Population Genetics

1
Population Genetics
we've already talked about a number of different
pieces of population genetics restriction
fragment length polymorphisms as a means of
identifying individuals sickle cell anemia
being found primarily in individuals from
Africa simple sequence polymorphisms found in
different individuals single nucleotide
polymorphisms are base changes in at least 5 of
the population in all cases, looking at
something that is differentially distributed
among individuals in some group
2
Population Genetics
population group of organisms of the same
species living in an area subpopulation small
group of organisms subdivided by a similar
feature local population size of a group in
which most indivduals will find a mate
3
Population Genetics
gene pool complete set of genetic information
found in all of the individuals of a
population-- ie. list of all the currently
existing mutations in every gene allelic
frequency how often a particular mutation is
found in a population
4
Population Genetics
another example-- AIDS resistance CCR5 receptor
on white blood cells that binds a particular
ligand also is the major protein which the
AIDS virus uses to infect cells one allele of
CCR5 is D32, a 32 bp deletion in the reading
frame of CCR5 ie. protein made is a frameshift
mutation and is nonfunctional D32 is found in
20 of individuals in HIV infected individuals
who fail to develop AIDS within 10 years, the
frequency is 40
5
Population Genetics
as an example 1000 individuals studied 795 AA
190 Aa 15 aa genotypes (A normal CCR5, a
D32 CCR5) represents a total of 2000 alleles
(ie. each individual is diploid) 7952 190
1780 A alleles /2000 total 0.89 89 190
152 220 a alleles / 2000 total 0.11
11 allele frequency times a gene appears in
a gene pool genotype frequency times a
genotype appears in a population ie. the aa
genotype frequency is 15/1000 1.5 the a
allele frequency calculated above is 11
6
Population Genetics
if all individuals in a population has an allele
(ie 100) said to be fixed if no individuals are
left carrying the allele (ie. 0), said to be
lost carry it further in a population, given
an allele frequency it is possible to predict
what percentage of offspring will have a given
genotype ie. for an AA individual 0.89 0.89
0.792 for an Aa indivdiual 2 0.89
0.11 0.196 for an aa individual 0.11
0.11 0.012 note that these are the expected
genome frequencies -- can be compared to the
experimental genomic frequencies using a chi
squared test
7
Population Genetics
random mating local population mate
independently of genotype ie. mutation cannot
prevent or select against a mating inbreeding
mating to a close relative-- ie. a small local
population plants undergo self-fertilization,
an extreme level of inbreeding for random
matings, the likelihood of any allele being
present is the same as the allele
frequency inbreeding increases the frequency
of rare dangerous alleles
8
Hardy-Weinberg Principle
Hardy-Weinberg principle for a gene with 2
alleles, genotypes are given by the binomial
theorem based on the frequency of each allele
p probability of A, q probability of a, and p
q1 (only 2 alleles)
for the general case, p probability of (A), q
probability of (a), the binomial theorem says
the ratios will always be AA p2 Aa
2pq aa q2 total probability 1 (all) if
q0.01 P(Aa) 2.99.010.0198 P(aa)
.01.01 .0001 most rare alleles will be found
in heterozygotes
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Hardy-Weinberg Principle
Hardy-Weinberg principles can also extend into
multiple alleles (3) total probability has to
add up to 1 (ie. p1 p2 ... pn 1) basically
each has a genotype frequency and you can
calculate the allele frequency ie. for 3
alleles of gene A A1, A2, and A3 with p1, p2,
and p3 the frequency of any homozygous allele is
the square of its probability thus frequency
of A1A1 is p12 the frequency of any two
heterozygous alleles is 2x the product of the
probabilities ie. frequency of A1A3 2 p1p3
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Population Genetics Problem
Gregor Mendel's brother Ivan Mendel went out into
the country and counted the number of purple
flowered peas vs. the number of white flowered
peas in the fields around his brother's
monastery. He found 930 true breeding purple
flowered peas, 370 true breeding white
flowered peas, and 1300 white flowered non-true
breeding peas. What is the allele frequency
of W (white) and w (purple) in the fields? do
Ivan's numbers make sense? total of alleles
2 (930 370 1300) 5200 probability of purple
(9302) 1300 3160 / 5200
0.61 probability of white (3702) 1300
2040 / 5200 0.39 using Hardy Weinberg, we
expect p2 0.372, 2pq 0.476, q2 0.152 to
be the genotype frequencies
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Population Genetics Problem
from 2600 plants, we would expect 2600 0.372
967 purple homozygotes 2600 0.476 1238
white heterozygotes 2600 0.152 395 white
homozygotes c2 S (observed-expected)2/expected
c2 (930-967)2/967 (1300-1238)2/1238
(370-395)2/395 c2 1369/967 3844/1238
625/395 c2 1.416 3.105 1.582 c2 6.103,
compared to chart with 2 degrees of freedom
just about significantly different!-- it may look
reasonably close, but MUST work through the
calculations!
