Download Chapter 23 (Mendelian) Population Gene Pool Genetic Variation

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Chapter 23
Frequency
25
20
15
10
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Population Genetics
0
A
B
C
D
F
Grade
N = 57
Avg = 79.5 %
(Mendelian)
Mendelian) Population
• A group of interbreeding, sexually
reproducing organisms that share a
common set of genes
Gene Pool
• For a given gene (or set of genes), the set
of alleles present in a population.
Genetic Variation
• Ubiquitous (its everywhere!)
• Genetic variation is the raw material for
evolution
• What forces shape and limit genetic
variation?
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We need a
mathematical
model!
Genotypic Frequencies
• Single locus, two alleles:
f(AA
AA) =
f(Aa
Aa) =
f(aa
aa) =
Number of AA individuals
N
Number of Aa individuals
N
Number of aa individuals
N
N = Population Size
Allelic Frequencies
f(Allele
Allele) =
Allelic Frequencies
Number of copies of Allele
f(Allele
Allele) =
Number of copies of all Alleles
p = f(A
A) =
q = f(a
a) =
Number of copies of Allele
Number of copies of all Alleles
p+q=1
2nAA + nAa
2N
q=1-p
2naa + nAa
2N
nAA = number of AA individuals
Making it More Complicated:
Mathematical Expansions
• Multiple alleles at a locus
• X linked loci
• Multiple loci
MN Blood Type Antigens in
Humans
Phenotype
Genotype
Number
MM
LMLM
182
MN
LMLN
172
NN
LNLN
44
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Calculate Genotypic and Allelic
Frequencies at this locus
• Genotypic Frequencies:
f(MM
MM) =
f(M
M N) =
f(NN
NN) =
Number of MM individuals
N
Number of MN individuals
N
Number of NN individuals
N
Calculate Genotypic and Allelic
Frequencies at this locus
• Allelic Frequencies:
f(Allele
Allele) =
Calculate Genotypic and Allelic
Frequencies at this locus
• Genotypic Frequencies:
f(MM
MM) =
f(M
M N) =
f(NN
NN) =
Number of MM individuals
N
Number of MN individuals
N
Number of NN individuals
q = f(N
N) =
=
=
182
398
172
398
44
398
=
0.457
=
0.432
=
0.111
Calculate Genotypic and Allelic
Frequencies at this locus
• Allelic Frequencies:
Number of copies of Allele
f(Allele
Allele) =
Number of copies of all Alleles
p = f(M
M) =
N
=
2nMM + nMN
2N
2nNN + nMN
2N
Hardy Weinberg Law
• Describes how reproduction and
Mendelian principles affect allelic and
genotypic frequencies of a population
Number of copies of Allele
Number of copies of all Alleles
p = f(M
M) =
q = f(N
N) =
2nMM + nMN
2N
2nNN + nMN
2N
=
=
2(182) + 172
2(398)
2(44) + 172
2(398)
= 0.673
= 0.327
Assumptions
• Infinitely large population
• Random mating
• No selection, mutation, migration
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Predictions
Hardy Weinberg Equilibrium
• Allelic frequencies of the population do not
change
• Genotypic frequencies reach equilibrium
after one generation
Genotypes are in the expected proportions of :
p2 = f(AA)
2pq = f(Aa)
q2 = f(aa)
Hardy Weinberg Equilibrium
p2 + 2pq + q2 = 1
When a population
is in HWE,
proportions of
genotypes are
determined by
allele frequencies.
Implications of the HardyHardyWeinberg Law
• Population cannot evolve if it meets HW
assumptions.
• Genotype frequencies predictable
(determined by allelic frequencies).
• A single generation of random mating
results in equilibrium frequencies.
Figure 23.3
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Hardy Weinberg
Estimating Allelic Frequencies
• Provides a framework for studying
population genetics.
• We can estimate Allelic frequencies in a
population when dominance is present.
