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: p 2 + 2pq + q 2 = 1 p= frequency of allele A q = Frequency of allele a p + q = 1. So p 2 = AA, q 2 = aa, and pq = Aa

Sophisticated Punnet square:

Genotype frequency Also 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 alleles Allele Frequencies P 1 + P 2 + P 3 = 1 Genotype Frequencies P P P P 1 P 2 + 2P 1 P 3 + 2P 2 P 3

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 resistance CCR5 –vs CCR5-Δ32 Δ32/Δ32 Homozygote confers resistance Should be sweeping towards fixation…right? It’s a “good” allele

Setting The Stage So lets assume the highest frequency 20% in Ashkenazi Jews Assume highest infection rate 25% 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 Africa Infection 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 Phenotypes D. melanogaster Lethal recesive

Why did frequency of viable allele stabilize?

Overdominance/Heterozygote advantage Results in stable equilibrium

Underdominance/Homozygot e 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 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….

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

But Could it even work? Assumed “Feeblemindedness” was recessive Assumed 1-2% frequency Outcome of selection?

Slow

R.A. Fisher Said “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?

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 > 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 Atrophy 0.01 frequency in Europeans Recessive Selection coefficient 0.9 Would require 0.9 x mutation rate Actual rate 1.1 x It works

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 Actual rate 6.7 x 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 malaria Why? 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