Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947)...

77
Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Transcript of Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947)...

Page 1: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Hardy Weinberg Equilibrium

Wilhem Weinberg(1862 – 1937)

Gregor Mendel

G. H. Hardy(1877 - 1947)

(1822-1884)

Page 2: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Lectures 4-11: Mechanisms of Evolution (Microevolution)

• Hardy Weinberg Principle (Mendelian Inheritance)

• Genetic Drift• Mutation• Recombination• Epigenetic Inheritance• Natural Selection

These are mechanisms acting WITHIN populations, hence called “population genetics”—EXCEPT for epigenetic modifications, which act on individuals in a Lamarckian manner

Page 3: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Evolution acts through changes in allele frequency at each generation

Leads to average change in characteristic of the population

Recall from Previous Lectures

Darwin’s Observation

Page 4: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

HOWEVER, Darwin did not understand how genetic variation was passed on from generation to generation

Recall from Lecture on History of Evolutionary Thought

Darwin’s Observation

Page 5: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Gregor Mendel, “Father of Modern Genetics”

• Mendel presented a mechanism for how traits got passed on

“Individuals pass alleles on to their offspring intact”

(the idea of particulate (genes) inheritance)

Gregor Mendel

(1822-1884)

http://www.biography.com/people/gregor-mendel-39282#synopsis

Page 6: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Gregor Mendel, “Father of Modern Genetics”

Mendel’s Laws of Inheritance• Law of Segregation

– only one allele passes from each parent on to an offspring

• Law of Independent Assortment– different pairs of alleles are passed to

offspring independently of each other

Gregor Mendel

(1822-1884)

http://www.biography.com/people/gregor-mendel-39282#synopsis

Page 7: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• In cross-pollinating plants with either yellow or green peas, Mendel found that the first generation (f1) always had yellow seeds (dominance). However, the following generation (f2) consistently had a 3:1 ratio of yellow to green.

Using 29,000 pea plants, Mendel discovered the 1:3 ratio of phenotypes, due to dominant vs. recessive alleles

Page 8: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• Mendel uncovered the underlying mechanism, that there are dominant and recessive alleles

Page 9: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• Mathematical description of Mendelian inheritance

Hardy-Weinberg Principle

Godfrey Hardy(1877-1947) Wilhem Weinberg

(1862 – 1937)

Page 10: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Testing for Hardy-Weinberg equilibrium can be used to assess whether a population is evolving

Page 11: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

The Hardy-Weinberg Principle

• A population that is not evolving shows allele and genotypic frequencies that are in Hardy Weinberg equilibrium

• If a population is not in Hardy-Weinberg equilibrium, it can be concluded that the population is evolving

Page 12: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Evolutionary Mechanisms (will put population out of HW Equilibrium):

• Genetic Drift• Natural Selection• Mutation• Migration

*Epigenetic modifications change expression of alleles but not the frequency of alleles themselves, so they won’t affect the actual inheritance of alleles

However, if you count the phenotype frequencies, and not the genotype frequencies , you might see phenotypic frequencies out of HW Equilibrium due to epigenetic silencing of alleles. (epigenetic modifications can change phenotype, not genotype)

Page 13: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Requirements of HWEvolution

Large population size Genetic drift

Random MatingInbreeding & other

No MutationsMutations

No Natural Selection Natural Selection

No Migration Migration

An evolving population is one that violates Hardy-Weinberg Assumptions

Violation

Page 14: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Fig. 23-5a

Porcupineherd range

Beaufort Sea NORTHWEST

TERRITORIESMAPAREA

ALA

SKA

CAN

ADA

Fortymileherd range

ALAS

KA

YUKO

N

• What is a “population?”

A group of individuals within a species that is capable of interbreeding and producing fertile offspring

(definition for sexual species)

Page 15: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Patterns of inheritance should always be in “Hardy Weinberg Equilibrium”

Following the transmission rules of Mendel

In the absence of Evolution…

Page 16: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Hardy-Weinberg Equilibrium

• According to the Hardy-Weinberg principle, frequencies of alleles and genotypes in a population remain constant from generation to generation

• Also, the genotype frequencies you see in a population should be the Hardy-Weinberg expectations, given the allele frequencies

Page 17: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

“Null Model”• No Evolution: Null Model to test if no

evolution is happening should simply be a population in Hardy-Weinberg Equilibrium

• No Selection: Null Model to test whether Natural Selection is occurring should have no selection, but should include Genetic Drift– This is because Genetic Drift is operating even

when there is no Natural Selection

Page 18: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Example: Is this population in Hardy Weinberg Equilibrium?

AAAa aa

Generation 1 0.25 0.50 0.25Generation 2 0.20 0.60 0.20Generation 3 0.10 0.80 0.10

Page 19: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Hardy-Weinberg Theorem

In a non-evolving population, frequency of alleles and genotypes remain constant over generations

You should be able to predict the genotype frequencies, given the allele frequencies

Page 20: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

important concepts• gene: A region of genome sequence (DNA or RNA), that

is the unit of inheritance , the product of which contributes to phenotype

• locus: Location in a genome (used interchangeably with “gene,” if the location is at a gene… but, locus can be anywhere, so meaning is broader than gene)

• loci: Plural of locus

• allele: Variant forms of a gene (e.g. alleles for different eye colors, BRCA1 breast cancer allele, etc.)

• genotype: The combination of alleles at a locus (gene)

• phenotype: The expression of a trait, as a result of the genotype and regulation of genes (green eyes, brown hair, body size, finger length, cystic fibrosis, etc.)

Page 21: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

important concepts• allele: Variant forms of a gene (e.g. alleles for different

eye colors, BRCA1 breast cancer allele, etc.)

• We are diploid (2 chromosomes), so we have 2 alleles at a locus (any location in the genome)

• However, there can be many alleles at a locus in a population.– For example, you might have inherited a blue eye allele from

your mom and a brown eye allele from your dad… you can’t have more alleles than that (only 2 chromosomes, one from each parent)

– BUT, there could be many alleles at this locus in the population, blue, green, grey, brown, etc.

Page 22: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• Alleles in a population of diploid organisms

A1

A2

A3

A4A1

A1

A2

Sperm

Eggs

• Genotypes

Random Mating (Sex)

Zygotes

A1A3

A1A1 A1A1

A2A4

A3A1

A1A1

A1

A2A1

A1

A3

A4

Page 23: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

So then can we predict the % of alleles and genotypes in the population at each generation?

A1

A2

A3

A4A1

A1

A2

Sperm

Eggs

Zygotes

A1A3

A1A1 A1A1

A2A4

A3A1

A1A1

A1

A2

A1

A1

A3

A4

Page 24: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Hardy-Weinberg Theorem

In a non-evolving population, frequency of alleles and genotypes remain constant over generations

Page 25: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Fig. 23-6

Frequencies of allelesAlleles in the population

Gametes produced

Each egg: Each sperm:

80%chance

80%chance

20%chance

20%chance

q = frequency of

p = frequency ofCR allele = 0.8

CW allele = 0.2

Hardy-Weinberg proportions indicate the expected allele and genotype frequencies, given the starting frequencies

Page 26: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• By convention, if there are 2 alleles at a locus, p and q are used to represent their frequencies

• The frequency of all alleles in a population will add up to 1

– For example, p + q = 1

Page 27: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

If p and q represent the relative frequencies of the only two possible alleles in a population at a particular locus, then for a diploid organism (2 chromosomes),

(p + q) 2 = 1

= p2 + 2pq + q2 = 1

– where p2 and q2 represent the frequencies of the homozygous genotypes and 2pq represents the frequency of the heterozygous genotype

Page 28: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

What about for a triploid organism?

Page 29: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

What about for a triploid organism?

• (p + q)3 = 1

= p3 + 3p2q + 3pq2 + q3 = 1

Potential offspring: ppp, ppq, pqp, qpp, qqp, pqq, qpq, qqq

How about tetraploid? You work it out.

Page 30: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Hardy Weinberg Theorem

ALLELESProbability of A = p p + q = 1Probability of a = q

GENOTYPESAA: p x p = p2

Aa: p x q + q x p = 2pqaa: q x q = q2

p2 + 2pq + q2 = 1

Page 31: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

More General HW Equations

• One locus three alleles: (p + q + r)2 = p2 + q2 + r2 + 2pq +2pr + 2qr

• One locus n # alleles: (p1 + p2 + p3 + p4 … …+ pn)2 = p12 + p2

2 + p3

2 + p42… …+ pn

2 + 2p1p2 + 2p1p3 + 2p2p3 + 2p1p4 + 2p1p5 + … … + 2pn-1pn

• For a polyploid (more than two chromosomes): (p + q)c, where c = number of chromosomes

• If multiple loci (genes) code for a trait, each locus follows the HW principle independently, and then the alleles at each loci interact to influence the trait

Page 32: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

ALLELE FrequenciesFrequency of A = p = 0.8

Frequency of a = q = 0.2

p + q = 1

Expected GENOTYPE FrequenciesAA: p x p = p2 = 0.8 x 0.8 = 0.64Aa: p x q + q x p = 2pq

= 2 x (0.8 x 0.2) = 0.32aa: q x q = q2 = 0.2 x 0.2 = 0.04

p2 + 2pq + q2

= 0.64 + 0.32 + 0.04 = 1

Expected Allele Frequencies at 2nd Generation

p = AA + Aa/2 = 0.64 + (0.32/2) = 0.8

q = aa + Aa/2 = 0.04 + (0.32/2) = 0.2

Allele frequencies remain the same at next generation

Page 33: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Hardy Weinberg Theorem

ALLELE FrequencyFrequency of A = p = 0.8 p + q = 1Frequency of a = q = 0.2

Expected GENOTYPE FrequencyAA: p x p = p2 = 0.8 x 0.8 = 0.64Aa: p x q + q x p = 2pq = 2 x (0.8 x 0.2) = 0.32aa : q x q = q2 = 0.2 x 0.2 = 0.04

p2 + 2pq + q2 = 0.64 + 0.32 + 0.04 = 1

Expected Allele Frequency at 2nd Generationp = AA + Aa/2 = 0.64 + (0.32/2) = 0.8q = aa + Aa/2 = 0.04 + (0.32/2) = 0.2

Page 34: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Similar example,But with different starting allele frequencies

p q

Page 35: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)
Page 36: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

p2

2pqq2

Page 37: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• The frequency of an allele in a population can be calculated from # of individuals:

– For diploid organisms, the total number of alleles at a locus is the total number of individuals x 2

– The total number of dominant alleles at a locus is 2 alleles for each homozygous dominant individual

– plus 1 allele for each heterozygous individual; the same logic applies for recessive alleles

Calculating Allele Frequencies from # of Individuals

Page 38: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

AA Aa aa120 60 35 (# of individuals)

#A = (2 x AA) + Aa = 240 + 60 = 300#a = (2 x aa) + Aa = 70 + 60 = 130Proportion A = 300/total = 300/430 = 0.70Proportion a = 130/total = 130/430 = 0.30

A + a = 0.70 + 0.30 = 1

Proportion AA = 120/215 = 0.56Proportion Aa = 60/215 = 0.28Proportion aa = 35/215 = 0.16

AA + Aa + aa = 0.56 + 0.28 +0.16 = 1

Calculating Allele and Genotype Frequencies from # of Individuals

Page 39: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Applying the Hardy-Weinberg Principle

• Example: estimate frequency of a disease allele in a population

• Phenylketonuria (PKU) is a metabolic disorder that results from homozygosity for a recessive allele

• Individuals that are homozygous for the deleterious recessive allele cannot break down phenylalanine, results in build up mental retardation

Page 40: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• The occurrence of PKU is 1 per 10,000 births• How many carriers of this disease in the

population?

Page 41: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

– Rare deleterious recessives often remain in a population because they are hidden in the heterozygous state (the “carriers”)

– Natural selection can only act on the homozygous individuals where the phenotype is exposed (individuals who show symptoms of PKU)

– We can assume HW equilibrium if:• There is no migration from a population with different

allele frequency• Random mating• No genetic drift• Etc

Page 42: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• The occurrence of PKU is 1 per 10,000 births(frequency of the disease allele):

q2 = 0.0001q = sqrt(q2 ) = sqrt(0.0001) = 0.01

• The frequency of normal alleles is:

p = 1 – q = 1 – 0.01 = 0.99

• The frequency of carriers (heterozygotes) of the deleterious allele is:

2pq = 2 x 0.99 x 0.01 = 0.0198or approximately 2% of the U.S. population

So, let’s calculate HW frequencies

Page 43: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Conditions for Hardy-Weinberg Equilibrium• The Hardy-Weinberg theorem describes a

hypothetical population

• The five conditions for nonevolving populations are rarely met in nature:

– No mutations – Random mating – No natural selection – Extremely large population size– No gene flow

• So, in real populations, allele and genotype frequencies do change over time

Page 44: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

DEVIATION from

Hardy-Weinberg EquilibriumIndicates that

EVOLUTIONIs happening

Page 45: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• In natural populations, some loci might be out of HW equilibrium, while being in Hardy-Weinberg equilibrium at other loci

• For example, some loci might be undergoing natural selection and become out of HW equilibrium, while the rest of the genome remains in HW equilibrium

Hardy-Weinberg across a Genome

Page 46: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Allele A1 Demo

Page 47: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

How can you tell whether a population is out of HW Equilibrium?

Page 48: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• Perform HW calculations to see if it looks like the population is out of HW equilibrium

• Then apply statistical tests to see if the deviation is significantly different from what you would expect by random chance

Page 49: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Example: Does this population remain in Hardy Weinberg Equilibrium across Generations?

AAAa aa

Generation 1 0.25 0.50 0.25Generation 2 0.20 0.60 0.20Generation 3 0.10 0.80 0.10

Page 50: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

AAAa aa

Generation 1 0.25 0.50 0.25Generation 2 0.20 0.60 0.20Generation 3 0.10 0.80 0.10

In this case, allele frequencies (of A and a) did not change.

***However, the population did go out of HW equilibrium because you can no longer predict genotypic frequencies from allele frequencies

For example, p = 0.5, p2 = 0.25, but in Generation 3, the observe p2 = 0.10

Page 51: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

How can you tell whether a population is out of HW Equilibrium?

1. When allele frequencies are changing across generations

2. When you cannot predict genotype frequencies from allele frequencies (means there is an excess or deficit of genotypes than what would be expected given the allele frequencies)

Page 52: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Testing for Deviaton from Hardy-Weinberg Expectations

• A c2 goodness-of-fit test can be used to determine if a population is significantly different from the expections of Hardy-Weinberg equilibrium.

• If we have a series of genotype counts from a population, then we can compare these counts to the ones predicted by the Hardy-Weinberg model.

• O = observed counts, E = expected counts, sum across genotypes

Page 53: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Example• Genotype Count: AA 30 Aa 55 aa 15• Calculate the c2 value:

Genotype Observed Expected (O-E)2/E AA 30 33

0.27 Aa 55 49

0.73 aa 15

18 0.50 Total 100 100 1.50

• Since c2 = 1.50 < 3.841 (from Chi-square table), we conclude that the genotype frequencies in this population are not significantly different than what would be expected if the population is in Hardy-Weinberg equilibrium.

Page 54: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

• One generation of Random Mating could put a population back into Hardy Weinberg Equilibrium

Page 55: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Examples of Deviation from Hardy-Weinberg Equilibrium

Page 56: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

What would Genetic Drift look like?

• Most populations are experiencing some level of genetic drift, unless they are incredibly large

Page 57: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Examples of Deviation from Hardy-Weinberg Equilibrium

AAAa aa

Generation 1 0.640.32 0.04Generation 2 0.630.33 0.04Generation 3 0.640.315 0.045Generation 4 0.650.31 0.04

Is this population in HW equilibrium?If not, how does it deviate?What could be the reason?

Page 58: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Examples of Deviation from Hardy-Weinberg Equilibrium

AAAa aa

Generation 1 0.640.32 0.04Generation 2 0.630.33 0.04Generation 3 0.640.315 0.045Generation 4 0.650.31 0.04

This is a case of Genetic Drift, where allele frequencies are fluctuating randomly across generations

Page 59: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Examples of Deviation from Hardy-Weinberg Equilibrium

AA Aa aa0.64 0.32 0

Is this population in HW equilibrium?If not, how does it deviate?What could be the reason?

Page 60: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Examples of Deviation from Hardy-Weinberg Equilibrium

AA Aa aa0.64 0.32 0

Here this appears to be Directional Selection favoring AA

Or… Negative Selection disfavoring aa

Page 61: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Examples of Deviation from Hardy-Weinberg Equilibrium

AA Aa aa0.25 0.70 0.05

Is this population in HW equilibrium?If not, how does it deviate?What could be the reason?

Page 62: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Examples of Deviation from Hardy-Weinberg Equilibrium

AA Aa aa0.25 0.70 0.05

This appears to be a case of Heterozygote Advantage (or Overdominance)

Page 63: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Examples of Deviation from Hardy-Weinberg Equilibrium

AA Aa aa0.10 0.10 0.80

Is this population in HW equilibrium?If not, how does it deviate?What could be the reason?

Page 64: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Examples of Deviation from Hardy-Weinberg Equilibrium

AA Aa aa0.10 0.10 0.80

Selection appears to be favoring aa

Page 65: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

(1) A nonevolving population is in HW Equilibrium

(2) Evolution occurs when the requirements for HW Equilibrium are not met

(3) HW Equilibrium is violated when there is Genetic Drift, Migration, Mutations, Natural Selection, and Nonrandom Mating

Summary

Page 66: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Hardy Weinberg Equilibrium

Wilhem Weinberg(1862 – 1937)

Gregor Mendel

G. H. Hardy(1877 - 1947)

(1822-1884)

Page 67: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Fig. 23-7-4

Gametes of this generation:

64% CR CR, 32% CR CW, and 4% CW CW

64% CR    +     16% CR    = 80% CR  = 0.8 = p

4% CW      +    16% CW    = 20% CW = 0.2 = q

64% CR CR, 32% CR CW, and 4% CW CW plants

Genotypes in the next generation:

