Materials Included In Kit

Additional Materials Required

Safety Precautions

Do not use pop beads with small children as they can inhale or ingest them. Follow all other normal laboratory safety rules.

Disposal

All materials may be stored for future use.

Teacher Tips

• Enough materials are provided in this kit for 30 students working in pairs, or for 15 groups of students. All materials are reusable. The laboratory can be completed in one 50-minute class period. If some beads get lost, use what are available and adjust the results and calculations.

• Basic genetic concepts are assumed in this activity and students should be familiar with them before attempting this lab. Meiosis, gamete formation, independent assortment, probabilities, phenotype and genotype are just a few of the assumed concepts.
• The activity can be conducted even if the Hardy-Weinberg calculations are not completed. Students can understand the major trends without necessarily doing the calculations. The calculations, however, make the points more dramatically and realistically.
• Data from both parts of the lab can be pooled into class data. The larger sample will achieve results much closer to the theoretical values. The activity can be expanded to make these comparisons.
• Encourage students to do their drawings of the pop beads very systematically and at random. If they do so, they will get very interesting trends.
• The assumptions of the Hardy-Weinberg Principle are not actually found in any real population. Thus, real populations are in continual change. Change in gene pools is the norm and over short periods of time selections for various traits will go completely undetected. Even though the Hardy-Weinberg Principle has its obvious shortcomings, it is an interesting tool for analyzing gene frequencies and possible trends in gene pools.
• Interested students may want to continue the selection process for more generations and see what happens to the gene frequencies. They can graph the frequencies through the generations. They will likely find that the frequency of the alleles will level off after several generations.

Answers to Questions

1. Calculate the theoretical frequency of each of the genotypes (RR, RW, WW) in the original population knowing the makeup of the gene pool. (Hint: R = 0.6 W = 0.4)

p = 0.6
q = 0.4 
p² = 0.36
2pq = 0.48
q² = 0.16

2. Use your random drawing data in the chart above to calculate the frequency of the alleles and genotypes in the next generation. Calculate p, q, p², 2pq and q².

p = 0.51
q = 0.49
p² = 0.26
2pq = 0.50
q² = 0.24

3. How do the frequencies of the original and the first generation compare? Is there a major change in the frequencies in the gene pool?

The gene pools are not identical, but they are very similar.

4. Use the data collected when selection against WW occurred to calculate the theoretical frequencies in the next generation. How does the calculated frequency of RR and RW compare to the actual?

p = 0.65
q = 0.35
p² = 0.42
2pq = 0.46
q² = 0.12

The frequency of RR and RW are very close to the predicted values.

5. After one generation of selection, what has happened to the gene pool?

The frequency of W in the gene pool has decreased from 0.40 to 0.35 in this example and the frequency of red has gone up from 0.60 to 0.65.

6. If the selection against WW continues, will all of the W genes be eliminated from the population? If so, why? If not, why not?

The W gene is not likely to be completely eliminated from the gene pool because of the heterozygous individuals carrying the recessive gene.

Introduction

What is a gene pool? What factors affect or change a gene pool over time?

Concepts

• Gene pool

• Gene pool shift
• Allele frequency
• Hardy-Weinberg Principle

Background

Early in the 20th century the mathematician G. H. Hardy and the physician W. Weinberg recognized a mathematical relationship that represents the allele frequencies found in a population at equilibrium. The mathematical relationship became known as the Hardy-Weinberg Principle.
The Hardy-Weinberg Principle makes certain assumptions about conditions of the population being studied:

1. The size of the population is assumed to be large enough that slight shifts in random events would not greatly alter frequencies.
2. The population is assumed to be stable and with little severe natural selection pressure being applied.
3. New mutations are not occurring within the population.
4. Matings within the population are strictly random.
5. Organisms with different alleles or allele frequencies do not migrate into the population.
6. Organisms with allele frequencies different than the population as a whole do not migrate out of the population.

