Population Genetics

Ben Hecht CRITFC Genetics Training

December 11, 2013

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http://darwin.eeb.uconn.edu/simulations/drift.html

Population Genetics

• The study of how populations change genetically over time under the influence of evolutionary forces

• By studying the frequency and interaction of alleles in populations

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Allele Frequency

• The frequency of the occurrence of an allele from a target locus within a population

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A1 A2

Allele Frequency

1. Count number of individuals = 12

2. Determine total number of alleles = 2 x 12 = 24

3. Count number of each allele present:

Number of A1 = 6 Number of A2 = 18 Verify that 6 + 18 = 24

3. Estimate frequency of each allele:

Frequency of A1 = 6/24 = 0.25

Frequency of A2 = 18/24 = 0.75 Verify that 0.25 + 0.75 = 1

Evolution = change in allele frequency over time 4

Evolutionary Forces

1. Natural Selection – favors an allele that offers a fitness advantage

2. Sexual Selection – (non-random mating) favors more “attractive” alleles (eye color, feather pattern, etc.)

3. Mutation – mistakes made by the cellular machinery when copying DNA, which introduces new alleles

4. Gene Flow – introduction of new alleles through dispersal of individuals (immigration/emigration)

5. Genetic Drift – random change in allele frequency due to a stochastic population decline (i.e. hurricane, fire, etc.)

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Hardy-Weinberg Equilibrium (HWE)

• HWE = Allele and genotype frequencies in a population remain constant from generation to generation

• HWE Assumptions 1. No Natural Selection

2. No Sexual Selection

3. No mutation

4. No migration

5. Infinite population size

• Allele frequency equation • p + q = 1

• Genotype frequency equation

p2 + 2pq + q2 = 1 • Provides an expectation to test hypotheses against

A1 A2

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HWE Genotype Frequency 1. Determine observed genotype frequencies:

Count the number of: A1A1 = 1, A1A2 = 4, A2A2 = 7 *Verify that 1 + 4 + 7 = 12

2. Determine expected HWE genotype frequencies:

Recall allele frequencies…: A1 = 6/24 = 0.25 = p and A2 = 18/24 = 0.75 = q

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…and plug them into the HWE equation: p2 + 2pq + q2 = 1

(0.25)2 + 2(0.25)(0.75) + (0.75)2 = 1 3. Convert frequency to expected number:

p2 = (0.25)2 = 0.0625, 12 x 0.625 = 0.75 2pq = 2(0.25)(0.75) = 0.375, 12 x 0.375 = 4.5 q2 = (0.75)2 = 0.5625, 12 x 0.5625 = 6.75 *Verify that 0.0625 + 0.375 + 0.5625 = 1

4. Compare observed to expected:

Obs_A1A1 = 1 vs Exp_A1A1 = 0.75 Obs_A1A2 = 4 vs Exp_A1A2 = 4.5 Obs_A2A2 = 7 vs Exp_A2A2 = 6.75

EXCERCISE

• Estimate allele and genotype frequencies

• Determine if in HWE

• See effects of…

– Natural Selection

– Genetic Drift

– Gene Flow

– Sexual Selection

…on allele frequencies

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Genetic Diversity

• A measure of variation across the genome • Genetic variation allows populations to adapt to

changing environments • Measured by estimating observed heterozygosity

(Ho) – Proportion of heterozygous (A1A2) individuals in a

population

• Populations with more diversity can adapt to changing environments

• Populations with low variation may not contain genetic material required to adapt

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Genetic Distance (FST)

• The level of genetic divergence/similarity between populations

– High levels suggest divergence (distant relationship/isolation)

– Low levels suggest similarity (close relationship/gene flow)

• Divergence is due to allele frequency (p and q) differences among populations

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Genetic Distance (FST)

• FST = (HT – HS)/ HT

• HT = Expected HWE heterozygosity of total population (multiple subpopulations considered as one)

• HS = Average HWE heterozygosity of subpopulations calculated as ((2p1q1 + 2p2q2)/2)

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Genetic Distance

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Weir

FST = (HT – HS)/ HT

HS = (0.375 + 0.375)/2 = 0.375

HT = 2(0.5)(0.5) = 0.5

FST = (0.5 – 0.375)/0.5 = 0.25

Obs. Genotype Frequency Allele Frequency Exp. Genotype Frequency

A1A1 A1A2 A2A2 A1 (p) A2 (q) A1A1 A1A2 A2A2

Lake A 0.583 0.333 0.083 0.75 0.25 0.5625 0.375 0.0625

7 4 1 - - 6.75 4.5 0.75

Lake B 0.083 0.333 0.583 0.25 0.75 0.0625 0.375 0.5625

1 4 7 - - 0.75 4.5 6.75

Weir 0.333 0.333 0.333 0.5 0.5 0.25 0.5 0.25

8 8 8 - - 6 12 6

Wahlund effect

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Neutral & Adaptive Genetic Variance

http://leavingbio.net/HEREDITY-ORDINARY%20LEVEL_files/image047.jpg

Neutral & Adaptive Genetic Variance

• Neutral variance – genetic variation that has no effect on the fitness of an individual

– Natural selection does not act on this variation

– Genetic variation that does not change protein or expression profile of a gene

– Generally these are variations in non-coding regions of the genome

– Do not violate HWE assumptions

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• Adaptive variance – genetic variation that effects the fitness of an individual

– Natural selection acts on this variation

– Variations that change the protein, or that change the expression profile of a gene

– Generally variations near or within a gene

– Violate HWE assumptions

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Neutral & Adaptive Genetic Variance

Questions?

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