Biology Reference
In-Depth Information
By making specific assumptions about these factors, Hardy (1908) and
Weinberg (1908) independently formulated what is now known as the
Hardy-Weinberg law. This fundamental principle of population genet-
ics states that, if there are two alleles at a single autosomal locus with
population frequencies
p
and
q
, then, for a random mating population in
equilibrium, the frequencies are
p
2
and
q
2
for the two homozygous
genotypes and 2
pq
for the heterozygous genotype. Moreover, these
frequencies remain the same from one generation to the next. Thus, if
the frequency of a recessive disorder in a population is 1 in 10,000 (that is,
q
2
= 0.0001), then
q
= 0.01 (and
p
= 0.99 because
p
+
q
= 1), and the
frequency of carriers of the deleterious gene can be calculated as 2
pq
,
which is 1 in 50.
The Hardy-Weinberg law does not hold if mating is not random in the
population. For example, if mating is consanguineous (between relatives)
or assortative (between individuals with the same phenotype, such as deaf-
ness, as discussed by Nance and Pandya in Chapter 5), then the frequency
of heterozygotes is less than 2
pq
, and the frequencies of homozygotes are
increased. Also, evolutionary forces such as mutation, migration, and selec-
tion change allele frequencies. However, Hardy-Weinberg equilibrium at
an autosomal locus will be restored in one generation after the force is no
longer disturbing the allele frequencies.
Now consider two autosomal loci, both with two alleles (
A
1
,
A
2
and
B
1
,
B
2
). During meiosis (cell division that results in the haploid germ cells),
crossing-over may take place between a pair of chromosomes. Suppose that
one chromosome has the
A
1
allele at the first locus and the
B
1
allele at the
second locus, while the other chromosome has
A
2
and
B
2
, respectively. If
crossing-over occurs, then the haplotype (the set of alleles on the same chro-
mosome) in a germ cell may be
A
1
B
2
, or
A
2
B
1
. If crossing-over does not
occur between these two loci, then all the germ cells will have the haplo-
types,
A
1
B
1
, or
A
2
B
2
. A recombination event is a result of crossing-over that
can be observed in the offspring and is explained in detail by Mueller, Van
Camp, and Lench in Chapter 4.
Linkage disequilibrium is present if the product of the population fre-
quencies of the
A
1
B
1
and
A
2
B
2
haplotypes is not equal to the product of
population frequencies of the
A
1
B
2
and
A
2
B
1
haplotypes. In general, this
means that not enough recombination events between the two loci have yet
taken place in the population to equalize these products. For two loci that
are close together, many thousands of generations may be required to reach
equilibrium at the two loci considered jointly.
The estimation of the frequency of recombination events is the basis of
linkage analysis, which is a method for mapping genes to chromosomes.
To detect linkage, family data (not population data) must be analyzed.
Two loci are said to be linked if the frequency of recombination events
among offspring is less than 50%. If recombination events are very rare
