HARDY-WEINBERG EQUILIBRIUM

At the time that Mendel's work was rediscovered, people began to
question if "dominant genes" (alleles) shouldn't "take over" and spread
through the population.

Hardy and Weinberg both published rational explanations of why gene
frequencies will not change "unless" forced to do so.

Basically, if there is "random mating" with regard to a trait (that is,
matings are made without consideration of the trait), the frequencies
of the dominant and recessive alleles in the population will also be the
frequencies found in the gametes.

Thus when there is random mating, the genotypic frequencies in the
next generation will be p²(AA) : 2pq (Aa) : q²(aa), and the allele
frequencies will still be p and q. This situation is referred to as Hardy-
Weinberg Equilibrium

The "forces" that can change gene frequencies are ;

• "Drift" or chance fluctuations

• Mutation

• Migration

• Selection

Driftwill be the primary factor affecting gene frequency when
populations are small. If the reproductive population only contains a
few individuals it is not surprising that chance is a major factor. For
example if we closed our eyes and counted out 10 jelly beans from a
bowl that contained an even mix of white and black beans, we would
not be surprised if we ended up with more of one color than the other,
or if by chance we got 7 white and 3 black beans. In genetics, to get to
the next generation, we would next draw from a bowl that had 70%
white and 30 % black beans, rather than the 50:50 split we started
with. Then it would not be surprising if we happened to get 6:4 or 8:2
in the next draw. If we follow the same procedure over several
generations, we will end up at "fixation"ie, where all the (alleles) in a
sample are either white or black. From then on, we will be drawing
from populations where only one type of allele is present. How quickly
fixation occurs is primarily a function of sample size; the smaller the
number of interbreeding individuals that contribute to the next
generation, the more rapidly fixation is likely to occur.

There are two special situations where chance can have an effect on
subsequent gene frequencies.

Founder effect: when a few individuals leave one population to start
a new population any allele present in one or more of the
individuals that was rare in the old population is automatically
increased in frequency. By the same token, any allele that is not
present will be lost. For example, none of the 28 original " Dunkers"
passed on a B blood type allele, so there are no persons with blood
types B or AB in todays population.

Pingelap Island; 2o survivors of 1900 hurricane - now 6% of
population have achromatophobia, a recessive condition.

Pitcairn's Island, founded by 6 mutineer's from the HMS Bounty
along with 2 Tahitian men and 8 Tahitian women shows unusual
frequencies for several loci that have been examined in recent
years.

Bottlenecksoccur when a "dissaster" reduces a population to a few
individuals. Often after a forest fire, only a few trees may survive to
repopulate the area, so any rare allele in a survivor will not be so

rare in the future. We may create bottlenecks in animal breeding by
selecting one bull for wide use in artificial insemination and later
find he carried a recessive lethal. In plants, it is not uncommon for
one "outstanding" individual to be selected and propagated
asexually, by selfing, or as a common parent in making hybrids ..
The same genotype may then be grown over a wide area. Later, as
in the case of T cytoplasm that was used in maize to simplify
creation of hybrid seed for sale to farmers, we may find that the
common genotype has an unexpected drawback. In the 1969 case
of maize, the use of "monoculture" in female parents led to disease
susceptibility from Florida all the way through the corn-belt as the
crop matured.

Mutation: Even at high mutation rates, changes in gene frequency
are very slow. To go from p = 1 to p = .99 will take 1,000 generations
with a mutation rate (μ)of 1 in 100,000 gametes. At the same mutation
rate, it would take 10,000 generations to go from p = 0.1 to 0.09. As
"A" mutates to "a", reverse mutations (ϖ)will also become important.
If mutation is the only factor in establishing Hardy-Weinberg
equilibrium, p_eqwill in theory eventually be ϖ/μ+ϖ. If the forward and
reverse rates are identical, each allele would settle at 0.5.

Migration: If migrants from another population with different gene
frequencies move in and contribute to the gene pool, a new gene
frequency will be established for the affected population. Of course if
individuals of a specific genotype leave a population "differentially",
there will also be a change in gene frequencies in the remaining
population.

In general, migration is sporadic; if you know the fraction and gene
frequencies of the original populations, it is relatively simple to
calculate new frequencies. Only a few migrants between populations
will prevent fixation and lead to a "blended" gene frequency in both
populations.

Selection: Selection can be very effective at changing gene
frequencies, even in large populations.

Examples:Sickle cell anemia and thalassemia heterozygotes are more
reproductive than homozygotes where malaria is a problem. Where
malaria is most severe, the frequency of the Hb-S allele can be nearly
0.2, even though Hb-S/Hb-Sis lethal.

"Industrial melanism" In the industrial cities of England where smoke
and coal dust darkened the environment, peppery moths with a gene
for dark pigment had a reproductive advantage while in rural areas,
those with a light color had an advantage. In either area, those that do
not blend well with the background are easy prey for birds.

Special case: Equilibrium may be established where selection against a
recessive lethal is balanced by mutation.

If there was no selective advantage for a recessive lethal in
heterozygotes, equilibrium would be established when the loss of q
alleles (q²) each generation is equal to the introduction of new
recessive lethals by mutation (μ•p)That means that when mutation is
balanced by selection against a recessive lethal, q_eqwill be equal to the
square root of the mutation rate.

Thus:
a) it will not be possible to eliminate recessive lethal alleles by
selection;
b) most of the recessive lethal alleles will be present in
heterozygotges.

Examples include diseases such as PKU

Important point:What will happen to the gene frequency for the pku
allele now that a special diet allows pku/pkuindividuals to reproduce.

REMEMBER:Gene frequencies will not change unless "forced to do so".
Removing selection in the balance between selection and mutation will
not add significantly to the human "Genetic Load"as some people fear.
If about 1 in 16,000 births in the past was a PKU infant it seems
unlikely that mutation alone (this would be a mutation rate of 1 in
16,000 gametes) accounts for the presence of the pkuallele. Even at
such a high mutation rate ,it would take many generations to see a

significant change in the gene frequency. In the meantime, the cure
should remain just as effective for future generations as it is today.

The relatively high incidence of Tay Sachs disease in Ashkenazi Jews
and of cystic fibrosis in Caucasions would not be characteristic of
selection balanced by mutation; the mutation rate would have to be
very high and differ from one population to another. Alternatively,
the differential high frequencies may be a consequence of
heterozygous advantage for resistance to TB ( Tay-Sachs) or cholera
and/or typhoid fever (CF) now or in past generations .