Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings D.4 High Level Only D.4 The Hardy-Weinberg Principle – D.4.1 Explain how the Hardy-Weinberg

Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings

D.4 High Level Only

• D.4 The Hardy-Weinberg Principle

– D.4.1 Explain how the Hardy-Weinberg equation is derived

– D.4.2 Calculate allele, genotype and phenotype frequencies for two alleles of a gene using the Hardy Weinberg Equation

– D.4.3 State the Assumptions made when the Hardy-Weinberg Equation is used


Hardy-Weinberg Equation Uses

• Useful in determining how fast a population is changing (allele frequency is changing)

• Predicting outcomes of mating crosses


• p = frequency of DOMNANT allele in a population

• q = frequency of RECESSIVE allele in a population

• Frequencies of the alleles on a chromosome must add up to 1

• THUS

• p + q = 1

D.4.1 Explain how the Hardy-Weinberg equation is derived


• p = frequency of DOMNANT allele in a population

– EXAMPLE: T frequency is 0.25 or 25%

• q = frequency of RECESSIVE allele in a population

– Example: t frequency is 0.75 or 75%

• Frequencies of the alleles on a chromosome must add up to 1 or 100%

• p + q = 1 .75 + .25 = 1



• Apply p + q = 1 to a diploid situation

• Because we are all diploid ( p + q )2 =1

• If you remember your mathematics about polynomials ( p + q )2 =1 can be changed to

– p2 + 2pq + q2 = 1

• Now you know how the Hardy-weinberg equation was derived



• If p and q represent the relative frequencies of the only two possible alleles in a population at a particular locus, then

– p2 + 2pq + q2 = 1

– And p2 and q2 represent the frequencies of the homozygous genotypes. Examples:

• p2 = p x p = TT (homozygous dominant)

• and 2pq represents the frequency of the heterozygous genotype

Hardy-Weinberg Equations---What it means..


• p2 + 2pq + q2 = 1

• p2 = p x p = TT (homozygous dominant)

• q2 = q x q = tt ( homozygous recessive)

• 2 pq Heterozygote

Hardy-Weinberg Equations---What it means..

T t

T TT Tt

t Tt tt


Hardy-Weinberg Equation Uses

• Useful in determining how fast a population is changing (allele frequency is changing)

• Predicting outcomes of mating crosses

Allele Frequencies

Recessive t q

Dominant T p

Genotype Frequencies

Homozygous Recessive q2

Heterozygote 2pq

Homozygous Dominant p2


Example Problems: p2 + 2pq + q2 = 1

One Square Two Square One square

Genotypes TT 2 Tt tt

Phenotypes ¼ ½ ¼

• Frequency of TT = p2 = ¼ • Frequency of Tt = 2pq = ½• Frequency tt = q2 = ¼ • ¼ + ½ + ¼ = 1• 0.25 + 0.50 + 0.25 = 1


Problem 1 calculating allele frequency

• Recessive allele t is 10% of a given population. Calculate the percentage of the dominant allele

• q = 0.10 or 10%

• p + q =1

• So…….p = 1 - 0.10

• p= 0.90 or 90%

• Remember this is allele frequency NOT genotype frequency.


Problem 2 calculating allele frequency

• In a study 989 members of the population from example 1, it was found that 11 people had showed the recessive phenotype (t). Calculate the frequency of of the recessive allele (t).

• 1st calculate the percentage of people who have the recessive phenotype (tt)

• 11/ 989 = 0.011 ----thus 1.1 % of the population have this phenotype tt)

• Hence q2 = 0.011

• To calculate q (frequency of recessive allele) just take the square root of q2 = 0.011

• √ q2 =√ 0.011 = 0.105

• This means that the frequency of this recessive allele is 10.5 % of the population


Problem 3 calculating genotype frequency

• Use the information from the previous problems to fill in the charter below:

Allele Frequencies

Recessive t q

Dominant T p

Genotype Frequencies

Homozygous Recessive q2

Heterozygote 2pq



Problem 3 calculating genotype frequency

• We know from problem 1, q= 0.10 so q2 = 0.01

• we know from problem 1, p = 0.9 so p2 = 0.81

• So 2pq = 2 x 0.10 x 0.9 = 0.18

Allele Frequencies

Recessive t q

Dominant T p

Genotype Frequencies Homozygous Recessive q2

Heterozygote 2pq


0.1

0.9

0.01

0.18

0.81


Practice Problem

In a randomly breeding population of mice, 640 had black fur and 360 brown fur. Black fur is dominant to brown fur. The Hardy-Weinberg Principle (p2 + 2pq + q2 =1) can be used to calculate allele and phenotype frequencies.

• (a) Calculate the frequency of the recessive allele (1 point).

• Solve for q

• Calculate q2 frequency of homozygous recessive genotype

• q2 = 360/640 = 0.5625

• q = √q2 = √0.5625 = 0.75 or 75%

•


The Hardy-Weinberg Theorem

• The Hardy-Weinberg theorem describes a

population that is not evolving

• It states that frequencies of alleles and genotypes in a population’s gene pool remain constant from generation to generation, provided that only Mendelian segregation and recombination of alleles are at work

• Mendelian inheritance preserves genetic variation in a population


Preservation of Allele Frequencies

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


Hardy-Weinberg Equilibrium

• Hardy-Weinberg equilibrium describes a population in which random mating occurs

• It describes a population where allele frequencies do not change


Conditions for Hardy-Weinberg Equilibrium

• The Hardy-Weinberg theorem describes a hypothetical population

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


• The five conditions for non-evolving populations are rarely met in nature:

– Extremely large population size

– No gene flow

– No mutations

– Random mating

– No natural selection


• More Help check out this tutorial

• http://www.youtube.com/watch?v=xPkOAnK20kw

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Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings D.4 High Level Only D.4 The Hardy-Weinberg Principle – D.4.1 Explain how the Hardy-Weinberg