• It is a NULL MODEL that describes what
happens in a population that is only
subject to the rules of Mendelian
inheritance.
• This is useful for diseases that are
recessive traits, such as Cystic Fibrosis.
Cystic Fibrosis in Humans
• We must assume H-W equilibrium
Cystic Fibrosis in Humans
Frequency of Cystic Fibrosis in North
American Caucasians is 1 in 2000
f(AA) = p2 = 0.982 = 0.960
q2 = f(aa) = 0.0005
f(Aa) = 2pq = 2(.02)(.98) = 0.0392
q = 0.02
p = 1 - q = 0.98
Assumptions
• Infinitely large population
This is the
frequency of
carriers in the
population
Nonrandom Mating
• Positive Assortative Mating
– Like individuals mate (eg height in humans)
• Random mating
• No selection, mutation, migration
• Negative Assortative Mating
– Unlike individuals mate
• Inbreeding
– Preferential mating between relatives
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Figure 23.4
Nonrandom mating
alters genotypic
frequencies, but not
allelic frequencies
Identical by descent
Identical by state
Inbreeding
• Frequency of homozygotes increases.
Inbreeding Coefficient
• Measures the probability that two alleles
are identical by descent (IBD).
• Frequency of heterozygotes decreases.
• Ranges from 0 (Random mating) to 1 (All
alleles IBD)
F
Inbreeding Depression
• Increase in frequency
of lethal and
deleterious traits with
inbreeding.
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Figure 23.5
Assumptions
• Infinitely large population
Figure 23.6
Mutation
• All genetic variation ultimately arises
through mutation.
• Random mating
• Mutation rates are low.
• No selection, mutation,
mutation migration
• Effect PER GENERATION is small
Mutation
• Mutation rate:
µ = forward mutation rate
When mutation is
incorporated into the
model, the forward and
reverse mutation rates
determine the
equilibrium allele
frequencies.
ν = reverse mutation rate
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Migration
Assumptions
• Infinitely large population
• Random mating
• No selection, mutation, migration
• Influx of alleles from other populations
• Also called gene flow
• Decreases genetic differences among
populations
• Increases genetic variation within
populations
Assumptions
• Infinitely large population
Then what
good is Hardy
Weinberg?
There are no
INFINITELY LARGE
populations.
• Random mating
• No selection, mutation, migration
Sampling Error
• In a finite population,
population only a sample of alleles
are transmitted to the next generation
• By chance, the frequency of the alleles in the
gametes may be different than the parental
frequencies
Genetic Drift
• Sampling error may lead to changes in
allelic frequency
• Direction of change is random
• Magnitude depends on population size
• The smaller the sample, the larger the potential
deviation
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Magnitude of Genetic Drift
• Depends on the population size
Magnitude of Genetic Drift
• Depends on the population size
BUT:
• Only individuals who contribute alleles to
the next generation are counted
Effective Population Size
Ne
• The size of an idealized population that
would undergo the same magnitude of
genetic drift as the population under
consideration
Ne < N
•
•
•
•
Uneven sex ratio
Variance in reproductive success
Fluctuations in N over time
Non random mating
Effect of Uneven Sex Ratio:
Ne =
4 x nmales x nfemales
nmales + nfemales
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Causes of Genetic Drift I
• Chronicly low population size caused by
ecological limitations
Causes of Genetic Drift II
• Founder Effect: a population is established
from a small number of founders
– Limited space, food, etc…
– Example: Desert pupfish
Causes of Genetic Drift III
• Genetic Bottleneck: a population
undergoes a drastic reduction in size
Effects of Drift
• Change in allelic frequencies in a
population
• Loss of genetic variation within
populations
Elephant Seals
went through a
bottleneck in the
late 1880s. As few
as 20 existed in
1884.
• Genetic divergence among populations
107 populations, Ne = 16
Genetic Drift can
cause divergence
among populations!
Figure 23.13
Ne = 20
Figure 23.14
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