Hardy-Weinberg equilibrium
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Hardy-Weinberg equilibrium. Hardy-Weinberg equilibrium. Is this a ‘true’ population or a mixture? Is the population size dangerously low? Has migration occurred recently? Is severe selection occurring?. Quantifying genetic variation: Genotype frequencies

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Hardy-Weinberg equilibrium

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Hardy weinberg equilibrium

Hardy-Weinberg equilibrium


Hardy weinberg equilibrium

Hardy-Weinberg equilibrium

Is this a ‘true’ population or a mixture?

Is the population size dangerously low?

Has migration occurred recently?

Is severe selection occurring?


Hardy weinberg equilibrium

Quantifying genetic variation:

Genotype frequencies

red flowers: 20 = homozygotes = AA

pink flowers:20 = heterozygotes = Aa

white flowers:10 = homozygotes = aa


Hardy weinberg equilibrium

Quantifying genetic variation:

Genotype frequencies

red flowers: 20 = homozygotes = AA

pink flowers:20 = heterozygotes = Aa

white flowers:10 = homozygotes = aa

N =

# alleles =

Genotype frequency =


Hardy weinberg equilibrium

Quantifying genetic variation:

Genotype frequencies

red flowers: 20 = homozygotes = AA

pink flowers:20 = heterozygotes = Aa

white flowers:10 = homozygotes = aa

N = 50

# alleles = 100

Genotype frequency = 20:20:10


Hardy weinberg equilibrium

Quantifying genetic variation:

Genotype frequencies

red flowers: 20 = homozygotes = AA

pink flowers:20 = heterozygotes = Aa

white flowers:10 = homozygotes = aa

N = 50

# alleles = 100

Genotype frequency = 20:20:10

Allelic frequencies:

A =

a =


Hardy weinberg equilibrium

Quantifying genetic variation:

Genotype frequencies

red flowers: 20 = homozygotes = AA

pink flowers:20 = heterozygotes = Aa

white flowers:10 = homozygotes = aa

N = 50

# alleles = 100

Genotype frequency = 20:20:10

Allelic frequencies:

A = red (20 + 20) + pink (20) = 60 (or 0.6)

a = white (10 + 10) + pink (20 ) = 40 (or 0.4)


Hardy weinberg equilibrium

Quantifying genetic variation:

Genotype frequencies

red flowers: 20 = homozygotes = AA

pink flowers:20 = heterozygotes = Aa

white flowers:10 = homozygotes = aa

N = 50

# alleles = 100

Genotype frequency = 20:20:10

Allelic frequencies:

A = red (20 + 20) + pink (20) = 60 (or 0.6) = “p”

a = white (10 + 10) + pink (20 ) = 40 (or 0.4) = “q”


Hardy weinberg equilibrium

Reduce these frequencies to proportions

Genotype frequencies: AA = 20 or 0.4

Aa = 20 0.4

aa = 10 0.2

Allelic frequencies: A = p = 0.6

a = q = 0.4


Hardy weinberg equilibrium

Check that proportions sum to 1

Genotype frequencies: AA = 20 or 0.4

Aa = 20 0.4AA + Aa + aa = 1

aa = 10 0.2

Allelic frequencies: A = p = 0.6 p + q = 1

a = q = 0.4


Hardy weinberg equilibrium

Genotype frequencies: AA = 20 or 0.4

Aa = 20 0.4AA + Aa + aa = 1

aa = 10 0.2

Allelic frequencies: A = p = 0.6 p + q = 1

a = q = 0.4

If we combined the alleles at random (per Mendel), then genotype

frequencies would be predictable by multiplicative rule:

AA =

Aa =

aa =


Hardy weinberg equilibrium

Genotype frequencies: AA = 20 or 0.4

Aa = 20 0.4AA + Aa + aa = 1

aa = 10 0.2

Allelic frequencies: A = p = 0.6 p + q = 1

a = q = 0.4

If we combined the alleles at random (per Mendel), then genotype

frequencies would be predictable by multiplicative rule:

AA = p x p = p2

Aa = p x q x 2 = 2pq

aa = q x q = q2


Hardy weinberg equilibrium

Genotype frequencies: AA = 20 or 0.4

Aa = 20 0.4AA + Aa + aa = 1

aa = 10 0.2

Allelic frequencies: A = p = 0.6 p + q = 1

a = q = 0.4

If we combined the alleles at random (per Mendel), then genotype

frequencies would be predictable by multiplicative rule:

