of the defect. A more severely affected parent is more likely to produce an affected child.
  4. Consanguinity slightly increases the risk for an affected child.
  5. Risk of affected relatives falls off very quickly with the degree of relationship. Contrast this with autosomal dominant inheritance with invomplete penetrance, where the recurrence risk falls off proportionately with the degree of relationship.
  6. If the two sexes have a different probability of being affected, the least likely sex, if affected, is the most likely sex to produce an affected offspring.

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