Sponge: Set up Cornell Notes on pg. 55

Topic: 5.4 Evolution: Hardy-Weinberg Principle

Essential Question: Is the Hardy-Weinberg principle a realistic model to use to study evolution?

BIOZONE: 238-251 due Wed 11/05

5.4 Evolution: Hardy-Weinberg Principle

Key Vocabulary:Hardy-Weinberg Principle

Is the Hardy-Weinberg principle a realistic model to use to study evolution?

BIOZONE: 238-251 due Wed11/05

The Hardy-Weinberg PrincipleHardy-Weinberg Principle: is used to predict genotype frequencies in a population• States that allelic frequencies will remain the same from generation to

generation assuming five conditions are met (below)• Describes populations that are NOT evolving• This principle is important because it gives biologists a standard from which

to measure changes in allele frequency in a population.

Allele frequencies will remain the same from generation to generation assuming five conditions are met:

1. Very large population: no genetic drift.

In each generation, some individuals may, just by chance, leave behind a few more descendants (and genes, of course!) than other individuals. The genes of the next generation will be the genes of the “lucky” individuals, not necessarily the healthier or “better” individuals.

2. No emigration or immigration: no gene flow. No organisms coming or going into the population.

The Hardy-Weinberg Principle

3. No mutations: No new alleles added to gene pool.

4. Random mating: No sexual selection. They will mate with any female/male.

5. No natural selection: All traits aid equally in survival. No traits are better than others.

The Hardy-Weinberg Principle

Real populations rarely meet all five conditions!!!

The Hardy-Weinberg Equation• In order to calculate the frequencies of alleles, genotypes, or phenotypes

within a population the Hardy-Weinberg equation is needed• Useful in determining how fast a population is changing or in predicting the

outcomes of matings or crosses• Values predicted by the equation are those that would be present if the population is

in equilibrium.

• The Hardy-Weinberg equation is based on Mendelian genetics. It is derived from a simple Punnett square in which p is the frequency of the dominant allele and q is the frequency of the recessive allele.

The Hardy-Weinberg Equation

2 (pxq)

The Hardy-Weinberg ExampleBB(p²)= 36% of population is homozygous dominantBb (2pq)= 48% of population is heterozygousBb (q²)= 16% of population is homozygous recessive

Freq of B allele?Freq of b allele?

How to find allele frequencies:

p + q = 1p= dominant allele frequencyq= recessive allele frequency

How can I find p if I know p²? • Use the square root! • √ of p² = p

• p= the frequency of the dominant allele (B) (p+ ½ 2pq)• q= frequency of the recessive allele (b) (q+ ½ 2pq)• Must add up to 1

p= .36+.24=.60q= .24+.16=.40

.60 + .40 = 1

p + q = 1How to find allele frequencies:

Albinism  is a rare genetically inherited trait that is only expressed in the phenotype of homozygous recessive individuals (aa).  The most characteristic symptom is a marked deficiency in the skin and hair pigment melanin.  This condition can occur among any human group as well as among other animal species.  The average human frequency of albinism in North America is only about 1 in 20,000.

Referring back to the Hardy-Weinberg equation (p² + 2pq + q² = 1), the frequency of homozygous recessive individuals (aa) in a population is q². 

Therefore, in North America the following must be true for albinism: q² = 1/20,000 = .00005

Figure out the predicted frequency of homozygous individuals, heterozygous individuals, and homozygous recessive individuals. (HINT: Find the square root of q² to find q.)

The Hardy-Weinberg Principle Practice

Referring back to the Hardy-Weinberg equation (p² + 2pq + q² = 1), the frequency of homozygous recessive individuals (aa) in a population is q². 

Therefore, in North America the following must be true for albinism: q² = 1/20,000 = .00005

Figure out the predicted frequency of homozygous individuals, heterozygous individuals, and homozygous recessive individuals. (HINT: Find the square root of p2 to find p.)

p² + 2pq + .00005

Sq. root of .00005= .007 q= .007

p + q= 1 p + .007= 1

1-.007= p p= .993

.993 + .007= 1

Referring back to the Hardy-Weinberg equation (p² + 2pq + q² = 1), the frequency of homozygous recessive individuals (aa) in a population is q². 

Therefore, in North America the following must be true for albinism: q² = 1/20,000 = .00005

Figure out the predicted frequency of homozygous individuals, heterozygous individuals, and homozygous recessive individuals. (HINT: Find the square root of p2 to find p.)

p2 + 2pq + .00005

Sq root of .00005= .007 q= .007

p + q= 1 p + .007= 1

1-.007= p p= .993

.993 + .007= 1

Now let’s input this information into the Hardy-Weinberg equation: (p² + 2pq + q² = 1) p²= 2pq= q²=

Referring back to the Hardy-Weinberg equation (p² + 2pq + q² = 1), the frequency of homozygous recessive individuals (aa) in a population is q². 