No real world population actually meets all of the Hardy-Weinberg criteria. The short term stability of many large populations, however, allows the population to be analyzed with the Hardy-Weinberg Principle and changes in gene frequencies within the gene pool can often be detected and theorized.

A population’s gene pool for a given trait is simply the total collection of the alleles for a trait contained in all the individuals in the population that have the potential to mate and pass their alleles to the next generation. The Hardy-Weinberg Principle can be applied to traits that have simple dominant/recessive relationships.

Furthermore, the frequency of two alleles for a trait are represented by the letters p and q. The allele for the dominant trait is represented by p and the recessive allele by q. The frequency of p and q add up to 1 (p + q = 1). A cross between two individuals can be shown in a Punnett Square (see Figure 1).

The Hardy-Weinberg Principle’s mathematical statement is shown in Equation 1.

where

p = frequency of allele p
q = frequency of allele q
p² = frequency of homozygous dominant
2pq = frequency of heterozygote
q² = frequency of homozygous recessive

The key to utilizing the mathematical statement on real populations depends on knowing the frequency of the homozygous recessive individuals in the population. This is because the phenotype is often clearly recognized and its frequency can be counted. Once q² is known, then q can be determined by taking the square root of q². Since p + q = 100% or 1, p can then be calculated once q has been determined. Once p and q are known p², 2pq and q² are all easily derived.
The following example illustrates the nature of Hardy-Weinberg calculations:

In a population of red and white individuals, it is found that 36% of the individuals are white (WW—homozygous recessive). What is the frequency of the white allele and red allele in the total population? What is the likely frequency of heterozygous individuals?

Solution:

              q² = 0.36
            ∴ q = √0.36 = 0.6
since p + q = 1
      p + 0.6 = 1
               p = 0.4
          ∴ p² = 0.16
           2pq = 2(0.4)(0.6) = 0.48

In summary, for this population the frequencies of alleles and genotypes would be as follows:

    q = W = 0.6
    p = R = 0.4
  p² = RR = 0.16 red homozygous
2pq = RW = 0.48 red heterozygous
  q² = WW = 0.36 white homozygous

Materials

Safety Precautions

Do not use pop beads with small children as they might be swallowed or inhaled. Follow other standard laboratory rules.

Procedure

1. Count 60 red pop beads and place them in the Styrofoam^® cup.
2. Count 40 white pop beads and add them to the same Styrofoam cup.
3. The 100 pop beads will be used to represent the gene pool of alleles for a population. The red beads (R) represent the trait red which is dominant to white (W). Cover the cup with your hand and shake it thoroughly to mix the beads.
4. Without looking, remove two alleles from the gene pool. This pair of alleles represents the diploid combination of an individual in the next generation.
5. Record the individual’s genotype with a tally mark on the Non-Selection Data Chart on the Gene Pool and Natural Selection Worksheet.
6. Replace the two alleles back into the cup, shake the cup again, and repeat the drawing procedure for another individual. Record the genotype, replace the two beads and repeat this drawing procedure until 100 individuals in the next generation have been recorded.
7. Count and record the total of the tallies for all three genotypes. Complete questions 1–3 on the Gene Pool and Natural Selection Worksheet.
8. Next collect data on a different generation of individuals. Follow steps 4–6 for shaking and drawing the alleles for each individual in the new generation. Whenever a homozygous recessive individual (WW) is drawn, select against this individual by setting the two white pop beads aside and do not return them to the cup (gene pool). Remove alleles in pairs as performed earlier to obtain a total of 100 offspring. Replace all the RR and RW alleles as they are drawn but eliminate the WW from the population.
9. Record all 100 individuals, in the appropriate row, in the second generation on the Selection Data Chart on the Gene Pool and Natural Selection Worksheet. Answer questions 4–6 on the worksheet.
10. If time permits, make a data chart and do one more generation using only the R and W beads remaining after step 8 (after one generation of WW has been selected against). Again, remove the WW individuals from the gene pool in this new generation as well. What is happening to the gene pool?

Student Worksheet PDF

10335_Student1.pdf