In Chapter 6, we explored the genetic relationships among relatives by discussing basic Mendelian patterns of inheritance. Here we approach the analysis of gene transmission within families again, but in a slightly more formal way. Superficially, a pedigree is really nothing more than a series of Mendelian genetic crosses involving relatives. But we often find that seeing the patterns of expression in a pedigree can yield important clues about a genetic condition that the study of one isolated patient or family cannot.
Various approaches can provide information about patterns of inheritance. One of the first studies of this kind was done by George Darwin, the son of Charles Darwin, who explored the frequency of first cousin marriages in Great Britain. Indeed, George Darwin was the product of a first-cousin marriage between his father and his mother, Emma, a member of the Wedgwood china family. George Darwin's focus was on marriages between people with the same surname and yielded a frequency of 2.25% to 4.5%, with the British upper classes being at the high end of the range. Studies now utilize DNA markers, especially short tandem repeats (STRs) in the paternally-transmitted Y chromosome and hypervariable region mutations in the maternally-transmitted mtDNA.
Pedigrees are organized by generation. Symbols used to summarize information about the phenotypes and biological relationships are shown in Figure 9-2. Here is a useful hint: to begin to interpret an inheritance pattern, reverse the way you normally think about gene transmission. Rather than looking for the appearance of a trait among the progeny of a family, look from the progeny generation backward toward the parents. In other words, begin by looking at transmission patterns by moving your attention up the pedigree, not down it. If, for example, a child shows a dominant trait, then you expect one of the parents to show it. The other direction is not as certain. Just because a parent has a dominant trait does not mean that one of their few children will necessarily inherit it. Examples of this logic are explored in the next section.
Symbols used in pedigree construction.
The proband (or propositus [male], proposita [female]) is the first member in a family to be evaluated by the physician. If affected, that individual is the index case for the pedigree. Relatives may be first degree (parents, siblings, offspring of the proband), second degree (grandparents, grandchildren, uncles, aunts, nieces, nephews), or third degree (cousins, and so forth).
Finally, as with any analysis of human inheritance, pedigrees are susceptible to confusion by what we might call extramarital involvements. Even adoption is not always acknowledged publicly. Sensitivity to such issues is a natural and necessary element of all human genetic analyses. There can be a fine balance when issues of privacy and scientific accuracy are in play. Although pedigrees might only rarely include complications of this type, such possibilities should never be forgotten.
One way to approach a pedigree is to ask a simple set of questions, since the number of common inheritance patterns is fairly small. To outline a logical approach, a few simplifying assumptions will be made. We will assume that the pedigree reflects the accurate biological relationships among genetically-related individuals and that the trait is a single-gene Mendelian characteristic, rather than a multiple-gene, or polygenic, predisposition.
First determine whether the trait is dominant or recessive. Dominance is easily recognized.
If the trait is dominant, each affected child will have an affected parent. The lineage of the trait can be traced continuously up the pedigree (Figure 9-3).
Furthermore, unaffected siblings will have only normal offspring.
Sample pedigree for a simple dominant trait.
But, if the trait commonly skips generations so that an affected child has phenotypically normal parents, then it does not fit the pattern of a dominant. The alternate hypothesis, recessive inheritance, is supported (Figure 9-4). To confirm recessive inheritance, note that if two affected individuals (both being recessive homozygotes) have offspring, all of the offspring will have the trait. Also be aware that recessive traits may show up more often in pedigrees involving consanguineous marriages (matings between close relatives).
Representative pedigree showing an autosomal recessive trait. The appearance of affected offspring from normal parents is consistent with recessive inheritance. For offspring II-8 to -10, there is evidence the trait is autosomal, since a homozygous female for a sex-linked trait must pass it to all of her sons. Can you find another piece of evidence in support of autosomal linkage?
If a trait generally follows one of these common patterns but an occasional exception occurs, then consider additional factors like incomplete penetrance (Figure 9-5). A dominant trait that occasionally appears to skip a generation may simply be non-penetrant in an affected member of the family and thus undetectable by general visual assessment.
This pedigree is consistent with dominant inheritance, except for individual III-3, who apparently passes on the dominant trait but does not express it. This can be interpreted as an example of incomplete penetrance.
The next step is to determine linkage relationships (Figure 9-6). Is the trait or DNA marker sex-linked (i.e., transmitted on an X chromosome or, more rarely, on a Y) or is it autosomal? For sex-linkage, we will limit our attention to the X chromosome. A good way to approach this question is to look for exceptions to the pattern expected for a sex-linked trait. If an exception to sex-linked transmission is found, the trait must be autosomal.
Representative pedigree for a sex-linked trait. Passage is never from father to a son, but an affected female has only affected sons. Here is a "test yourself" question: could the parents III-3 and III-4 be theoretically able to produce an affected daughter? The answer is "no." Why not?
