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POPULATION DYNAMICS
INTRODUCTION
In Hoot Woods there are two kinds of mice, those with colored fur and those with albino
(white) fur. 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.
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.
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. How many genes are in the gene pool? ________
Aa aa AA Aa aa AA aa Aa aa Aa aa aa AA aa aa AA aa aa Aa aa Aa
aa aa aa Aa aa Aa aa aa Aa Aa AA aa aa Aa aa Aa aa aa Aa aa aa
Aa aa Aa Aa Aa aa Aa Aa Aa Aa aa AA Aa Aa aa Aa aa aa aa aa Aa
aa aa Aa aa Aa aa aa Aa aa aa Aa AA aa
aa
aa Aa Aa aa AA aa Aa
aa aa Aa aa aa Aa aa aa Aa AA aa Aa aa Aa aa Aa
aa Aa aa aa
aa Aa aa aa Aa aa Aa aa aa aa AA aa Aa Aa Aa Aa aa AA Aa aa
Aa
Aa
Aa aa
aa Aa aa Aa aa Aa Aa Aa Aa aa Aa AA Aa Aa aa Aa aa Aa aa Aa aa
Aa aa Aa
Aa aa Aa aa Aa AA aa Aa aa Aa aa Aa aa Aa Aa Aa aa aa
Aa Aa aa Aa aa AA Aa aa Aa aa aa Aa aa Aa Aa aa Aa Aa aa
aa aa AA aa AA Aa Aa AA AA
aa aa
1. What is the total number of “A” alleles in this gene pool? ___________________
2. What is the total number of “a” alleles in this gene pool? ___________________
3. What is the frequency of the “A” gene? ______________
(# of A’s/total))
4. What is the frequency of the “a” gene? ______________
(# of a’s/total)
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.
# albino mice (aa)
Frequency of albino mice =
total # of mice
5. Calculate the frequency of albino mice in the population. Show your work.
6. Is this frequency greater or smaller than the frequency of the “a” gene?
7. 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.
8. What is q2 (the frequency of the recessive trait, ss)?
9. What is the frequency of the dominant trait?
10. 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.
11. Calculate p for the owl population. Show your work.
If q2 is the frequency of the homozygous recessive trait (ss) in the population, p2 must
be the frequency of the homozygous dominant traits (SS).
12. 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 values in the following
equation:
frequency of homozygous recessive owls (q2)
+ frequency of homozygous dominant owls (p2)
+ frequency of the heterozygotes (2pq)
1.0 or 100 percent
13. Calculate 2pq (the frequency of the heterozygous trait, Ss). Show your work.
The two Hardy-Weinberg equations are:
p+q=1
p2 + 2pq + q2 = 1.0
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
14. 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.
q2 = __________
q = __________
p2 = __________
2pq = __________
p = __________
15. Match each of the following symbols with the phrase that defines it.
p
_____
q
_____
a. The frequency of homozygous dominant individuals in the
population.
b. The frequency of the dominant gene.
p2
_____
c. The frequency of heterozygotes in the population.
2pq _____
d. The frequency of the recessive gene.
q2
e. The frequency of homozygous recessive individuals in the
population.
_____
16. Write the two Hardy Weinberg equations: