AP Biology: Laboratory

The Hardy-Weinberg Equation

How can we make predictions about the characteristics of a population?

Part 1

Punnett squares provide an easy way to predict the possible genotypes for an offspring, but it is not practicalto perform a Punnett square analysis on all possible combinations of all members of a population topredict what the population might look like in the future. For that we must turn to statistics. The Hardy-Weinberg equation is a tool biologists use to make predictions about a population and to show whether ornot evolution is occurring in that population.

When it comes to mating in natural populations with hundreds or even millions of individuals, it is difficult, maybe even impossible, to think of all the mating scenarios. After several generations of leavingthings up to nature, the alleles that are present in the population will become more and more randomized. Statistics can help biologists predict the outcome of the population when this randomization has occurred. If the population is particularly nonrandom to start, this randomization may take several generations.

Figure 1 below displays a population of 24 beetles with an equal number of males and females. There are two possible phenotypes for exoskeleton color: black and white.

Figure 1

  1. According to the information in the passage and Figure 1, predict the dominant phenotype for exoskeleton color in the beetle population. Explain your reasoning.
  1. According to the passage, why is it difficult to predict the genotype and phenotype frequencies of the offspring of the beetle population in Figure 1?
  1. How many total alleles are in the population in Figure 1? Explain your reasoning.
  1. What is the probability of an offspring from the Figure 2 population getting a dominant allele? Explain your reasoning.
  1. What is the probability of an offspring from the Figure 2 population getting a recessive allele? Explain your reasoning.
  1. In the Hardy-Weinberg equation, p is used to represent the frequency of the dominant allele and q is used to represent the frequency of the receive allele.
  1. According to your answers to questions 4 and 5, what do p + q equal?
  1. For any given trait in any population of organisms, will p + q always equal the value identified in part a? Why or why not?
  1. Recall that to find the probability that two events will happen (for example, an organism inherits a dominant allele from its mother and a recessive allele from its father), one must multiply the probabilities of the two events. According to your answers to questions 4 and 5, what is the probability of an offspring from Figure 2 being:
  1. Homozygous dominant for exoskeleton color?
  1. Heterozygous for exoskeleton color? (Don’t forget there are two ways to get a heterozygous offspring – Bb or bB)
  1. Homozygous recessive for exoskeleton color?
  1. Sum your answers from 7a, 7b, and 7c together. What do they equal? Why is this logical?
  1. Using p and q as variables, write formulas for calculating the probability of an offspring from a population having each of the following genotypes. Explain your reasoning.

Genotype / Homozygous Dominant / Heterozygous / Homozygous Recessive
Formula
  1. Write an equation that sums the formulas from part 9 and sets this sum equal to a specific value. Explain why this equation is true.

Part 2

The equations you have developed, p + q = 1 and p2 + 2pq +q2= 1, were first developed by G. H.Hardy and Wilhelm Weinberg. They represent the distribution of alleles in a population when

  • The population is large.
  • Mating is random.
  • All genotypes are equally likely to reproduce (there is no natural selection).
  • No organisms enter or leave the population (there is no immigration or emigration).
  • No mutations occur.

In other words, the group of alleles available in the population must be very stable from generationto generation. If the distribution of genotypes in a population matches that predicted by the Hardy-Weinberg equation, then the population is said to be in Hardy-Weinberg equilibrium. If the distributionof genotypes in a population does not match that predicted by the Hardy-Weinberg equation, then thepopulation is said to be evolving.

  1. Considering the requirements, in the natural world, are populations likely to be in Hardy-Weinberg equilibrium? Explain your reasoning.
  1. Phenylthiocarbamide (PTC) is a chemical that resembles toxic alkaloids found in some poisonous plants. It has the same bitter taste as the toxins without being harmful when ingested. In humans, the ability to taste PTC is due to a single dominant allele. A student samples 215 individuals and determines that 150 could detect the bitter taste of PTC and 65 could not.
  1. What is the frequency of individuals with at least one dominant allele for PTC tasting in the population sampled? Explain your reasoning.
  1. What is the frequency of individuals with only recessive alleles for PTC tasting in the population sampled? Explain your reasoning.
  1. Which value from the Hardy-Weinberg equations (p, q, p2, q2, or 2pq) is equal to the frequency found in part b? Explain your reasoning.
  1. Assuming that this population is in Hardy-Weinberg equilibrium, determine the frequency of the dominant allele AND the frequency of heterozygous individuals.
  1. Sixty flowering plants are planted in a flowerbed. Forty of the plants are red-flowering homozygous dominant. Twenty of the plants are white-flowering homozygous recessive. The plants naturally pollinate and reseed themselves for several years. In a subsequent year, 128 red-flowered plants, 140 pink-flowered plants and 132 white-flowering plants.
  1. According to the information provided, what genotypes results in red-, pink-, and white-flowering plants? Explain your reasoning.
  1. Determine p and q for the original population of 60 plants.
  1. Using the values calculated in part b, predict the genotype frequencies (p2, 2pq, and q2) for the original population of 60 plants IF it reaches Hardy-Weinberg equilibrium.
  1. Determine the genotype frequencies for the population of 400 plants that is observed in the subsequent year.
  1. If a population is not in Hardy-Weinberg equilibrium, it is evolving. Based on this information and your answers to parts c and d, what conclusion can you draw about this plant population? Explain your reasoning.