Are there examples of both a father and a son expressing a dominant trait? Here the focus is on excluding sex-linkage by finding exceptions. The father only passes his X chromosome to his daughters. If a son inherits the trait from the father, it cannot be sex-linked (see, for example, Figure 9-5). Of course, one must be careful when a trait is common in the population or when both sides of the family carry it. In those cases a son and father might both be affected with a sex-linked condition, but the son inherited from the mother, not the father.
For a recessive sex-linked trait, all sons of an affected (i.e., homozygous) mother will express the trait.
When a sex-linked trait is recessive, it will appear most commonly, and perhaps exclusively, in the males of a pedigree. With only one X chromosome, a male will express a trait no matter whether it is dominant or recessive in females. But if the sex-linked trait is dominant, it might be expected to occur somewhat more frequently in females if a large number of individuals in a population are screened. This is simply because 2/3 of all X chromosomes are found in females.
Of course, there will be exceptions to these typical patterns. One must combine information about the pattern of inheritance with knowledge about the phenotype. If the trait is gender-specific, like female lactation, or is sex-influenced, like pyloric stenosis found more often in males or lupus erythematosis in females, then a simple analysis of affected genders in the pedigree alone can be misleading. Pedigree analysis is, after all, a kind of puzzle.
Sample Pedigree Evaluation: Applying the Rules
One reason to determine the mode of transmission and expression for a pedigree is to allow predictions about children who will be born into it. Once a trait has been characterized, it is possible to assign genotypes, or at least probabilities of a given genotype, to members of the pedigree and use that information to predict the trait's expression in the next generation.
Consider the pedigree in Figure 9-7. The first question is the type of expression, dominant or recessive. In this case, we hypothesize that the trait is recessive. The affected daughter in the second generation (II-7) shows the trait, but both parents are normal. Next, is the trait inherited autosomally or on the X chromosome? If the trait were sex-linked, the affected daughter would be homozygous and must have inherited the trait from both parents. With only one X chromosome, the father must express it, but he does not. Thus, we can conclude that the recessive trait is autosomally inherited.
A pedigree to evaluate as a sample problem (see text).
Now knowing the manner of transmission, we can begin to assign genotypes to some individuals. For example, the first generation parents in the right-hand side of the pedigree (the female I-3 and male I-4) must both be heterozygous since they produce a homozygous recessive daughter. For convenience, let us assign the symbol A for the dominant and a for the recessive alleles (Figure 9-7b). On the left-hand side, a phenotypically normal AA female I-1 and affected aa male I-2 have a phenotypically normal, thus heterozygous, daughter (II-3). In the absence of any conflicting evidence, we always assume that individuals, like male II-4, marrying into the pedigree are genetically normal for the trait. The mating that gives rise to male III-1 is, therefore, Aa × AA, and there is a ½ chance that male III-1 is heterozygous Aa.
Returning again to the right-hand side of the pedigree, let's consider the genotype of male II-5. In order for the child of interest (IV-1) to be homozygous for the a allele, the allele must be passed on by male II-5. What is his probability of his being heterozygous? The answer is 2/3. This number might initially surprise you (a common error is to say the probability is ½), but the logic is simple. Of the four possible outcomes of a mating between two heterozygous parents, one is eliminated by the pedigree; the male II-5 is not aa since he does not express the recessive trait. Thus, among the remaining three possible outcomes involving phenotypically normal offspring, two are Aa heterozygotes and the third is homozygous normal (AA). Then, if II-5 is heterozygous, there is a 0.5 chance of his passing the recessive allele to his daughter, III-2. For the yet-to-be-born child, IV-1, to show the recessive trait (a ¼ chance if both parents are heterozygotes), then all of these transmission events must have occurred. The overall probability requires applying the product rule.
The product rule applied to probabilities is simply that the likelihood of two or more events occurring together is the product of their individual probabilities. For example, the probability of flipping two nickels and getting a head both times is ½ (the probability of a head the first time) times ½ (the probability of getting a head the second time) = ¼. The other three outcomes are: head + tail; tail + tail; and tail + head. An assumption is, of course, that the events in question are independent.
Each member in a pedigree is the product of an independent fertilization event. The probability of inheriting the mutant a allele from a Aa heterozygote is, therefore, ½. The overall probability of a given outcome can be calculated by multiplying the probabilities of each required step leading to that hypothetical outcome. We can multiply the required steps in any order we wish, as long as all are included in the calculation. Ignoring the certainties (a probability of 1.0) and moving from generation II through IV, the calculation is ⅔ × ½ × ½ × ¼ = 1/24 of child IV-1 being aa and showing this recessive condition.
The analysis of a pedigree is, therefore, a combination of applying known information and calculating probabilities for elements that are unknown. By first determining the probable mode of transmission, one can convert individual phenotypes into genotypes. Then, breaking the pedigree down into individual families, one can predict the likelihood of specific transmission events. The overall assessment factors in these individual probabilities. Having a logical structure like this to work from allows you to approach even the most complex pedigree in an organized and confident manner.