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Hardy-Weinberg Assumptions
matings must be random-- homozygotes cannot
prefer each other! population must be 'large'
ie. chance cannot change the outcomes
13
Hardy-Weinberg Assumptions
all genotypes are equal in survival and fertility
(no selective advantage) mutation does not
occur (ie. can only have 2 alleles)
aa
Aa
AA
AA
Aa
Aa
Aa
Aa
AA
aa
aC
Aa
AA
AA
Aa
Aa
Aa
Aa
AA
aa
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Hardy-Weinberg Assumptions
allele frequencies are the same in males and
females (otherwise the the probability of
A or a depends upon the parents and not
random) migration into the population does not
occur (ie. population is isolated)
aa
Aa
AA
AA
Aa
Aa
Aa
Aa
AA
aa
aa
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Hardy-Weinberg Special Cases
for 2 alleles that do not give a selective
survival advantage, the allele frequency does
not change over time for the next generation, p'
is the probability of A p' prob(AA) 1/2
prob(Aa) (all AA gametes are A, only half of
Aa) p' p2 1/2 2pq p' p2 pq p' p
(pq) (pq)1 (because there are only 2 alleles
for a given gene) p' p thus the frequency
does not change for a given allele
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Hardy-Weinberg Special Cases
Hardy-Weinberg principle p2 2pq q2
frequencies if q is very small (ie. probability
of a mutant is low), homozygotes for a rare
allele will be extremely small if q 3, a bit
more than 5.8 of the population are heterozygous
for that allele (genotype frequency), but
0.09 (less than 1 in 1000) are homozygous for
the same allele if q 1, .01 (1 in 10,000
people) are homozygous... goes way down note
in a mating between two heterozygotes, the
probability of having a homozygous individual
with a rare allele is the normal
25 Hardy-Weinberg assumes a random mating in
the local population
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Hardy-Weinberg Special Cases
X linked genes have a different formula because
males have only 1 copy females have the same
ratios for both X linked and somatic alleles for
gametes with a Y chromosome (male gametes)
genotype frequency is the exact same as the
allele frequency (ie. for A1, allele frequency is
p1) if the X linked trait is rare and recessive,
many more males will have the phenotype than
females for example, if p 0.02 for a recessive
X linked allele, 0.02 0.02 0.0004, or
0.04 of females will have the phenotype 0.02,
or 2 of males will have the phenotype-- 50x more!
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DNA Typing
many genes are polymorphic blood types (A,
B, O) sickle cell anemia (hemoglobin) DNA
typing use of genetic markers for identifying an
individual when using DNA analysis for
identification, several highly polymorphic
regions are used DNA from tiny amounts of tissue
(skin cells, hair, etc) is amplified by the
polymerase chain reaction (PCR) the more alleles
match, the more likely the person is the culprit
most used in DNA typing are simple sequence
repeats (SSRs) many different alleles are
possible (ie. each length), but 1 person must
carry at most 2 different alleles (may carry 2
of the same allele)
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DNA Typing
most individuals are heterozygous for
SSRs fragment sizes cover a large range (a few
to hundreds of copies) DNA typing is
generally based on at least 3 (preferably more)
different SSRs more loci, less chance of a
random match likelihood of a random match for
multiple SSRs is the product of their
individual probabilities (ie. multiplication
rule for independent events) different
subpopulations can have different allele
frequencies (ie. sickle cell anemia is high
among those of african descent)