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Population Dynamics
PURPOSE
To determine the frequency of genes in a population through the use of the Hardy-Weinberg Law.
MATERIALS
paper pencil
INTRODUCTION
In Hoot Woods there are two kinds of mice: those with colored fur and those with albino (white) fur. These
phenotypes have been recorded over several generations in a pedigree. The pedigree shows that two
albino mice can have only albino offspring, and that two colored mice or one colored mouse and one
albino mouse can have both colored and albino offspring. Therefore, the gene for colored fur is dominant
and the gene for albino fur is recessive.
The number of a particular gene in a population is known as the gene frequency of that gene. Frequency
is expressed as either a percent or a decimal. For example, in an entire population of mice 80 percent of
the genes for fur color might be for albino fur and 20 percent for colored fur. The gene frequency of the
albino gene is therefore 80 percent, or 0.8.
In stable environmental conditions, the frequency of genes for a trait in a genetically balanced population
that mates randomly tends to remain the same.
Thus, if the environment does not change, the frequency of the genes for albino fur will remain 0.8 or 80
percent, generation after generation. The maintenance of gene frequencies in this way is known as the
Hardy-Weinberg Law. In this lab you will learn the mathematical expression of this law and how it applies
to actual populations.
" I didn't count on you showing up'."
PROCEDURE
Let A stand for the gene for colored fur, and a for the gene for albino fur. Mice with the AA or the Aa
genotype have colored fur. Mice with the aa genotype have albino fur. Here are the genotypes of 200
mice:
To determine the frequency of these genes in the population, count the total number of genes, the
number of As, and the number of as. Use the following formulas to calculate the gene frequencies. When
calculating frequencies, use the decimal notation rather than the percent.
1. Calculate the frequency of the genes in the population. Express your answer as a decimal.
Frequency of the a gene =
Frequency of the A gene =
If you have done the calculations properly, the sum of the two frequencies will be 1.0, or 100 percent.
In the Hardy-Weinberg equations, the frequency of the dominant gene in a population is designated p,
and the frequency of the recessive gene is designated q. Thus, the general equation for the frequency of
genes in a population is:
p + q = 1.0 (or 100 percent)
Now, examine the relationship between the frequency of albino mice and the frequency of the albino gene
in the population. Use the following equation to determine the frequency of albino mice.
number of albino mice
2. Calculate the frequency of albino mice in the population.
3. Is this frequency greater or smaller than the frequency of the a gene?
4. If q = the frequency of a (the recessive gene) in the population, is the frequency of albino mice in the
population equal to 2q or to q2?
You have learned that p + q = 1, and that q2 * the frequency of the recessive phenotype in the population.
With this information, you can determine the frequency of the genes in a population, even if you do not
know all the genotypes (as you did with the mice).
Consider the following situation. There are 100 owls in Hoot Woods. You can make some easy
calculations to determine the frequencies of the phenotypes and the frequencies of the genes in this
population. Of the 100 owls, 64 have the dominant phenotype of a long tail, and 36 have the recessive
short tail. With S as dominant and s as recessive, the genotype must be: SS or Ss for long tail, and ss for
short tail.
5. What is q2 (the frequency of the recessive trait, ss)?
6. What is the frequency of the dominant trait?
7. If q2= .36, what does q equal?
When you know the value of q, you can calculate p from the equation, p + q = 1. By subtracting q from
both sides of the equation, you get p = 1 — q.
8. Calculate p for the owl population.
If q2 is the frequency of the homozygous recessive trait (ss) in the population, p 2 must be the frequency of
the homozygous dominant traits (SS).
9.
Calculate p2 (the frequency of the homozygous dominant trait, SS).
The only frequency that you have not determined is the frequency of the heterozygotes in the population,
designated 2pq. You know the first two addends in the following equation:
10. Calculate 2pq (the frequency of the heterozygous trait, Ss).
The two Hardy-Weinberg equations are:
The Hardy-Weinberg Law indicates that the frequency of the genes for a trait will remain constant in a
genetically balanced population living in a stable environment. Therefore, a recessive or a dominant gene
can have a very low frequency in a population and still remain in the population generation after
generation. It is for this reason that recessive traits do not simply disappear from a population over time,
which one might initially expect.
ANALYSIS
11. In a population of 200 mice, 8 have short tails, which is a recessive trait. The rest have long tails.
Determine the frequencies of the genotypes and of the dominant and recessive genes.
The frequency with which mice of any two genotypes mate can be calculated as follows. (We are
assuming that tail length does not influence selection of a mate.) The frequency of the males with a
certain genotype (such as homozygous dominant, p2) is multiplied by the frequency of the females with a
certain genotype (such as homozygous recessive, q2), or p2 x q2.
12. Using the information obtained in question 11, what is the frequency of the mating between
homozygous dominant males and homozygous recessive females?
13. The cross 2pq X 2pq describes the mating of what two kinds of individuals?
15. Write the two Hardy-Weinberg equations.