Download Population Genetics

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Evolution
• The process of change in the genetic
makeup of populations.
• The basis of the change is change in
gene frequencies over time.
• How the frequency of a mutant allele
change in time under various
evolutionary forces.
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Population
• A population is any group of members of
the same species in a given geographical
area.
• Gene pool refers to the collection of all
alleles in the members of the population.
• Population genetics refers to the study of
the genetics of a population and how the
alleles vary with time.
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Allele Frequencies
# of particular allele /total # of alleles
• count both chromosomes of each individual
• Allele frequencies affect the genotype
frequencies or the frequency of each type of
homozygote and heterozygote in the
population.
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Fixation of an allele:
An allele must increase in frequency
and ultimately become fixed in the
population (all individuals have the
same allele).
Fitness: of a genotype, a measure of
individual’s ability to survive and
reproduce (it is rather relative with
respect to other individuals).
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Allele frequencies can change creating
microevolution
Conditions in which allele frequencies can change:
• Individuals of one genotype
reproduce more often with each
Nonrandom mating
other
• Individuals migrate between
Migration
populations
• Population size is small or a
Genetic drift
group becomes reproductively
isolated within a larger population
• Mutation introduces new alleles
Mutation
or new copies of alleles
• Individuals with a particular
Selection
genotype are more likely to have
viable, fertile offspring (negative,
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neutral, or positive selection)
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Hardy-Weinberg Equilibrium
A condition in which allele frequencies remain
constant is called Hardy-Weinberg equilibrium
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Hardy-Weinberg Equilibrium
A condition in which allele frequencies remain
constant is called Hardy-Weinberg equilibrium
p+q=1
p
q
p2
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All of the allele frequencies together
equals 1 or the whole collection of alleles
allele frequency of one allele
allele frequency of a second allele
+ 2pq +
q2 =
1
All of the genotype frequencies
together equals 1
p2 and q2
genotype frequencies for each homozygote
2pq
genotype frequency for heterozygotes
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Hardy-Weinberg Equilibrium
Generation 1
p allele frequency of D normal finger length = .7
q allele frequency of d short middle finger = .3
Genotype
frequencies
DD
p2 = (.7)2 = .49
Dd
2pq = 2 (.7)(.3) = .42
Gamete
.49
frequencies
Frequency D gamete= .7
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.21
dd
q2 = (.3)2= .09
.21
.09
frequency d gamete = .3
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Hardy-Weinberg Equilibrium
Generation 1
p allele frequency of D normal finger length = .7
q allele frequency of d short middle finger = .3
Frequency D gamete= .7
frequency d gamete = .3
Male gametes
d
D
q=.3
p=.7
Female D
DD
Dd
gametes p=.7 p2=.49 pq=.21
d
Dd
dd
q=.3 pq=.21 q2=.09
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Proportion
Possible
matings
In population
Male
Female
Frequency of
offspring
genotypes
DD
Dd
dd
.49 DD .49 DD .2401 (DDxDD)
.2401
.49 DD .42 Dd
.2058 (DDxDd)
.1029 .1029
.49 DD
.42 Dd
.42 Dd
.42 Dd
.09 dd
.49 DD
.42 Dd
.09 dd
.0441 (DDxdd)
.2058 (DDxDd)
.1764 (DdxDd)
.0378 (Ddxdd)
.0441
.1029 .1029
.0441 .0882 .0441
.0189 .0189
.09 dd
.09 dd
.09 dd
.49 DD .0441 (DDxdd)
.42 Dd .0378 (Ddxdd)
.09 dd .0081 (ddxdd)
.0441
.0189 .0189
.0081
Resulting offspring frequencies
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.49
.42
.09
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Application of Hardy-Weinberg Equilibrium:
calculating risk
Risk of being a carrier of cystic fibrosis
for an Caucasian American depends upon
Frequency of disease in population = 1 / 2000
q2 = .0005
Frequency of CF disease allele
=
=q
q2 = .022
Frequency of wildtype CF allele
=p
p + q = 1, so
= 1 - q = .977
Frequency of being heterozygote
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= 2pq
= 2 (.977)(.022) = .043
1 in 23
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How to calculate p and q from
genotypic frequencies:
If you don’t know p and q, but you can
distinctly identify homozygotes from
heterozygotes, then p:
(2 times # of homozygotes + number of heterozygotes)/2N
If you don’t know p and q, but you
know (p2+2pq) and q2; then assume
equilibrium and calculate q from q2:
q = square root of q2
p = 1-q
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Carrier Frequency for Cystic Fibrosis
Population
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Carrier
Frequency
African American
1 in 66
Asian American
1 in 150
Caucasian American
1 in 23
Hispanic American
1 in 46
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Application of Hardy-Weinberg Equilibrium:
calculating risk with X-linked traits
Females:
p2 + 2pq + q2 = 1
Males:
p+q=1
All of the women
in the population
All of the men
in the population
Hemophilia is X-linked and occurs in 1 in 10,000 males
p= 1/10,000 = .0001
q= .9999
Carrier females
= 2pq = 2 (.0001) (.9999)
= .0002
1 in 5000 are carriers
Affected females = p2 = (.0001) 2
= .00000001 1 in 100 million women
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will have hemophilia
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Application of Hardy-Weinberg Equilibrium:
DNA identification
SNPs or Single nucleotide polymorphisms
Single base differences between chromosomes
Repeated sequences
Variation in the number of repeats present
Variation in DNA sequences outside of genes are subject
to Hardy-Weinberg equilibrium.
