Download Hardy-Weinberg Practice

Addendum to Exercise 13
Population Genetics and the Hardy-Weinberg Equation
All the members of a species living in one location make up a population. The occurrence of
evolution within a population is established by determining that the genetic makeup of a population
has changed. This is done by showing that the frequency of alleles in a population’s gene pool has
changed over time.
The Hardy-Weinberg law, which is a way to calculate gene pool frequencies, provides a baseline by
which to judge whether or not evolution has occurred. It shows that the relative frequencies of alleles
do not change in large populations from one generation to the next, unless there is an evolutionary
agent, such as genetic drift, natural selection, nonrandom mating, mutation or gene flow.
Remember that the dominant phenotype characteristic is displayed by both the homozygous dominant
and the heterozygous genotypes. The homozygous recessive genotype automatically results in the
recessive phenotype; therefore, the frequency of the recessive phenotype equals the frequency of the
homozygous recessive genotype in a population. The frequency of the recessive and dominant allele
and the other two genotypes (homozygous dominant and heterozygous) can be determined by using
the Hardy Weinberg law.
In 1908, G.H.Hardy and W. Weinberg independently suggested a scheme whereby evolution could be
viewed as changes in frequency of alleles in a population of organisms. In this scheme, if A and a are
alleles for a particular gene locus and each diploid individual has two such loci, then p can be
designated as the frequency of the A allele and q as the frequency of the a allele. For example, in a
population of 100 individuals (each with two loci) in which 40% of the alleles are A, p would be 0.40.
The rest of the alleles would be (60%) would be a and q would be equal to 0.60. We can generalize
that:
p+q=1
These are referred to as allele frequencies. The frequency of the possible diploid combinations of
these alleles ( AA, Aa, aa ) is expressed as:
p2 +2pq +q2 = 1.0
Hardy and Weinberg also argued that if 5 conditions are met, the population's alleles 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. (Reduces the problem of genetic drift.)
Mating is random. (Individuals show no preference for a particular mating type.)
There is no mutation of the alleles.
No differential migration occurs. (No immigration or emigration.)
There is no natural selection. (All genotypes have an equal chance of surviving and
reproducing.)
The Hardy-Weinberg equation describes an existing situation. If the five conditions are met, then no
change will occur in either allele or genotype frequencies in the population. Of what value is such a
rule? It provides a yardstick by which changes in allelic frequencies can be measured. If a population's
allelic frequencies change it is undergoing evolution.
Estimating Allele Frequencies for a Specific Trait within a Sample Population:
Using the class as a sample population, the allele frequency of a gene controlling the ability to taste the
chemical PTC (phenylthiocarbamide) could be estimated. A bitter-taste reaction to PTC is evidence of
the presence of the dominant allele in either the homozygous condition (AA) or heterozygous
condition (Aa). The inability to taste the chemical at all depends on the presence of the 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 non- tasting allele), because only the
genotype of the homozygous recessive individuals in known for sure (i.e. those that show the
dominant trait could be AA or Aa).
Procedure
1. Obtain one piece each of PTC paper and untreated taste paper from your instructor. Place the
untreated paper on your wet tongue to see how it tastes. Dispose of this piece of paper in the trash
can.
2. Next, place the PTC paper on your wet tongue to see if you can taste the chemical. Discard the
PTC paper in the trash can. Record yourself as either a “taster” or “nontaster” phenotype:
My Phenotype: ____________________
3. Based on your phenotype, determine your possible genotype(s). Since tasting PTC is governed by
a dominant gene, if you are a taster then your possible genotypes are TT and Tt. You must include
both in your answer, because without further testing or pedigree analysis (looking at the traits of
your family members) you cannot tell if you are homozygous dominant or heterozygous for the
trait, just that you do carry the dominant gene. If you are a nontaster, then your genotype is tt.
Record you possible genotypes.
My possible genotype(s): __________________________
4. Once you have determined your phenotype and genotype(s), the instructor will tally the number of
tasters and non-tasters in the class. Record the results below:
Tasters: _________________ Non-tasters: _____________ Total: ______________
5.
A decimal number representing the frequency of tasters (p2+2pq) should be calculated by dividing
the number of tasters in the class by the total number of students in the class. A decimal number
representing the frequency of the non tasters (q2) can be obtained by dividing the number of non
tasters by the total number of students. You should then record these numbers in Table 1.
6. Use the Hardy-Weinberg equation to determine the frequencies (p and q) of the two alleles. The
frequency q can be calculated by taking the square root of q2. Once q has been determined, p can
be determined because 1 - q = p. Record these values in Table 1 for the class and also calculate and
record values of p and q for the North American population.
Table 1: Phenotypic Proportions of Tasters and Nontasters and Frequencies of the Determining
Alleles
Allele Frequency Based
on the H-W Equation
Phenotypes
Tasters (p2 + 2pq)
Class Population
# = _____
North American
Population
% = ____
0.55
Non-tasters (q2)
# = _____
p
q
% = ____
0.45
Topics for Discussion
What is the percentage of heterozygous tasters (2pq) in your class? ______________________
What percentage of the North American population is heterozygous for the taster trait?
_________________________________
Hardy-Weinberg Problems
1. In Drosophila, the allele for normal length wings is dominant over the allele for vestigial wings. In
a population of 1,000 individuals, 360 show the recessive phenotype. How many individuals
would you expect to be homozygous dominant and heterozygous for this trait?
2. The allele for the ability to roll one's tongue is dominant over the allele for the lack of this ability.
In a population of 500 individuals, 25% show the recessive phenotype. How many individuals
would you expect to be homozygous dominant and heterozygous for this trait?
3. The allele for the hair pattern called "widow's peak" is dominant over the allele for no "widow's
peak." In a population of 1,000 individuals, 510 show the dominant phenotype. How many
individuals would you expect of each of the possible three genotypes for this trait?
4. In a certain population, the dominant phenotype of a certain trait occurs 91% of the time. What is
the frequency of the dominant allele?