Download Population Genetics:

Population Genetics:
From previous lecture you know that Sickle Cell anemia and
Thalassemia, both genetic diseases that prevent normal globin
production occurs more often in some populations than others. For both
of these conditions, which are recessive lethals, heterozygotes are more
reproductive in areas of the world where malaria is a problem than
either homozygous class. What we are going to do in the next two
lectures is to take a look at this situation in a more formal way. This
branch of genetics is usually called POPULATION GENETICS.
To begin, let's narrow the field a great deal as to the type of genes and
situations we will consider to simplify the concepts.
1) we will look only at one gene at a time;
2) we will only consider the cases where there are only two alleles A
vs a, or B' vs B;
3) we will only look at Mendelian situations, that is genes in diploid
organisms that reproduce sexually; .not in bacteria, viruses etc.
A "population" is a group of potentially interbreeding individuals; it
may be a local population such as the mice in one barn or it could be as
large as an entire species.
Gene frequency vs genotypic frequency.
Genotypic frequencies are the actual frequency of each genotype;
example; a population has 0.81 AA; 0.18 Aa: 0.01 aa (this is the same as
81% AA, 18% As and 1% aa) These are actual frequencies of each
genotype.
Standard usage in population genetics uses the term gene frequency for
what is actually allele frequency. For example if f(A) = 0.9 and f(a) is
0.1 these are referred to as the gene frequencies. By convention f(A)= p
and f(a) = q
Since we are only looking at cases with two alleles p + q + 1
Further, many of the gene frequencies we deal with may not be genes
at all. They may be frequencies of chromosomal aberrations, RFLPs or
PCR products of an unknown gene; anything that produces a detectable
polymorphism (difference) in the DNA or gene products in individuals
in the population will be included when we talk about gene frequencies.
Lets calculate gene frequencies for a couple of examples, starting with
an easy case where we can differentiate all the genotypes.
The MN blood types of 100 people are determined to be:
50 I MI M: 20 IMI N: 30INI N
What are the frequencies of the M and N alleles in this population of
100 people?
f(M)
= p =50 X 2 (each M person has 2 IM alleles)
+ 20 X 1 (each heterozygote has 1 IM allele)
divided by 100 X 2 total alleles in this population
=120/200 =0.6
then q = 1-p = 0.4 is the frequency of the IN allele.
An alternate way of calculating p is f(MM) + 1/2 f(MN) = 0.5 + 1/2 X 0.2
=0.6
Examine the data in the figure below that shows a gel that was stained
to detect activity of an enzyme after electrophoresis. Since the enzyme
functions as a dimer, when only the normal peptide "a" is present, aa
dimers migrate to the same location and are visible after staining. The
mutant form, a', resulted from a missense mutation where the
substituted amino acid had a charged side chain, so a'a' dimers move to
a different location. In heterozygotes, aa a'a, aa' and a'a' dimers result
in a 3 banded pattern in a 1:2:1 ratio.
AA
(81)
A'A (18)
A'A' (1)
If a population of 100 individuals shows the patterns in the frequencies
indicated, what are the frequencies of the A' and A alleles?
[Answer: f(A) = p = 0.9; f(A') = q = 0.1]
When the heterozygote cannot be discerned, the calculation must be
changed.
Lets use brown eyes versus blue eyes as an example
If we assume B_ is brown and bb is blue, which ignores all the other
shades, modifying genes etc, we can use eye color as a one gene trait
with two alleles.
In Italy 91 % are brown eyed and 9 % are blue. The browns are a mix
of BB and Bb, but we can't look at them and tell, so we cant calculate as
before.
Here we have to make an assumption; the assumption is that the blue
eyed individuals represent the random union of two b gametes. (There
is "random mating" so far as eye color is concerned) Then if b eggs
fertilized by b sperm gives f(bb), the square root of the bbs, tells us
how often b gametes were present:
0.09 = 0.3 = q = f(b)
if q = 0.3, then p = 0.7 = f(B)
In Sweden only 5% have brown eyes and 95% have blue eyes. We again
have to assume "random mating" to get the frequency of the b allele:
0.95 = 0.975 = q
Here we have calculated frequencies for two "populations" as defined by
political/geographic basis and we see large differences in the
frequencies of the two alleles. Both populations have both alleles, the
only thing that differs is the relative frequencies: this is the basis for
differences among all human "populations"
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.
eggs
p (A)
q(a)
p (A) p 2 (AA) pq(Aa)
sperm
q(a) pq(Aa)
or p 2 AA + 2pq Aa + q 2 aa
q 2 (aa)
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 HardyWeinberg Equilibrium
The "forces" that can change gene frequencies are;
• "Drift" or chance fluctuations
• Mutation
• Migration
• Selection
Drift will 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.
Bottlenecks occur 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 leter
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 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,
peq will 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 is very effective at changing gene frequecies,
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-S is lethal.
If there was no selective advantage for a recessive lethal, equilibrium
would be established when the loss of q alleles (q2) 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,
qeq will 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,