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Genetic mapping is an essential first step in characterizing a new mutation causing an interesting phenotype (that is, trait). Consider first the situation of (1) a laboratory organism in which experimental matings can be set up at will and (2) traits that are monogenic and fully penetrant (that is, the phenotype is completely determined by the genotype at a single gene). For example, a Drosophila geneticist might find a dominantly acting mutation at a locus A causing flies to have an extra set of wings (in fact, such mutations exist). He would set up crosses with strains carrying different genetic markers (that is, variants in other genes of known location) in order to find the regions showing correlated inheritance. Figure 2.3A shows a backcross of this type. The gene A is clearly not linked to locus B but is tightly linked to locus C. The proportion of recombinant chromosomes provides a straightforward statistical estimator of the recombination frequency. In this case, the recombination frequency between A and C is about 20/200 = 10 percent. The gene A can be positioned more precisely by using the three-point cross shown in Figure 2.3B, in which two nearby genetic markers are segregating. Here, it is clear that A maps about midway between genes C and D (see figure caption).

For experimental organisms and simple traits, genetic mapping provides a straightforward way to locate the trait-causing gene to a small interval—typically about I centimorgan or less. In essence, one need only ''count recombinants." Because the analysis is so easy, Drosophila geneticists rarely need to appeal to statistical or mathematical concepts. For geneticists studying human families or complex traits, however, the situation is quite different.

Challenges of Genetic Mapping: Human Families and Complex Traits

Medical geneticists studying diseases face two major problems: (1) for human diseases, one cannot arrange matings at will but rather must retrospectively interpret existing families; and (2) for both human diseases and animal models of these diseases, the trait may not be simply related to the genotype at a single gene. Owing to these complications, genetic mapping of disease genes often requires sophisticated mathematical analysis.

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The first problem is the inability to arrange matings. To offset this limitation, human geneticists need to have a huge collection of frequent, naturally occurring genetic markers so that the inheritance pattern of each chromosomal region can be followed just as if one had deliberately set up a cross incorporating specific genetic markers. Throughout most of the century, only a small number of such naturally occurring genetic markers were known (an example is the ABO blood types), and thus human genetic mapping remained a dormant field. In 1980, David Botstein set off a revolution by recognizing that naturally occurring DNA polymorphisms in the human population filled the need (Botstein et al., 1980). By 1994, over 4,000 DNA polymorphisms had been identified and mapped relative to one another.

Even with a dense genetic map of DNA polymorphisms, human genetic mapping confronts several special problems of incomplete information:

· For individuals homozygous (a₁ / a₁) at a gene, one cannot distinguish at this location between the two homologous chromosomes (that is, the maternally and paternally inherited copies of the chromosome).

· For individuals heterozygous (a₁ / a₂) at a gene, one cannot tell which allele is on the paternal chromosome and which is on the maternal chromosome unless one can study the individual's parents.

· Information for deceased individuals (or for those who choose not to participate in a genetic study) is completely missing from the pedigree. Because of these uncertainties, one often cannot simply count recombinants to estimate recombination frequencies.

Another problem is that many traits and diseases do not follow simple Mendelian rules of inheritance. This problem has several aspects:

·Incomplete penetrance. For some "disease genes," the probability that an individual inheriting the disease gene will have the disease phenotype may be less than 1. This probability is called the penetrance of the disease genotype. Penetrance may depend

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Figure 2.3
Examples of three-point crosses. (A) Locus A is  unlinked to locus B but is
linked to locus C at a recombination fraction of 10 percent.

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Figure 2.3
(B) Locus A is located between loci C and D, at about 10
percent recombination  fraction from each. The first two
types of progeny involve chromosomes with no
recombination; the next four involve a single
recombination, and the last two involve
double recombination (between C-A and
A-D). The double recombinant class is
always least frequent, a property that
allows one to determine the order of
three linked loci from a cross in
which they are all segregating.

on other unknown genes, age, environmental exposure, or random chance. For example, a gene called BRCA1 on chromosome 17 predisposes to early onset of breast cancer in some women, but the penetrance is estimated to be about 60 percent by age 50 and 85 percent by age 80. As a result, one cannot conclude that an unaffected person has inherited a normal copy of the gene.