Counting Buttons: demonstrating the Hardy-Weinberg principle Teach article

Pongprapan Pongsophon, Vantipa Roadrangka and Alison Campbell from Kasetsart University in Bangkok, Thailand, demonstrate how a difficult concept in evolution can be explained with equipment as simple as a box of buttons!

“The Hardy-Weinberg principle is the most difficult concept for me. I have not been clear about this topic since I started teaching it ten years ago. I know how to solve Hardy-Weinberg problems and can explain the procedures to students but…I really don’t see what we use it for and how it relates to evolution. To me, this topic is more mathematics than biology.”
Mrs Karnika, a secondary-school biology teacher in Bangkok

The Hardy-Weinberg principle is one of the most difficult topics in evolution for many teachers and students (Mertens, 1992). They may feel threatened by mathematics and the quantitative aspects of population genetics, and may be unable to apply the principle to make sense of evolutionary phenomena. Many of them wonder about the relevance of the Hardy-Weinberg principle to understanding evolution. To help Mrs Karnika and other teachers who face the same difficulties, I would like to introduce the Counting Buttons activity. This is a simple demonstration of the Hardy-Weinberg equilibrium and how natural selection affects the allele frequency of a population. This activity is appropriate for high-school and university students studying evolution. The activity was originally developed by staff in the Department of Genetics at Kasetsart University in Thailand and later modified, as part of a PhD project, for use with high-school students.

Evolution is a change in allele frequency in a population over a period of time (Skelton, 1993; Strickberger, 1996). A population is a group of individuals of the same species in a given area whose members can interbreed and hence share a common group of genes known as a gene pool. Each gene pool comprises all alleles for all characteristics of all individuals. The allele frequency is the number of alleles of a given type as a proportion of the total number of alleles for that trait. In 1908, Hardy and Weinberg constructed a model of a population that was not evolving, and laid out the conditions in which such a population would exist (Abedon, 2005): a large population size with no migration, no mutation, no natural selection, and random mating. If we track allele frequencies in a population over a succession of generations and find that the frequencies of alleles deviate from the values expected from the Hardy-Weinberg equilibrium, then the population is evolving.

The Counting Buttons exercise simulates both a population in genetic equilibrium and a population undergoing natural selection. Natural selection acts on organisms’ phenotypes: physical traits, metabolism, physiology and behaviour, “and adapts a population to its environment by increasing or maintaining favorable genotypes in the gene pool” (Campbell & Reece, 2002). In a changing environment, natural selection favours any existing genotypes that have already adapted to the new conditions.

Note to teachers: Teachers should review students’ understanding of Mendelian genetics, especially monohybrid crosses, before running this exercise. This is an activity for groups of four to five students, and should take three hours.

Objectives of the activity

After completing this activity, students will have simulated a population at genetic equilibrium and examined the effect of natural selection on the allele frequency of a population over five generations.

Materials

1. Three kinds of button: black on black, black on white, and white on white (50 each). Each button is actually made from two buttons glued together (see below).
2. Tables 1, 2, and 3 for recording parents and offspring, and calculating allele frequencies^w1
3. Plain paper, graph paper

Each button represents one diploid individual in a population. Each side of the button represents an allele: black on black is an individual with genotype RR, black on white is Rr, and white on white is rr.

Each pair of buttons will produce four offspring; the genotypes of the offspring are determined according to Mendel’s first law.

Procedure

Experiment I: a population at equilibrium

1. Place 16 black/black, 32 black/white, and 16 white/white buttons in a box. These buttons represent the initial population (generation 0).
2. Shake the box, randomly select two buttons at a time, and record their genotypes in the ‘parent’ column of Table 1. Put these pairs to one side.
3. Repeat step 2 until the box is empty. You should have 32 pairs of genotypes in the parent column.
4. Use Mendel’s law of segregation to calculate the genotypes of the four offspring for all 32 pairs, and record their frequencies in the ‘offspring’ column of the mating table (Table 1).
5. From your spare buttons, find those that represent the genotypes of the offspring. These 128 buttons represent the genotypes of the first offspring (generation 1) in a community.
6. Discard all of the parent buttons in the parent column. Sort the offspring buttons into three groups: black/black, black/white and white/white.
7. Count the number of buttons in each group and divide this number by two in order to maintain the population size at 64. Otherwise, your population will grow exponentially!
8. Write these numbers down in the ‘genotype’ column of Table 2.
9. Use the number of each genotype to work out the frequencies of the R and r alleles and write them in the appropriate columns in Table 2.
10. Put the buttons representing the first offspring generation back into the box.
11. Repeat steps 2-10 four times to obtain genotype and allele frequency data from a total of five generations.
12. On graph paper, plot the frequency of the recessive allele (r) against time.

Experiment II: an evolving population

Suppose the individuals with genotype rr die out before they reproduce. You will need to eliminate white/white buttons from each generation after the first.

