Page 19 - Applied Probability

1. Basic Principles of Population Genetics
2
TABLE 1.1. Phenotypes at the ABO Locus
Phenotypes
A
A/A, A/O
B/B, B/O
B
AB Genotypes
A/B
O O/O
AB (antigens A and B both detected), and O (neither antigen A nor B
detected). These correspond to the genotype sets given in Table 1.1.
Note that phenotype A results from either the homozygous genotype
A/A or the heterozygous genotype A/O; similarly, phenotype B results
from either B/B or B/O. Alleles A and B both mask the presence of the
O allele and are said to be dominant to it. Alternatively, O is recessive
to A and B. Relative to one another, alleles A and B are codominant.
The six genotypes listed above at the ABO locus are unordered in the
sense that maternal and paternal contributions are not distinguished. In
some cases it is helpful to deal with ordered genotypes. When we do, we
will adopt the convention that the maternal allele is listed to the left of the
slash and the paternal allele is listed to the right. With three alleles, the
ABO locus has nine distinct ordered genotypes.
The Hardy-Weinberg law of population genetics permits calculation of
genotype frequencies from allele frequencies. In the ABO example above,
if the frequency of the A allele is p A and the frequency of the B allele
is p B , then a random individual will have phenotype AB with frequency
2p Ap B . The factor of 2 in this frequency reflects the two equally likely
ordered genotypes A/B and B/A. In essence, Hardy-Weinberg equilibrium
corresponds to the random union of two gametes, one gamete being an
egg and the other being a sperm. A union of two gametes, incidentally, is
called a zygote.
In gene mapping studies, several genetic loci on the same chromosome
are phenotyped. When these loci are simultaneously followed in a human
pedigree, the phenomenon of recombination can often be observed. This
reshuffling of genetic material manifests itself when a parent transmits to
a child a chromosome that differs from both of the corresponding homol-
ogous parental chromosomes. Recombination takes place during the for-
mation of gametes at meiosis. Suppose, for the sake of argument, that in
the parent producing the gamete, one member of each chromosome pair is
painted black and the other member is painted white. Instead of inheriting
an all-black or an all-white representative of a given pair, a gamete in-
herits a chromosome that alternates between black and white. The points
of exchange are termed crossovers. Any given gamete will have just a
few randomly positioned crossovers per chromosome. The recombination
fraction between two loci on the same chromosome is the probability that