Pre-Lab

In this activity, your class will simulate a breeding population of diploid organisms. You have four cards, which represent gametes produced by meiosis. The letter of the card represents an allele that is inherited with the gamete. You will contribute one gamete to each of your offspring. Everyone in the class begins with the same four cards, two A and two a. Read the procedure on page 7 and answer the pre-lab questions that follow.

Questions

  1. Design two data tables, 1 for Experiment 1 and 1 for Experiment 2, on page 7.
  1. The cards used in this simulation represent gametes. Why do the cards contain only 1 letter on them (A or a) rather than two letters?
  1. Based on the information provided, what can you assume is the genotype of every individual in the class at the start of this simulation? Explain your answer.
  1. Determine the initial frequency of alleles A and a in this simulation. Explain your answer.
  1. Reread Step 4 of the procedure.
  1. What are the three possible genotypes of your Generation 1 offspring?
  1. For each of the genotypes listed in part a, describe what four cards you would need to obtain to represent that offspring. Explain your answer.
  1. Assume that at the end of Generation 5, you class includes the following genotypes: 5 individuals are AA, 12 individuals are Aa, and 7 individuals are aa.
  1. What will be the frequencies of A and a for the population?
  1. Would you conclude that the population has experienced evolution? Why or why not?

Procedure

Experiment 1

  1. Determine the initial frequencies of alleles A and a in the class. Record these in Table 1.
  2. Shuffle your cards face-down. Pair with another student. Draw the top card from your hand and match it with your partner’s card. These two cards represent the genotype of your first offspring. One of you should record this as the Generation 1 Genotype in Table 1.
  3. Retrieve your card and reshuffle your hand. Repeat Step 1 with the same partner to produce a second offspring. The individual who did not record a Generation 1 Genotype in Step 1 should record this result in Table 1 for Generation 1.
  4. Now, assume the genotype of your Generation 1 offspring by obtaining four cards to represent the four appropriate gametes that your offspring would produce with his/her genotype.
  5. When your teacher gives you the signal, randomly pair with a different student and repeat this process for five generations.
  6. Gather the class data for how many AA, Aa, and aa individuals there are in each generation.
  7. Determine the frequencies of A and a in the class for Generation5. Record these in Table 1.

Experiment 2

  1. Experiment 1 will be repeated, however your teacher will be forcing mutations in gametes (changing an “A” allele to an “a” or vice-versa) during mating events.

Data Tables

Analysis

  1. Record the population data in the Table below:

Generation / Experiment 1 Frequencies / Experiment 2 Frequencies
AA / Aa / aa / AA / Aa / aa
1
2
3
4
5
  1. Use the Hardy-Weinberg equation to determine the following for Experiment 1:
  1. The frequency of the dominant and recessive allele in the initial population.
  1. The predicted frequency of homozygous dominant, homozygous recessive, and heterozygous individuals in the initial population.
  1. The frequency of the dominant and recessive allele in the final population.
  1. The predicted frequency of homozygous dominant, homozygous recessive, and heterozygous individuals in the final population.
  1. Use the Hardy-Weinberg equation to determine the following for Experiment 2:
  1. The frequency of the dominant and recessive allele in the initial population.
  1. The predicted frequency of homozygous dominant, homozygous recessive, and heterozygous individuals in the initial population.
  1. The frequency of the dominant and recessive allele in the final population.
  1. The predicted frequency of homozygous dominant, homozygous recessive, and heterozygous individuals in the final population.
  1. Did the populations modeled in Experiment 1 and Experiment 2 maintain Hardy-Weinberg equilibrium or evolve? Explain your answer and propose an explanation for why this occurred in each population.
  1. The Founder Effect is a form of genetic drift in which a small group in a population splinters off from the original population and forms a new one. Imagine that Experiment 1 was repeated, but the Founder Effect was modeled by moving 6 students to another location after Generation 1 and having them only “mate” with each other. Would the two separated populations be likely to have the same allele frequencies as each other at the end of Generation 5? Why or why not?

1