1. Put 16 black/black and 32 black/white buttons into the box, and shake it.
2. Randomly select two buttons at a time and record their genotypes in a new copy of Table 1.
3. Repeat step 2 until the box is empty. You should have 24 pairs in the parent column.
4. Calculate the genotypes of all offspring and write them in the offspring column of Table 1. Discard the parent buttons.
5. Find the buttons representing the offspring genotypes.
6. Now you will have 96 buttons in the offspring column representing the genotypes of the first offspring generation.
7. Sort the offspring buttons into three groups: black/black, black/white and white/white.
8. Count the number of buttons in each colour group and multiply each group by K (K = 64/N; N is the sum of the three genotypes) to make the population size of the next generation remain at 64 (its initial population). N and K values vary from generation to generation. In the first round, N = 96 and K = 2/3. Multiply the number of each genotype by 2/3. The sum of the outcomes should be 64. If multiplication produces a decimal number, you can raise or lower a fraction to the next whole number to make the sum of all genotypes equal to 64. Write the number of each genotype in Table 3 in the genotype columns.
9. Put the buttons corresponding to the numbers from the first generation row back into the box and do not forget to remove white/white buttons from the box because they die before they are able to reproduce.
10. Repeat all steps above four times to obtain R and r allele frequencies over five generations.
11. Plot the frequency of the r allele over time and compare this with the graph from the first experiment.

Note: The students might find that, in some rounds, there is a single unpaired button left in the box after selecting pairs of buttons. This remaining button must be removed from the population because it does not have a chance to mate with other individuals.

Example results

When there is no selection pressure, the frequency of the two alleles fluctuates slightly (Table 5). When there is a selective pressure against the homozygous recessive genotype (that is, if rr individuals die before they reproduce), the frequency of the r allele in the population declines over time (Table 6).

Table 4: Mating

NO.				Genotypes of offspring
				RR	Rr	rr
1	RR	Rr	→	2	2	0
2			→
3			→
4			→
5			→

Table 5: Allele frable equency (no selection)

Generation	Number of each genotype			requency of allele R	Frequency of allele r
	RR	Rr	rr
0	16	32	16	0.5	0.5
1	D1 =   17	H1 =  34	R1 =  13	0.53	0.47
2	D2 =   14	H2 =  35	R2 =  15	0.49	0.51
3	D3 =   16	H3 =  32	R3 =  16	0.50	0.50
4	D4 =   15	H4 =  31	R4 =  18	0.48	0.52
5	D5 =   16	H5 =  33	R5 =  15	0.50	0.50

Table 6: Allele frequency (selection)

Generation	Number of each genotype			Frequency of allele R	Frequency of allele r
	RR	Rr	rr
0	16	32	16	0.5	0.5
1	D1 =    21	H1 =  29	R1 =  14	0.55	0.45
2	D2 =  30	H2 =  24	R2 =  10	0.65	0.35
3	D3 =  36	H3 =  21	R3 =  17	0.72	0.28
4	D4 =  41	H4 =  17	R4 =  6	0.77	0.23
5	D5 =  48	H5 =  12	R5 =  4	0.84	0.16

D = dominant
H = heterozygous
R = recessive

Questions for discussion

Compare the graphs of allele frequency from the stable and the evolving population. Do they differ?

How does natural selection affect allele frequencies of a population over time?

Will a dominant allele of a trait always have the highest frequency in a population and a recessive allele always have the lowest frequency? Explain your answer.

Teachers should be aware that students may misinterpret the graphs, focusing only on two or three points and not noticing that there are fluctuations from generation to generation. The teacher should also emphasise that in a natural population it usually takes more than five generations before we can detect any change in allele frequency. Evolution takes time.

After conducting the second experiment, some students might conclude that natural selection always increases the frequency of a dominant allele and decreases the frequency of a recessive allele in a population. However, not all selections would result in a progressive decrease in a recessive allele. The allele – dominant or recessive – that is selected out is determined by the environmental conditions at the time. In order to avoid this misunderstanding, it is advisable for the teacher to ask the students to consider examples in which the recessive allele is common, or the dominant allele is rare: type O blood is a recessive trait but the majority of people in some populations have this blood type; Huntington’s disease is a dominant trait but only 4-10 individuals in 100 000 have it. More examples of other kinds of natural selection are described in O’Neil (2006).

Summary

Counting Buttons is a simple and concrete way to demonstrate the Hardy-Weinberg principle. By engaging in this activity, students will gain insight into a population at equilibrium and into natural selection as a force for biological adaptation. Students will have to apply Mendelian law and mathematical skills to make sense of the data and interpret the results. Counting Buttons is an example of how to teach biology in an integrated fashion and to use mathematics to make sense of complex biological phenomena.

“Counting Buttons helped me make sense of the Hardy-Weinberg principle. Now, I can explain to students what the principle is used for and how to link it to other topics of evolution meaningfully. I feel more confident and enjoy teaching this topic. Obviously, the students paid more attention to the lesson. They were very happy to work hands-on and collaboratively in this lab exercise.”
Mrs Karnika, after running Counting Buttons