Hardy-Weinberg:

1
Hardy-Weinberg

• An introduction

2
Hardy-Weinberg Theorem

• Allele frequencies stay constant if there is no
  selection and it's other assumptions are met
• Heterozygosity will also stay the same

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Starts and end the same
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Figure 6-7a
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Calculating HW
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Two allele equation

• p2 2pq q2 1
• p frequency of allele A
• q Frequency of allele a
• p q 1.
• So p2 AA, q2 aa, and pq Aa

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Sophisticated Punnet square
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Genotype frequencyAlso Constant
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Calculating Genotype Frequencies Product Rule
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Assumptions

• Random mating
• Very large Population size
• Diploid
• Sexual
• Non-overlapping generations
• No migration
• No mutation
• No selection.

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Figure 6-11
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So what good is it?

• Provides an evolutionary baseline
• Calculate deviations from the H.W. Ideal

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More than 2 alleles

• Allele Frequencies
• P1 P2 P3 1
• Genotype Frequencies
• P12 P22 P32 2P1P2 2P1P3 2P2P3

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Hardy-Weinberg and Selection
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No Selection
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Add Selection
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Selection Over Time
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Empirical Research Alcohol Dehydrogenase
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Selection Can Change Genotype Frequency
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When is Selection Not Enough?

• Recessive Alleles
• HIV resistance
• CCR5 vs CCR5-?32
• ?32/?32 Homozygote confers resistance
• Should be sweeping towards fixationright?
• Its a good allele

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Setting The Stage

• So lets assume the highest frequency
• 20 in Ashkenazi Jews
• Assume highest infection rate
• 25 in Zimbabwe, Swaziland, Namibia, Botswana

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Figure 6-17a
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But are these assumptions reasonable?
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Europe

• 20 ?32 Reasonable
• But HIV infection rate less than 1

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Figure 6-17b
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Parts of Africa

• Infection rate up to 25
• But ?32 is almost absent

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Figure 6-17c
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Why doesnt selection work?

• Selection pressure is strong
• There are a few copies of ?32

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Patterns of Selection
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Recessive Lethal in Flour Beetles
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Decreased lethal alleles over time
32
But Why arent they eliminated?
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Two Phenotypes

• D. melanogaster
• Lethal recesive

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Why did frequency of viable allele stabilize?
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Overdominance/Heterozygote advantage

• Results in stable equilibrium

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Underdominance/Homozygote advantage

• Results in unstable equilibrium
• Equilibrium depends on selection pressure

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Figure 6-23f
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Figure 6-23g
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Frequency Dependent Selection

• Fitness depends on frequency in population

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Figure 6-24a

• Elderflowers

• Purple or Yellow
• Dont provide nectar
• Bees alternate color
• Looking for reward
• Eventually leave
• Rare color visited more often
• Since bees alternate
• How did frequency affect fitness?

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Figure 6-24b
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Figure 6-24c
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Types of selection
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American Eugenics Movement

• Social Darwinism
• Starting in the late 1800s
• Big after WWI
• Immigration
• Obvious inequalities
• All of societies ills were genetic
• And could be eliminated
• 1911 list of ways to eliminate bad genes
• 8 was euthanasia.

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Implementation in the US

• Immigration law
• Ethnicity set quotas
• Forced Sterilization
• Feeblemindedness
• Amoral behavior
• Folks institutionalized for many reasons
• Rape
• Child of previous marriage
• Real physical/mental disability

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But Could it even work?

• Assumed Feeblemindedness was recessive
• Assumed 1-2 frequency
• Outcome of selection?

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Slow
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R.A. Fisher

• Said anti-eugenics propaganda
• Drop from 100/10,000 to 82.6/10,000 would reduce
  public expenditure and personal misery

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And of course their genetics were all wrong

• Environment
• Multiple genes
• Many institutionalized for other reasons
• Genetics of morality?

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Where did this lead?
51
Hitler

• 1924 Mein Kampf
• Quoted American egenicists
• He praised our immigration laws
• Also noted forced sterilization laws
• Start of Third Reich
• Praise by American eugenics movement
• By 1934 gt 5000 sterilized per month
• Eventually moved to solution 8.

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Only after WWII did America Move Away From
Eugenics

• Supreme Court Justice Oliver Wendell Holmes
  wrote, It is better for all the world, if
  instead of waiting to execute degenerate
  offspring for crime, or to let them starve for
  their imbecility, society can prevent those who
  are manifestly unfit from continuing their kind .
  . . Three generations of imbeciles are enough.
  1927

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Mutation and Hardy Weinberg

• Assume p has a frequency of 1
• What is the frequency of q ?
• Now allow a mutation to occur from p to q
• Instant evolution!

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Mutation rate of 1/10,000 (Very High)
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Overall affect?
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Over Time?
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So why does in matter?

• Raw material for evolution
• Creates new genes
• Mutation selection balance

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• Inbreed Stocks to make clones
• 30 generations stressed or unstressed
• Raise on 5 salt
• Where did ability to live on salt come from?
• Why did it increase?

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Mutation Selection Balance

• Rate of production of deleterious alleles offset
  by selection
• Has some equilibrium point
• q vµ/s

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Spinal Muscular Atrophy

• 0.01 frequency in Europeans
• Recessive
• Selection coefficient 0.9
• Would require 0.9 x 10-4 mutation rate
• Actual rate 1.1 x 10-4
• It works

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Cystic Fibrosis

• Opens respiratory system to Psedomonas aeruginosa
• Historically death pre-reproductive
• Recessive
• 0.02 frequency among europeans
• Assume selection coefficient of 1
• Requires mutation rate of 4 x 10-4
• Actual rate 6.7 x 10-7
• Way too low!

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Explanations?

• Possibly heterozygote advantage?
• Resistance to diarrheal diseases like typhoid
• Protects intestine

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Figure 6-31a
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Correlation with typhoid fever outbreaks
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But why so common in Northern Europe?

• Diversity of alleles higher elsewhere
• Selective advantage occurs elsewhere
• Other evolutionary forces.

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Genetic Engineering and Malaria

• Protect mosquitos from malaria
• Why?
• The genes exist
• But is it enough to have a mosquito with the gene?

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Have to increase frequency Link to a gene that
will increase in frequency
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Offspring from a cross

• But how does this increase frequency???

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Selfish genes
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Frequency of Medea with Time