Extra Credit Question List two assumptions of the Hardy-Weinberg Equilibrium Principle: Print your name, TA, and section # at top of card. Thanks!

Announcements Midterm on Tuesday March 8! HW #3 due before 9am on Tuesday, March 8. Solutions to Recommended Problems 2 posted Recommended Problems 3 posted Old Exam posted

Population Genetics

Macrophage

CCR5 CCR5-D32

What accounts for this variation. Random What accounts for this variation? Random? Past epidemics (plague, smallpox)? What will happen to this variation in the future? Will D32 allele increase in frequency?

These are the questions that “population genetics” is designed to address

Genotype & Allele Frequencies in a Genetic Cross Genotype Frequency Allele Frequency (A) P: F1: F2: F3: AA x aa p = 0.5 all Aa p = 0.5 25% AA : 50% Aa : 25% aa p = 0.5 25% AA : 50% Aa : 25% aa p = 0.5

MN Blood Group: Codominant Alleles Genotype & Allele Frequencies in a Population Sample MN Blood Group: Codominant Alleles .298 .489 .213 p=1085/2000 p=.5425 q=915/2000 q=.4575

frequency of MM = p2 frequency of MN = 2pq frequency of NN = q2 (expansion of [p + q]2 )

Hardy-Weinberg Principle Allele frequencies remain constant from generation to generation unless some outside force is acting to change them When an allele is rare, there are many more heterozygotes than homozygotes (if p is small, then p2 is very small)

Usefulness of H-W If you know the allele frequencies, you can predict the genotype frequencies: Q: In S. France, the frequency of the D32 allele is 10% (i.e., q=0.10). What proportion of individuals will be homozygous for the allele? What proportion will be heterozygous? AA Aa aa p2 2pq q2

Usefulness of H-W If you know the frequency of one of the homozygous genotypes, you can estimate allele frequencies, and predict the frequencies of the other genotypes. Q: Among individuals of European descent, 1/1700 newborns have cystic fibrosis (a recessive genetic disorder). What proportion of this population are heterozygous carriers? Hint: q2 = 1/1700 = 0.00059 A: 2pq = 0.047

H-W principle also can be used for sex-linked traits: treat sexes separately Homogametic Sex XA XA p2 XA Xa 2pq Xa Xa q2 Heterogametic Sex (Allele Freq=Genotype Freq) XA Y p Xa Y q Q: If 8% of men are colorblind, what percent of women are color blind? Hint: q=0.08 A: q2 = 0.0064

If 8% of men are color blind => Xa allele frequency q = 0.08 XA allele frequency p = 1 - q = 0.92 What proportion of women are heterozygous carriers?

Multiple Alleles: ABO blood types p = freq of A allele q = freq of B allele r = freq of O allele Expansion of [p + q + r]2 = p2 + q2 + r2+ 2pq + 2pr + 2qr

What assumptions are made by H-W? Gamete production is unbiased (no fertility selection) Gamete union (mating) is random

What assumptions are made by H-W? Zygotes equally viable (no viability selection)

Other assumptions of H-W? AA aa Aa migrants? No migration

Other assumptions of H-W? AA Aa aa aa aa Aa Aa Population is large so random change in allele frequency is unlikely

Assumptions of H-W Mating is random across the entire population. All genotypes have equal viability and fertility (no selection). Migration into the population can be ignored. Mutation does not occur, or is so rare it can be ignored. Population is large enough that the allele frequencies do not change from generation to generation due to chance (random genetic drift). Allele frequencies are the same in females and males.

What happens when any of these assumptions are violated? Selection Mutation Non-random mating Migration Genetic Drift If any of these processes are occurring, will tend to get deviations from H-W expected proportions

How can we detect deviation from H-W expectations? Do observed genotype frequencies match HW expectations?

Do observed genotype frequencies match HW expectations? S(O-E)2/E

Do This for Thursday’s Extra Credit Problem Caution! Degrees of freedom in this problem are not what you might expect. Df=1, not 2 Anyone know why?

Importance of H-W H-W is an important tool for population genetics. If assumptions are met, we can use it to estimate allele and genotype frequencies that would otherwise be difficult to measure. If assumptions are not met (can be tested statistically), then we know that some outside force is perturbing allele or genotype frequencies.

Change in allele frequencies over generations Evolution is defined as a change in allele (or genotype) frequencies over generations, and evolution will be caused by violation of any of the assumptions of H-W.

Forces that cause deviation from H-W (evolution) Selection Mutation Genetic Drift Nonrandom Mating Gene Flow (Migration)

Genotype A has a constitutive mutation for enzyme production in the lactose operon. B is the normal inducible lactose operon. A and B grown together in environment with limited lactose.

New allele frequencies? p = (25+25)/95 = 0.53 q = (25+20)/95 = 0.47 Genotypes Number: AA 25 Aa 50 aa Survival to reproduction 100% = 1 20 80% = 0.8 Gamete contribution 25/95 A 25/95 A; 25/95 a 20/95 a New allele frequencies? p = (25+25)/95 = 0.53 q = (25+20)/95 = 0.47 New genotype frequencies (assume random mating): AA Aa aa 0.28 0.50 0.22

Consistent differences in survival or reproduction between genotypes = genotypic-specific differences in fitness When fitness values are expressed on a scale such that highest fitness=1, then the values are called relative fitness To conveniently calculate change in allele frequency due to selection, need concept of average fitness

Change in allele frequency Genotype AA Aa aa Genotype Frequency p2 2pq q2 Relative Fitness WAA WAa Waa (W=average fitness= p2WAA/W+ 2pqWAa/W + q2WAa/W) Freq of A after one gen. of selection: p' = p2 WAA/W + pqWAa/W Freq of a after one gen. of selection: (1-p’) or: q'= q2 Waa/W + pqWAa/W

CCR5 Example Genotype frequency: W/W 0.81 W/D32 0.18 D32/D32 0.01 Relative Fitness 0.99 1.0 Average fitness W = 0. 81*0.99 + 0.18*0.99 + 0.01*1 = 0.9901 q'=q2Waa/W + pqWAa/W = 0.01009 +0.089991=0.100091 p’= 1-q’ = 0.89999 Next generation genotype freq. 0.80998 0.18016 0.01002

Selection will increase the frequency of D32 allele Selection is relatively weak The favored allele is recessive and the favored genotype is very rare The change in allele frequency (response to selection) will be relatively slow