Teacher Guide: Hardy-Weinberg Equilibrium
Learning Objectives
Students will …
· Determine that the ratios of alleles tend to remain nearly constant in a randomly-mating population.
· Determine that the ratios of genotypes also tend to remain nearly constant in a randomly-mating population.
· Measure the ratio of heterozygous to homozygous individuals in a population, and see that this ratio remains fairly constant over time.
· Use the Hardy-Weinberg equation to calculate the percentages of genotypes in a population.
Vocabulary
allele, genotype, Hardy-Weinberg equation, Hardy-Weinberg principle, heterozygous, homozygous, Punnett square
Lesson Overview
Many factors can influence the frequencies of different alleles and genotypes in a population. Predation, sexual selection, immigration, disease, competition, or natural selection may cause some alleles to become more common and others to become less common.
To understand if a population is being influenced by one of these factors, it is first necessary to understand how a population reacts if none of these factors are present. The Hardy-Weinberg Equilibrium Gizmo™ allows students to explore how the proportions of alleles and genotypes change over time in a population that is not undergoing any form of selection.
The Student Exploration sheet contains two activities:
· Activity A – Students discover that in normal circumstances allele and genotype percentages tend to remain stable over time.
· Activity B – Students derive the Hardy-Weinberg equation and use it to calculate genotype and allele percentages.
Suggested Lesson Sequence
1. Pre-Gizmo activities ( 10 – 20 minutes)
The Hardy-Weinberg Equilibrium Gizmo explores the mathematical laws that govern allele and genotype percentages in a population. Before beginning the Gizmo, review basic genetic terms such as allele, genotype, phenotype, homozygous, and heterozygous. Practice filling in Punnett squares for various combinations of parent genotypes, and predict the percentages of each offspring genotype and phenotype. The Mouse Genetics (One Trait) Gizmo provides a helpful review of these topics.
2. Prior to using the Gizmo ( 10 – 15 minutes)
Before students are at the computers, pass out the Student Exploration sheets and ask students to complete the Prior Knowledge Questions. Discuss student answers as a class, but do not provide correct answers at this point. Afterwards, if possible, use a projector to introduce the Gizmo and demonstrate its basic operations. Demonstrate how to take a screenshot and paste the image into a blank document.
3. Gizmo activities ( 15 – 20 minutes per activity)
Assign students to computers. Students can work individually or in small groups. Ask students to work through the activities in the Student Exploration using the Gizmo. Alternatively, you can use a projector and do the Exploration as a teacher-led activity.
4. Discussion questions ( 15 – 30 minutes)
As students are working or just after they are done, discuss the following questions:
· Suppose there is a rare recessive allele in a large population. If the allele confers no advantage or disadvantage, what would you expect to happen over time? [If the population is in equilibrium, the proportion of the rare allele should remain constant over time.]
· The Hardy-Weinberg Equilibrium Gizmo focuses on a population that is in equilibrium. How could you determine if a population is affected by natural or artificial selection?
· Suppose the green and yellow (Dd) parrots were particularly popular in the illegal pet trade. How could you determine if a wild parrot population was affected by poachers? [In a normal population, the ratios of DD, Dd, and dd parrots should be p2: 2pq: q2, where p is equal to the proportion of DD parrots plus half the proportion of Dd parrots, and q is equal to the proportion of dd parrots plus half the proportion of Dd parrots. If the parrot population is affected by poachers, the Dd population will be smaller than what this proportion predicts.]
5. Follow-up activity: Microevolution ( 30 – 60 minutes)
The Hardy-Weinberg Equilibrium Gizmo focuses on a population of parrots that is not under any directed selection pressures. To explore what happens when selection is occurring, have students work through the Microevolution Gizmo. In this Gizmo, the parrot population lives in a grove of trees and is predated on by hawks. Well-camouflaged parrots are less likely to be eaten and will tend to reproduce and pass on their alleles to the next generation. This Gizmo allows students to explore scenarios such as a deleterious recessive gene and heterozygote superiority.
Scientific Background
The early 1900s was an important time in biology. Just as Charles Darwin’s theory of evolution by natural selection was gaining wide acceptance among scientists, Gregor Mendel’s laws of heredity were rediscovered. Elements of both of these revolutionary ideas were incorporated into a new field of science called population genetics.
Population geneticists sought to understand how natural selection and other factors would affect allele and genotype frequencies over time. The first step in this process was to determine what a population would look like when no natural selection or other disturbing factors were present.
The Hardy-Weinberg principle states that in the absence of natural selection and other factors both allele and genotype frequencies will remain constant over time. This applies to populations that satisfy the following conditions:
· The population is large.
· Mating is random.
· All individuals mate, and all mated pairs produce the same number of offspring.
· There is no immigration or emigration.
· There is no mutation.
· There is no selection pressure for or against any particular trait.
The Hardy-Weinberg principle also allows one to predict the genotype frequencies that result from a particular distribution of alleles. This is illustrated on the Punnett square at right. If the proportion of the dominant allele (D) is p and the proportion of the recessive allele (d) is q, then the probability of genotype DD is p 2, the probability of genotype dd is q 2, and the probability of genotype Dd is 2pq.
The genotype frequencies predicted by Hardy-Weinberg can be arranged as follows:
This arrangement provides a quick way to test if natural selection or another disturbing factor is present. If the ratio of Dd 2 to DD·dd is not close to 4, then one of the conditions listed above must not be true for the population.
Historical Connection: Discovery of the Hardy-Weinberg principle
In the early days of population genetics, some scientists believed that the “stronger” dominant genes would eventually overwhelm the “weak” recessive genes in a population, causing traits such as blond hair to go extinct. This phenomenon was called genophagy, or “gene-eating.” If that was the case, how did recessive genes survive at all?
In 1908, the Cambridge geneticist Reginald Punnett mentioned this conundrum to his colleague G. H. Hardy. Hardy was a pure mathematician who boasted, “Nothing I have ever done is of the slightest practical use.” Surprised that this “simple problem” had not been solved already, Hardy quickly worked out the rule and published his discovery in the July, 1908, issue of Science.
In fact, the principle had been previously discovered by the German physician Wilhelm Weinberg. Weinberg presented his version of the Hardy-Weinberg principle in a January 1908 lecture to the Württemberg Natural History Society. Weinberg’s work was unknown to English-speaking scientists until the oversight was finally noticed in 1943.
Selected Web Resources
Hardy-Weinberg principle: http://anthro.palomar.edu/synthetic/synth_2.htm
History of Hardy-Weinberg principle: http://www.genetics.org/cgi/content/full/179/3/1143
G. H. Hardy’s letter to Science: http://www.vacadsci.org/jsr/hardy.htm
Related Gizmos:
Mouse Genetics (One Trait): http://www.explorelearning.com/gizmo/id?449
Microevolution: http://www.explorelearning.com/gizmo/id?521