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ROCK POCKET MOUSE ALLELE FREQUENCIES ACTIVITY
PART 1: REVIEWING THE PRINCIPLES OF THE HARDY-WEINBERG THEOREM
The genetic definition of ‘‘evolution’’ is ‘‘a change to a population’s gene pool.’’ ‘‘Gene pool’’ is defined as ‘‘the total number of alleles present in a population at any given point in time.’’ According to the Hardy-Weinberg theorem, a population is in equilibrium (and is therefore not evolving) when all of the following conditions are true:
- The population is very large and well mixed.
- There is no migration.
- There are no mutations.
- Mating is random.
- There is no natural selection.
To determine whether a population’s gene pool is changing, we need to be able to calculate allelic frequencies. Suppose, for example, a gene has two alleles, A and a. Each individual has one of three genotypes: AA, Aa, or aa. If the population is in equilibrium, the overall number of A alleles and a alleles in the gene pool will remain constant, as will the proportion of the population with each genotype. If allele frequencies or genotype frequencies change over time, then evolution is occurring.
Two equations are used to calculate the frequency of alleles in a population, where p represents the frequency of the dominant allele and q represents the frequency of the recessive allele:
p + q = 1.0 and p^2 + 2pq + q^2 = 1..
The first equation says that if there are only two alleles for a gene, one dominant and one recessive, then 100% of the alleles are either dominant (p) or recessive (q).
The second equation says that 100% of individuals in the population will have one of these genotypes: AA, Aa, and aa.
Let’s look at each genotype one by one to understand the equation: If p represents the frequency of the A allele, then the frequency of the genotype AA will be p ⋅ p, or p^2. If q represents the frequency of the a allele, then the frequency of the genotype aa will be q ⋅ q, or q^2 For heterozygotes, we must allow for either the mother or the father to contribute the dominant and recessive alleles. You can think of it as allowing for both genotypes Aa and aA. So, we calculate the frequency of the heterozygous genotype as 2pq.
In rock pocket mice, several genes code for fur color. Each gene has several possible alleles. That’s why there is a range of fur color from very dark to light. For simplicity, we will work with two alleles at one gene. The allele for dark-colored fur (D) is dominant to the allele for light-colored fur (d). In this scenario, individual rock pocket mice can have one of three genotypes and one of two phenotypes, as summarized in the table below.
Rock Pocket Mice Genotypes and Phenotypes Population Genotype Phenotype
Homozygous dominant DD Dark
Heterozygous Dd Dark
Homozygous recessive dd V Light
IGHT
So, applying Hardy-Weinberg, we have the following: p = the frequency of the dominant allele (D) q = the frequency of the recessive allele (d) p 2 = the frequency of DD 2 pq = the frequency of Dd q 2 = the frequency of dd
We can also express this as the frequency of the DD genotype + the frequency of the Dd genotype + the frequency of the dd genotype = 1.
SAMPLE PROBLEM
In a hypothetical population consisting of 100 rock pocket mice, 81 individuals have light, sandy-colored fur. Their genotype is dd. The other 19 individuals are dark colored and have either genotype DD or genotype Dd. Find p and q for this population and calculate the frequency of heterozygous genotypes in the population.
It is easy to calculate q 2. q 2 = 81/100 = 0.81, or 81%
Next, calculate q. q = √0.81 = 0.
Now, calculate p using the equation p + q = 1. p + 0.9 = 1 p = 0.
Now, to calculate the frequency of heterozygous genotypes, we need to calculate 2pq. 2 pq = 2(0.1)(0.9) = 2(0.09) 2 pq = 0.
QUESTIONS
1. If there are 12 rock pocket mice with dark-colored fur and 4 with light-colored fur in a population, what is the value of q? Remember that light-colored fur is recessive. 2. If the frequency of p in a population is 60% (0.6), what is the frequency of q? 3. In a population of 1,000 rock pocket mice, 360 have dark-colored fur. The others have light-colored fur. If the population is at Hardy-Weinberg equilibrium, what percentage of mice in the population are homozygous dominant, dark-colored mice?
LESSON
T HANDOUT
The Making of the Fittest:
p^2 + 2pq + q^2 = 1
p + q = 1
7. In a separate study, 76 rock pocket mice were collected from four different, widely separated areas of dark lava rock. One collecting site was in Arizona. The other three were in New Mexico. Dr. Nachman and colleagues observed no significant differences in the color of the rocks in the four locations sampled. However, the dark- colored mice from the three New Mexico locations were slightly darker than the dark-colored mice from the Arizona population. The entire Mc1r gene was sequenced in all 76 of the mice collected.
The mutations responsible for the dark fur color in the Arizona mice were absent from the three different populations of New Mexico mice. No Mc1r mutations were associated with dark fur color in the New Mexico populations. These findings suggest that adaptive dark coloration has occurred at least twice in the rock pocket mouse and that these similar phenotypic changes have different genetic bases. How does this study support the concept that natural selection is not random?
Natural selection is not random as supported by the fact that different genetic mutations produce the
same phenotypic results in different areas and these similar adaptations are favored under similar
conditions.
8. To determine if the rock pocket mouse population is evolving, explain why it is necessary to collect fur color frequency data over a period of many years.
The data collected represent only one moment in time. If the population is evolving, the frequency of
the two alleles for fur color will change over time. If the population is not under selective pressure, or
is not evolving, the frequencies will remain approximately the same.
