Hardy Weinberg Population Genetics

Kevin Hall
Biology, Self-directed
1-2 Class periods (45 minutes each)
High School AP/IB Biology
v1

Overview

Biology students will use the Hardy Weinberg Classroom Model Net Logo program created by Kenneth Letendre. They will use the computer simulation to analyze how variables such as the proportion of alleles, population size, and selection against alleles can influence the genetics of a population. The Hardy Weinberg principle predicts the genotype and phenotype frequencies given that five assumptions (large population size, mating is random, no mutations, no migration, and no selection) hold true in a population.

Standards

Next Generation Science Standards
  • Life Science
    • [HS-LS3] Heredity: Inheritance and Variation of Traits
    • [HS-LS4] Biological Evolution: Unity and Diversity
Computational Thinking in STEM
  • Data Practices
    • Collecting Data
    • Creating Data
    • Manipulating Data
    • Analyzing Data
  • Modeling and Simulation Practices
    • Using Computational Models to Find and Test Solutions
    • Using Computational Models to Understand a Concept
  • Computational Problem Solving Practices
    • Assessing Different Approaches/Solutions to a Problem
  • Systems Thinking Practices
    • Investigating a Complex System as a Whole
    • Thinking in Levels
    • Understanding the Relationships within a System

Activities

  • 1. Introduction
  • 2. Case I
  • 3. Case II Selection
  • 4. Hardy Weinberg Practice Problems

Student Directions and Resources


Biology students will use the Hardy Weinberg Classroom Model Net Logo program created by Kenneth Letendre. They will use the computer simulation to analyze how variables such as the proportion of alleles, population size, and selection against alleles can influence the genetics of a population. The Hardy Weinberg principle predicts the genotype and phenotype frequencies given that five assumptions (large population size, mating is random, no mutations, no migration, and no selection) hold true in a population.

You will need the following resources to complete this assignment.

1. Introduction


Hardy Weinberg Population Genetics

In 1908 G.H. Hardy and W. Weinberg independently suggested a scheme whereby evolution could be viewed as changes in the frequency of alleles in a population of organisms. In this scheme, if (A) and (A) are alleles for a particular gene locus and each diploid individual has two such loci then (p) can be designated as the frequency of the (A) allele and (q) as the frequency of the a allele. Thus in a population of 100 individuals (each with two loci) in which 40% of the alleles are (A), (p) would be .40. The rest of the alleles (60%) would be (a), and (q) would be .60. (i.e. p + q = 1.0).

These are referred to as allele frequencies. The frequency of the possible diploid combinations of these alleles (AA, Aa, and aa) is expressed as (p2 + 2pq + q2 = 1.0).

Hardy and Weinberg also argued that if five conditions are met, the populations allele and genotype frequencies will remain constant from generation to generation. These conditions are as follows:

  1. The breeding population is large.
  2. Mating is random.
  3. There is no mutation of the alleles.
  4. No differential migration occurs.
  5. There is no selection.

Purpose

Students will learn about the Hardy Weinberg law of genetic equilibrium. The students will study the relationship between evolution and changes in allele frequency of a population by using the Net Logo Hardy Weinberg computer modeling simulation.

Learning Objectives

1. Understand how natural selection can alter allelic frequencies in a population.

2. Apply the Hardy Weinberg equation and its use in determining the frequency of alleles in a population.

3. Analyze the effects on allelic frequencies of selection against the homozygous recessive population or other genotypes.

4. Explain natural selection and other causes of microevolution as deviations from the conditions required to maintain Hardy Weinberg equilibrium.


2. Case I


Procedure Need to take initial readings as well to compare and totals are important.

Using the Net Logo Hardy Weinberg model you will run a simulation of a population of randomly heterozygous individuals with an initial gene frequency of 0.5 for the dominant allele (A) and the recessive allele (a).

  1. Before moving on spend 5 minutes familiarizing yourself with how the model works by... 
  2. Set up your population size to 500.
  3. On the bottom left side of your simulation set your max- generation to 100.
  4. Select the species you would like to observe... turtles, humans, etc...
  5. Click on the “set up” button.
  6. Collect initial data in the data table before moving on.
  7. Click on “go.”
  8. Monitor the population closely by observing the species and graphs (genotype, phenotype, and allele)
  9. Analyze the data after 100 generations and complete the table below.

Thank goodness for computer simulations!

 

 

 


Question 2.1

What trend do you observe for the genotype frequency?



Question 2.2

What trend do you observe for the phenotype frequency?



Question 2.3

What trend do you observe for the allele frequency?



Question 2.4

What does the Hardy Weinberg equation predict for the new p and q?



Question 2.5

Do the results you obtained in this simulation agree? If not, why?



3. Case II Selection


In this case II you will modify the simulation to make it more realistic. In the natural environment, not all genotypes have the same rate of survival; that is, the environment might favor some genotypes while selecting against others. An example, is the human condition of sickle cell anemia. This is a disease caused by a mutation on one allele, and individuals who are homozygous recessive often do not survive to reach reproductive maturity. For this simulation you will assume that the homozygous recessive individuals never survive (100% selection against) and that heterozygous and homozygous dominant individuals survive 100% of the time.

Procedure

1. Using the Net Logo Hardy Weinberg model you will run a simulation of a population of randomly heterozygous individuals with an initial gene frequency of .5 for the dominant allele A and the recessive allele a.

2. Set up your “population size” to 500.
3. On the bottom left side of your simulation set your “max- generation” to 100.
4. