Hardy Weinberg Equilibrium

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Gregor Mendel. Hardy Weinberg Equilibrium. Wilhem Weinberg (1862 – 1937). (1822-1884). G. H. Hardy (1877 - 1947). Recall from Previous Lectures. Darwin’s Observation. Evolution acts through changes in allele frequency at each generation - PowerPoint PPT Presentation

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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

Darwins Observation1/29/142Lectures 4-11: Mechanisms of Evolution (Microevolution)

Hardy Weinberg Principle (Mendelian Inheritance)Genetic DriftMutationRecombinationEpigenetic InheritanceNatural Selection

These are mechanisms acting WITHIN populations, hence called population geneticsEXCEPT for epigenetic modifications, which act on individuals in a Lamarckian manner

4 Major Evolutionary Mechanisms acting at the population level, changing allele frequencies:

Genetic DriftNatural SelectionMutationMigration

1/29/144So Evolution acts through Genetic Drift or Natural Selection acting on the genetic variation caused by mutations or recombination, or lack of variation caused by inbreeding

Testing for Hardy-Weinberg equilibrium can be used to assess whether a population is evolving5The Hardy-Weinberg PrincipleA 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

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Fig. 23-5aPorcupineherd rangeBeaufort SeaNORTHWESTTERRITORIESMAPAREAALASKACANADAFortymileherd rangeALASKAYUKONWhat is a population?

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

(definition for sexual species)7Figure 23.5 One species, two populations

Fig. 23-5Porcupine herdPorcupineherd rangeBeaufort SeaNORTHWESTTERRITORIESMAPAREAALASKACANADAFortymileherd rangeFortymile herdALASKAYUKON8Figure 23.5 One species, two populationsMathematical description of Mendelian inheritance

Hardy-Weinberg Principle1/29/149Hardy-Weinberg EquilibriumAccording to the Hardy-Weinberg principle, frequencies of alleles and genotypes in a population remain constant from generation to generation

In a given population where gametes contribute to the next generation randomly, allele frequencies will not change

Allelic and genotypic frequencies follow the transmission rules of Mendelian inheritance, which maintains constant proportions in a population across generations10So, if a population is out of HW Equilibrium, what is the way to get it back into HW Equilibrium?Patterns of inheritance should always be in Hardy Weinberg Equilibrium

Following the transmission rules of Mendel

In the absence of Evolution1/29/1411Requirements of HWEvolutionLarge population size Genetic drift

Random MatingInbreeding & other

No MutationsMutations

No Natural SelectionNatural Selection

No Migration MigrationAn evolving population is one that violates Hardy-Weinberg AssumptionsViolation12Null ModelNo 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 DriftThis is because Genetic Drift is operating even when there is no Natural Selection

Hardy-Weinberg Theorem

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

1/29/1414important conceptsgene:A region of genome sequence (DNA or RNA), that is the unit of inheritance , the product of which contributes to phenotypelocus: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 locusallele: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.)

important conceptsallele: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 cant 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.

Alleles in a population of diploid organismsA1A2A3A4A1A1A2SpermEggsGenotypesRandom Mating (Sex)ZygotesA1A3A1A1A1A1A2A4A3A1A1A1A1A2A1A1A3A4So then can we predict the % of alleles and genotypes in the population at each generation?A1A2A3A4A1A1A2SpermEggsZygotesA1A3A1A1A1A1A2A4A3A1A1A1A1A2A1A1A3A4

Hardy-Weinberg Theorem

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

1/29/1419

Fig. 23-6Frequencies of allelesAlleles in the populationGametes producedEach egg:Each sperm:80%chance80%chance20%chance20%chanceq = frequency ofp = frequency ofCR allele = 0.8CW allele = 0.2Hardy-Weinberg proportions indicate the expected allele and genotype frequencies, given the starting frequencies20Figure 23.6 Selecting alleles at random from a gene pool

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

21If 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 genotype22What about for a triploid organism?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.Hardy Weinberg TheoremALLELESProbability of A = pp + q = 1Probability of a = q

GENOTYPESAA:p x p = p2Aa:p x q + q x p = 2pqaa:q x q = q2

p2 + 2pq + q2 = 1

1/29/1425More General HW EquationsOne locus three alleles: (p + q + r)2 = p2 + q2 + r2 + 2pq +2pr + 2qr

One locus n # alleles: (p1 + p2 + p3 + p4 + pn)2 = p12 + p22 + p32 + p42 + pn2 + 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 ALLELE FrequenciesFrequency of A = p = 0.8Frequency of a = q = 0.2p + 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 = 1Expected Allele Frequencies at 2nd Generationp = AA + Aa/2 = 0.64 + (0.32/2) = 0.8q = aa + Aa/2 = 0.04 + (0.32/2) = 0.2

Allele frequencies remain the same at next generation1/29/1427Hardy Weinberg TheoremALLELE FrequencyFrequency of A = p = 0.8p + 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 1/29/1428

Similar example,But with different starting allele frequenciespq1/29/1429

1/29/1430

p22pqq21/29/1431

Fig. 23-7-4Gametes of this generation:64% CR CR, 32% CR CW, and 4% CW CW64% CR + 16% CR= 80% CR = 0.8 = p4% CW + 16% CW = 20% CW = 0.2 = q64% CR CR, 32% CR CW, and 4% CW CW plantsGenotypes in the next generation:SpermCR (80%)CW (20%)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 CWEggsPerform the same calculations using percentages32Figure 23.7 The Hardy-Weinberg principle

Fig. 23-7-1SpermCR (80%)CW (20%)80% CR ( p = 0.8) CW (20%)20% CW (q = 0.2) 16% ( pq) CRCW 4% (q2) CW CWCR (80%) 64% ( p2) CRCR 16% (qp) CRCWEggs33Figure 23.7 The Hardy-Weinberg principle

Fig. 23-7-2Gametes of this generation:64% CRCR, 32% CRCW, and 4% CWCW64% CR + 16% CR= 80% CR = 0.8 = p4% CW + 16% CW= 20% CW = 0.2 = q34Figure 23.7 The Hardy-Weinberg principle

Fig. 23-7-3Gametes of this generation:64% CRCR, 32% CRCW, and 4% CWCW64% CR + 16% CR= 80% CR = 0.8 = p4% CW + 16% CW= 20% CW = 0.2 = q64% CRCR, 32% CRCW, and 4% CWCW plantsGenotypes in the next generation:35Figure 23.7 The Hardy-Weinberg principleThe 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 allelesCalculating Allele Frequencies from # of Individuals36AAAaaa1206035 (# 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 = 0.30A + a = 0.70 + 0.30 = 1

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