Download Determining Allele Frequencies Using Hardy Weinberg Equations

Determining Allele Frequencies Using Hardy Weinberg Equations
Integrated Science 4
Name:
3/06
Per:
Background
In 1908 G. H. Hardy and W. Weinberg independently suggested a scheme whereby evolution could
be viewed as changes in the frequency of alleles in a population of organisms. In this scheme, if A and a
are alleles for a particular gene and each diploid individual has two alleles for each gene, then p can be
designated as the frequency of the A allele and q as the frequency of the a allele. In a population with 100
individuals, in which 40% of the alleles are A, the frequency of the dominant allele p would be equal to
0.40. The rest of the alleles (60%) would be a, and the frequency of the recessive allele q would be equal
to 0.60, because p + q = 1. These are referred to as allele frequencies. The frequency of the possible
diploid combinations, or genotypes, of these alleles (AA, Aa, aa) is expressed as p2 + 2pq + q2 = 1.0.
These are referred to as genotype frequencies.
Hardy and Weinberg also argued that if five conditions are met, the population’s allele and genotype
frequencies will remain constant from generation to generation. These conditions are as follows:
1.
2.
3.
4.
5.
The breeding population is large. (The effect of chance is greatly reduced)
Mating is random. (Individuals show no mating preference for a particular phenotype)
There is no mutation of alleles. (No alteration in the DNA sequence of alleles)
No differential migration occurs. (No immigration or emigration)
There is no natural selection. (All genotypes have an equal chance of surviving and reproducing)
Review of Hardy-Weinberg Mathematical Formulas
Using information from above and additional class activities, identify what each of the following
components of the Hardy-Weinberg mathematical formulas represents:
Component
p
Description
q
p2
2pq
q2
Activity
Using the class as a sample population, the allele frequency of a gene controlling the ability to taste
the chemical PTC (phenylthiocarbamide) can be estimated. A bitter-taste reaction to PTC is evidence of
the presence of a dominant allele in either the homozygous (AA) of the heterozygous (Aa) condition.
The inability to taste the chemical at all depends on the presence of homozygous recessive alleles (aa).
To estimate the frequency of the PTC-tasting allele in the population, one must find p. To find p, one
must first determine q (the frequency of the nontasting PTC allele), because only the genotype of the
homozygous recessive individuals is known for sure (those that show the dominant phenotype could be
AA or Aa).
Procedure
 Part 1 – Determine Your Phenotype and Genotype For a Specific Trait in a Sample Population
1. Using the CONTROL taste test paper provided, press the strip to your tongue. Record your
observations in the space below.
2. Using the PTC taste test paper provided, press the strip to your tongue. If you taste a bitter flavor,
you possess a dominant allele for this trait. You are considered to be a ‘taster’. If you did not taste a
bitter flavor, you possess two recessive alleles for this trait, and you are a non-taster. Record your
phenotype (taster or non-taster), and possible genotypes in Table 1.
Table 1 - PTC Tasting Ability Phenotype and Possible Genotypes
Phenotype (taster or non-taster)
Possible Genotype(s)
 Part 2 – Compile Class Data For a Specific Trait in a Sample Population
1. Complete Table 2, by determining the total number of students, tasters and non-tasters in the class.
Table 2 – Class Data
Total Number of Students in Class
Total # of Tasters
Total # of Non-Tasters
 Part 3 – Determine Phenotype Frequencies For a Specific Trait in a Sample Population
1. Calculate the frequency of tasters (p2 + 2pq) by dividing the number of tasters in the class by the total
number of students in the class. Show your work in the space below and record the decimal value in
Table 3.
2. Calculate the frequency of non-tasters (q2) by dividing the number of non-tasters by the total number
of students in the class. Show your work in the space below and record the decimal value in
Calculate these values and record in Table 3.
Table 3 - Phenotype Frequencies
Frequency of Tasters (p2 + 2pq)
Frequency of Non-Tasters (q2)
 Part 4 – Determine Allele Frequencies For a Specific Trait in a Sample Population
Use the Hardy-Weinberg equation to determine the frequencies (p and q) of the two alleles.
1. Determine the frequency of the recessive allele (q), by taking the square root of (q2). Show your work
in the space below and record the decimal value in Table 4.
2. Once q has been determined, p can be determined using the formula p + q = 1. Show your work in
the space below and record the decimal value in Table 4.
Table 4 - Allele Frequencies
p
q
 Part 5 – Determine Genotype Frequencies For a Specific Trait in a Sample Population
1. Using the decimal values from Table 4, calculate the frequency of heterozygous tasters (2pq) and
homozygous dominant tasters (p2) in your class. Show your work in the space below and record the
decimal values in Table 5.
2. In the entire population of North America, the frequency of tasters (p2 + 2pq) was determined to be
0.55 and the frequency of non-tasters (q2) was determined to be 0.45. Using the Hardy-Weinberg
equations and skills learned during this activity, calculate the frequency of heterozygous tasters (2pq)
and homozygous dominant tasters (p2)in North America. Show your work in the space below and
record the decimal values in Table 5.
Table 5 – Genotype Frequencies
(p2)
(2pq)
(q2) - See Table 3
Your Class
North America
.45
Analysis Questions
1. Analyze the data in Table 5. Were your class results the same as the results for North America.
Explain why this may or may not have been the case.
2. Consider the population of students in your class. What conditions might cause the allele
frequencies and genotype frequencies you calculated for the trait ‘PTC tasting’ to change over time?
3. If changes in allele frequencies are measured in future generations, what is said to have occurred?