Noncoding variation is useful as it is not subject to as many
impacts that lead to deviations in H-W equilibrium namely
selection and assortative mating.
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Application of Hardy-Weinberg Equilibrium:
DNA identification
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Application of Hardy-Weinberg Equilibrium:
DNA identification
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Forces that alter allele frequencies
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Migration
• Changes in allele frequency can be
mapped across geographical or linguistic
regions.
• Allele frequency differences between
current populations can be correlated to
certain historical events.
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Mapping a trait geographically can
suggest patterns of migration
Frequencies of
galactokinase deficiency
decrease westward from
Bulgaria.
Gradients in allele
frequencies between
successive neighboring
populations are called
clines.
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Genetic variation in space and time & natural variation in populations:
•
Genetic structure of populations and frequency of alleles varies in
space or time.
•
Allele frequency cline =
allele frequencies change
in a systematic way
geographically.
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Fig. 22.6, Allele frequency
clines in the blue mussel.
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Genetic Drift
Events that create small populations
enhance the effect of genetic drift.
Founding a new population
Bottlenecks (natural disaster, famine)
Geographic separation (islands)
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Genetic drift
A population bottleneck occurs when a large
population is drastically reduced in size.
Rebounds in population size occur with
descendants of a limited number of survivors.
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Genetic drift:
•
Chance alone may result in changes in allele frequency, including
fixation and extinction.
•
Genetic drift is analogous to sampling effect.
•
Genetic drift has important consequences for small populations.
Example:
•
Island population of 10 individuals; 5 with brown eyes (BB) and 5
with green eyes (bb); f(B) = 0.5, f(b) = 0.5.
•
Typhoon devastates the island; 5 people with brown eyes (BB) die.
•
Allelic frequency of b , f(b) = 1.0; chance events have radically
changed the allele frequencies and the population evolves.
•
Now imagine the same scenario for an island of 10,000 inhabitants.
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Genetic drift:
•
Chance deviations from expected ratios of gametes and zygotes also
produce genetic drift.
•
Cross Aa x aa  expect 50% Aa and 50% aa, but not all of the time
insofar that sampling is limited (sampling error).
•
Sampling variance: sp2 = pq/2N
*N = number of individuals in the population.
•
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Variance is large for small populations, and small for large
populations.
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Effective population size (Ne)
When number of males and females are not
equal, the Ne is:
Ne = (4 x Nf x Nm)/(Nf + Nm), where Nf and Nm
are breeding females and males, respectively.
If Nf = 36 and Nm = 36, Ne equals Ntotal:
Ne = (4 x 36 x 36)/(36+36) = 72
If Nf = 70 and Nm = 2:
Each male contributes ½ x ½ = 0.25 of the alleles to the
next generation (both males 0.5 of all alleles)
Each female contributes ½ x 1/70 = 0.0071 of all alleles.
Ne = (4 x 70 x 2)/(70+2) = 7.8 (~8 breeding adults).
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Sampling variance of p
Remember sampling variance:
sp2 = pq/2N
Consider unequal number of
breeding males and females:
sp2 = pq/2Ne
Standard error: sp = √pq/2Ne
95% confidence limit = p  2sp
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Buri’s study of genetic drift in
Drosophila
Actual data for 107
experimental populations.
Randomly selected 8 males
and 8 females (N = 16) from
each population for the next
generation for 19
consecutive generations.
Calculated the frequency of
bw75 allele, and generated
a frequency distribution
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Mutation
Allele frequencies change in response to mutation.
Mutation can introduce new alleles.
Mutation can convert one allele to another.
Mutation has a minor impact unless coupled with
another effect (small population size, selection).
Selection acts to eliminate deleterious alleles.
•Dominant deleterious alleles disappear quickly.
•Recessive deleterious alleles are eliminated
when homozygotes appear and fail to reproduce.
The collection of recessive deleterious alleles
present in a population is called the genetic load.
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Mutation:
•
Heritable changes within DNA.
•
Source of all truly new genetic variation.
•
Raw material for evolution.
Mutation rate varies between loci and among species:
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•
~10-4 to 10-8 mutations/gene/generation.
•
Mutation rate is abbreviated
•
Some mutations are neutral (no effect on reproductive fitness).
•
Others are detrimental or lethal (depends on environment).
•
If population size is large, effects of mutation act slowly.
.
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Mutation:
Irreversible mutation:
Allele A is fixed (p =1.0) and mutates A  a at rate of
Hartl & Clark (1997) Principles of Population Genetics
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 = 10-4:
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Fig. 22.3, Frequencies of genotypes AA, Aa, and aa relative to the
frequencies of alleles A and a in populations at Hardy-Weinberg
equilibrium.
Max. heterozygosity
@ p = q = 0.5
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