Therefore, in North America the following must be true for albinism: q² = 1/20,000 = .00005

Figure out the predicted frequency of homozygous individuals, heterozygous individuals, and homozygous recessive individuals. (HINT: Find the square root of p2 to find p.)

p2 + 2pq + .00005

Sq root of .00005= .007 q= .007

p + q= 1 p + .007= 1

1-.007= p p= .993

.993 + .007= 1

Now let’s input this information into the Hardy-Weinberg equation: (p² + 2pq + q² = 1) p²= .9862pq= .014q²= .00005 Change to %s to find the

frequency for each in the population

p²= predicted freq. of homozygous dominant individuals= .986….98.6%

2pq= predicted freq. of heterozygous individuals= .014…..1.4 %

q²= predicted freq. of homozygous recessive individuals= .00005…..005%

• With a frequency of .005% (about 1 in 20,000), albinos are extremely rare.  • However, heterozygous carriers for this trait, with a predicted frequency of 1.4% (about 1 in 72), are far more

common than most people imagine.  • There are roughly 278 times more carriers than albinos.  • Clearly, though, the vast majority of humans (98.6%) probably are homozygous dominant and do not

have the albinism allele.

• You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

1. The frequency of the "aa" genotype.2. The frequency of the "a" allele.3. The frequency of the "A" allele.4. The frequencies of the genotypes "AA" and "Aa."5. The frequencies of the two possible phenotypes if "A" is completely dominant over "a."

The Hardy-Weinberg Principle Practice

Find:q²=q=p=p²=2pq=

• You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

The Hardy-Weinberg Principle Practice

aa= 36….. q²= .36Sq. Root of .36= .6q = .6

p + q = 1

_____ + .6= 1

p= .4

Now let’s input this information into the Hardy-Weinberg equation: (p² + 2pq + q² = 1) Change to %s

• You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

The Hardy-Weinberg Principle Practice

Now let’s input this information into the Hardy-Weinberg equation: (p² + 2pq + q² = 1) Change to %s

p² + 2pq + q² = 1

(.4)² + 2(.4x.6) + (.6)² = 1.16 + .48 + .36 = 1

AA= 16%Aa= 48%aa= 36%

• You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

1. The frequency of the "aa" genotype.

36%

The Hardy-Weinberg Principle Practice

• You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

2. The frequency of the "a" allele.

.36 + . 24 (1/2 of 2pq)= .6 or 60%

The Hardy-Weinberg Principle Practice

• You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

3. The frequency of the "A" allele.

.16 + .24 (1/2 of 2pq) = .4 or 40%

The Hardy-Weinberg Principle Practice

• You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

4. The frequencies of the genotypes "AA" and "Aa”.

AA= 16% Aa= 48%

The Hardy-Weinberg Principle Practice

• You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

5. The frequencies of the two possible phenotypes if "A" is completely dominant over "a.“

48+ 16= 64% of the population will show the trait. 36% will be recessive for the trait.

The Hardy-Weinberg Principle Practice

• Please complete the Hardy-Weinberg practice problems (both sides)

The Hardy-Weinberg Principle Practice

• Solve. • Fill out table

The Hardy-Weinberg Principle Pre-Lab

Find:q²=q=p=p²=2pq=

Genotype Frequency of allele pairs in

population

Gene frequency (Freq. #/Total)

Homozygous Dominant

LL .25 p²

Heterozygous Ll 2pq

Homozygous Recessive

ll q²

Total

• Read your Hardy-Weinberg Principle notes for background• Write hypothesis. What do you think is going to happen to the allele

frequencies as we move from generation to generation?

The Hardy Har Har-Weinberg Principle Lab

P 1 (Parental Generation) P1

Homozygous Dominant (LL)

Heterozygous(Ll)

Homozygous Recessive (ll)

Calculate gene frequencies for each.

8 816

.25 .50 .25

P 1 (Parental Generation) P2

Homozygous Dominant (LL)

Heterozygous(Ll)

Homozygous Recessive (ll)

Calculate gene frequencies for each.

9 918

.25 .50 .25

F1 (Generation 1)

Homozygous Dominant (LL)

Heterozygous(Ll)

Homozygous Recessive (ll)

Calculate gene frequencies for each.

F2 (Generation 2)

Calculate gene frequencies for each.

Homozygous Dominant (LL)

Heterozygous(Ll)

Homozygous Recessive (ll)

F3 (Generation 3)

Calculate gene frequencies for each.

Homozygous Dominant (LL)

Heterozygous(Ll)

Homozygous Recessive (ll)

F4 (Generation 4)

Calculate gene frequencies for each.

Homozygous Dominant (LL)

Heterozygous(Ll)

Homozygous Recessive (ll)

F5 (Generation 5)

Calculate gene frequencies for each.

Homozygous Dominant (LL)

Heterozygous(Ll)

Homozygous Recessive (ll)

• Please answer the 7 analysis questions on a separate piece of paper• Staple to lab notes/data sheet

The Hardy Har Har-Weinberg Principle Lab

•Hypothesis•Data collection

• 1-2 data tables•Data Processing/Analysis

•1-2 Graphs•Conclusion

•Only part I

The Hardy-Weinberg Principle Lab Report