AA = p x p = p2 = 0.36

Aa = p x q x 2 = 2pq = 0.48

aa = q x q = q2 = 0.16


Hardy weinberg equilibrium

Genotype frequencies: AA = 20 or 0.4

Aa = 20 0.4AA + Aa + aa = 1

aa = 10 0.2

Allelic frequencies: A = p = 0.6 p + q = 1

a = q = 0.4

If we combined the alleles at random (per Mendel), then genotype

frequencies would be predictable by multiplicative rule:

AA = p x p = p2 = 0.36

Aa = p x q x 2 = 2pq = 0.48

aa = q x q = q2 = 0.16

check: sum of the three genotypes

must equal 1


Hardy weinberg equilibrium

AA = p x p = p2 = 0.36

Aa = p x q x 2 = 2pq = 0.48

aa = q x q = q2 = 0.16

Thus, frequency of genotypes can be expressed as

p2 + 2pq + q2 = 1this is also (p + q)2


Hardy weinberg equilibrium

AAAA

Aap, qAa

aa aa

parental generation gamete offspring (F1)

genotypes frequenciesgenotypes

reproduction


Hardy weinberg equilibrium

Hardy-Weinberg (single generation)

observedallele expected

genotypes frequencies genotypes

AAAA

Aap, qAa

aa aa

calculateddeduced

parental generation gamete offspring (F1)

genotypes frequenciesgenotypes

reproduction


Hardy weinberg equilibrium

Under what conditions would genotype frequencies ever NOT be the same as predicted from the allele frequencies?

observed expected

AAAA

Aap, qAa

aa aa

calculateddeduced


Hardy weinberg equilibrium

Hardy-Weinberg equilibrium

Observed genotype frequencies are the same as expected frequencies if alleles combined at random


Hardy weinberg equilibrium

Hardy-Weinberg equilibrium

Observed genotype frequencies are the same as expected frequencies if alleles combined at random

Usually true if

- population is effectively infinite

- no selection is occurring

- no mutation is occurring

- no immigration/emigration is occurring


Hardy weinberg equilibrium

Chi-squares, again!

Observed data obtained experimentally

Expected data calculated based on Hardy-Weinberg equation


Hardy weinberg equilibrium

Chi-squares, again!

Observed data obtained experimentally

Expected data calculated based on Hardy-Weinberg equation

genotype observedexpected

AA 18

Aa 90

aa 42

Total N 150


Hardy weinberg equilibrium

Chi-squares, again!

p = (2*18 + 90)/300 = 0.42

q = (90 + 2*42)/300 = 0.58

= # alleles in population of 150)

genotype observedexpected

AA 18

Aa 90

aa 42

Total N150


Hardy weinberg equilibrium

Chi-squares, again!

p = (2*18 + 90)/300 = 0.42p2= 0.422 = 0.176

q = (90 + 2*42)/300 = 0.58q2= 0.582 = 0.336

2pq = 0.42*0.58 = 0.487

genotype observedexpected

AA 18

Aa 90

aa 42

Total N150


Hardy weinberg equilibrium

Chi-squares, again!

p = (2*18 + 90)/300 = 0.42p2= 0.422 = 0.176

q = (90 + 2*42)/300 = 0.58q2= 0.582 = 0.336

2pq = 0.42*0.58 = 0.487

genotype observedexpected

AA 18 26.5

Aa 90 73.1

aa 42 50.5

Total N150 150

Multiply by N to obtain frequency

(note: total observed frequencies must equal total expected frequencies)


Hardy weinberg equilibrium

Chi-squares, again!

Chi square = Χ2 = (observed – expected)2

expected

dev. from exp. (obs-exp)2

genotype observedexpected (obs-exp) exp

AA 18 26.5-8.52.70

Aa 90 73.1 16.93.92

aa 42 50.5 -8.51.42

Total N150 150


Hardy weinberg equilibrium

Chi-squares, again!

Chi square = Χ2 = (observed – expected)2

expected

dev. from exp. (obs-exp)2

genotype observedexpected (obs-exp) exp

AA 18 26.5-8.52.70

Aa 90 73.1 16.93.92

aa 42 50.5 -8.51.42

Total N150 150 sum = 8.04 = X2

degrees of freedom = 2 (= N – 1)


Hardy weinberg equilibrium

*

p <0.05 (observed data significantly different)

from expected data at 0.05 level)

df = 2

X2 = 8.04


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