HardyWeinberg An introduction HardyWeinberg Theorem Allele frequencies stay

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 -7 a

Calculating HW

Two allele equation: �p 2 + 2 pq + 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 12 + P 22 + P 32 + 2 P 1 P 3 + 2 P 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 � CCR 5 –vs CCR 5 -Δ 32 � Δ 32/Δ 32 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 -17 a

But are these assumptions reasonable?

Europe � 20% Δ 32 Reasonable �But HIV infection rate less than 1%

Figure 6 -17 b

Parts of Africa �Infection rate up to 25% �But Δ 32 is almost absent

Figure 6 -17 c

Why doesn’t selection work? �Selection pressure is strong �There a few copies of Δ 32

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/Homozygote advantage �Results in unstable equilibrium �Equilibrium depends on selection pressure

Figure 6 -23 f

Figure 6 -23 g

Frequency Dependent Selection �Fitness depends on frequency in population

Figure 6 -24 a 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 -24 b

Figure 6 -24 c

Types of selection

American Eugenics Movement �Social Darwinism �Starting in the late 1800 s �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 10 -4 mutation rate �Actual rate 1. 1 x 10 -4 �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 10 -4 �Actual rate 6. 7 x 10 -7 �Way too low!