Hardy-Weinberg:An introduction

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

Starts and end the same

Figure 6-7a

Calculating HW

Two allele equation: p2 + 2pq + q2 = 1

p= frequency of allele Aq = Frequency of allele a p + q = 1. So p2 = AA, q2 = aa, and pq = Aa

Sophisticated Punnet square:

Genotype frequencyAlso Constant

Calculating Genotype Frequencies & Product Rule

Assumptions: Random mating

Very large Population size

Diploid

Sexual

Non-overlapping generations

No migration

No mutation

No selection.

Figure 6-11

So what good is it? Provides an evolutionary baseline

Calculate deviations from the H.W. Ideal

More than 2 allelesAllele Frequencies

P1 + P2 + P3 = 1

Genotype FrequenciesP1

2 + P22 + P3

2 + 2P1P2 + 2P1P3 + 2P2P3

Hardy-Weinberg and Selection

No Selection

Add Selection

Selection Over Time:

Empirical Research: Alcohol Dehydrogenase

Selection Can Change Genotype Frequency

When is Selection Not Enough?

Recessive Alleles

HIV resistanceCCR5 –vs CCR5-Δ32Δ32/Δ32 Homozygote confers resistance

Should be sweeping towards fixation…right? It’s a “good” allele

Setting The StageSo lets assume the highest frequency

20% in Ashkenazi Jews

Assume highest infection rate25% in Zimbabwe, Swaziland, Namibia, Botswana

Figure 6-17a

But are these assumptions reasonable?

Europe

20% Δ32 Reasonable

But HIV infection rate less than 1%

Figure 6-17b

Parts of AfricaInfection rate up to 25%

But Δ32 is almost absent

Figure 6-17c

Why doesn’t selection work?

Selection pressure is strong

There are a few copies of Δ32

Patterns of Selection

Recessive Lethal in Flour Beetles

Decreased lethal alleles over time

But Why aren’t they eliminated?

Two PhenotypesD. melanogaster

Lethal recesive

Why did frequency of viable allele stabilize?

Overdominance/Heterozygote advantage

Results in stable equilibrium

Underdominance/Homozygote advantage

Results in unstable equilibrium

Equilibrium depends on selection pressure

Figure 6-23f

Figure 6-23g

Frequency Dependent Selection

Fitness depends on frequency in population

Figure 6-24a

Elderflowers

Purple or Yellow

Don’t provide nectar

Bees alternate color Looking for reward Eventually leave

Rare color visited more often Since bees alternate

How did frequency affect fitness?

Figure 6-24b

Figure 6-24c

Types of selection

American Eugenics MovementSocial Darwinism

Starting in the late 1800s

Big after WWI ImmigrationObvious inequalities

All of societies ills were geneticAnd could be eliminated

1911 list of ways to eliminate bad genes #8 was euthanasia….

Implementation in the USImmigration law

Ethnicity set quotas

Forced SterilizationFeeblemindedness Amoral behaviorFolks institutionalized for many reasons

RapeChild of previous marriageReal physical/mental disability

But Could it even work?Assumed “Feeblemindedness” was recessive

Assumed 1-2% frequency

Outcome of selection?

Slow

R.A. FisherSaid “anti-eugenics propaganda”

Drop from 100/10,000 to 82.6/10,000 would reduce public expenditure and personal misery

And of course their genetics were all wrong

Environment

Multiple genes

Many institutionalized for “other” reasons

Genetics of morality?

Where did this lead?

Hitler1924 Mein Kampf

Quoted American egenicists

He praised our immigration laws

Also noted forced sterilization laws

Start of Third ReichPraise by American eugenics movement

By 1934 > 5000 sterilized per month

Eventually moved to solution #8….

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

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!

Mutation rate of 1/10,000 (Very High)

Overall affect?

Over Time?

So why does in matter?Raw material for evolution

Creates new genes

Mutation selection balance

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?

Mutation Selection Balance

Rate of production of deleterious alleles offset by selection

Has some equilibrium point

q = √μ/s

Spinal Muscular Atrophy0.01 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

Cystic FibrosisOpens 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!

Explanations?Possibly heterozygote advantage?

Resistance to diarrheal diseases like typhoid

Protects intestine

Figure 6-31a

Correlation with typhoid fever outbreaks

But why so common in Northern Europe?

Diversity of alleles higher elsewhere

Selective advantage occurs elsewhere

Other evolutionary forces….

Genetic Engineering and Malaria

Protect mosquitos from malariaWhy?

The genes exist

But is it enough to have a mosquito with the gene?

Have to increase frequency: Link to a gene that will increase in frequency

Offspring from a cross

But how does this increase frequency???

Selfish genes

Frequency of Medea with Time