SpermCR

(80%)

CW

(2

0%)

80% CR ( p = 0.8)

CW (20%)

20% CW (q = 0.2)

16% ( pq) CR CW

4% (q2) CW CW

CR

(80%

)

64% ( p2) CR CR

16% (qp) CR CW

E gg s

Perform the same calculations using percentages

Page 68: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Fig. 23-7-1

SpermCR

(80%)

CW

(2

0%)

80% CR ( p = 0.8)

CW (20%)

20% CW (q = 0.2)

16% ( pq) CRCW

4% (q2) CW CW

CR

(80%

)

64% ( p2) CRCR

16% (qp) CRCW

E gg s

Page 69: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Fig. 23-7-2

Gametes of this generation:

64% CRCR, 32% CRCW, and 4% CWCW

64% CR   +    16% CR    = 80% CR = 0.8 = p

4% CW     +    16% CW   = 20% CW = 0.2 = q

Page 70: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Fig. 23-7-3

Gametes of this generation:

64% CRCR, 32% CRCW, and 4% CWCW

64% CR   +    16% CR    = 80% CR = 0.8 = p

4% CW     +    16% CW   = 20% CW = 0.2 = q

64% CRCR, 32% CRCW, and 4% CWCW plants

Genotypes in the next generation:

Page 71: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Gregor Mendel

Page 72: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

1. Nabila is a Saudi Princess who is arranged to marry her first cousin. Many in her family have died of a rare blood disease, which sometimes skips generations, and thus appears to be recessive. Nabila thinks that she is a carrier of this disease. If her fiancé is also a carrier, what is the probability that her offspring will have (be afflicted with) the disease?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 3/4

(E) zero

Page 73: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

The following are numbers of pink and white flowers in a population.

Pink White

Generation 1: 901 302

Generation 2: 1204 403

Generation 3: 1510 504

2. Which of the following is most likely to be TRUE?

(A) The heterozygotes are probably pink

(B) The recessive allele here (probably white) is clearly deleterious

(C) Evolution is occurring, as allele frequencies are changing greatly over time

(D) Clearly there is a heterozygote advantage

(E) The frequencies above violate Hardy-Weinberg expectations

Page 74: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

The following are numbers of purple and white peas in a population. (A1A1) (A1A2)

(A2A2)

Purple PurpleWhite

Generation 1: 360 480160

Generation 2: 100 200 200

Generation 3: 0 100300

3. What are the genotype frequencies at each generation?(A) Generation 1: 0.30, 0.50, 0.20

Generation 2: 0.20, 0.40, 0.40

Generation 3: 0, 0.333, 0.666

(B) Generation 1: 0.36, 0.48, 0.16

Generation 2: 0.10, 0.20, 0.20

Generation 3: 0, 0.10, 0.30

(C) Generation 1: 0.36, 0.48, 0.16

Generation 2: 0.20, 0.40, 0.40

Generation 3: 0, 0.25, 0.75

(D) Generation 1: 0.36, 0.48, 0.16

Generation 2: 0.36, 0.48, 0.16

Generation 3: 0.36, 0.48, 0.16

Page 75: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

4. From the example on the previous slide, what are the frequencies of alleles at each generation?

(A) Generation1: Dominant allele (A1) = 0.6, Recessive allele (A2) = 0.4

Generation2: Dominant allele = 0.4, Recessive allele = 0.6

Generation3: Dominant allele = 0.125, Recessive allele = 0.875

(B) Generation1: Dominant allele = 0.6, Recessive allele = 0.4

Generation2: Dominant allele = 0.6, Recessive allele = 0.4

Generation3: Dominant allele = 0.6, Recessive allele = 0.4

(C) Generation1: Dominant allele = 0.6, Recessive allele = 0.4

Generation2: Dominant allele = 0.5, Recessive allele = 0.5

Generation3: Dominant allele = 0.25, Recessive allele = 0.75

(D) Generation1: Dominant allele = 0.4, Recessive allele = 0.6

Generation2: Dominant allele = 0.5, Recessive allele = 0.5

Generation3: Dominant allele = 0.25, Recessive allele = 0.75

Page 76: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

5. From the example two slides ago, which evolutionary mechanism might be operating across generations?

(A) Mutation

(B) Selection favoring A1

(C) Heterozygote advantage

(D) Selection favoring A2

(E) Inbreeding

Page 77: Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) Gregor Mendel G. H. Hardy (1877 - 1947) (1822-1884)

Answers:

1. Parents: Aa x Aa = Offspring: AA (25%), Aa (50%), aa (25%)Answer = A2. A3. C4. A5. D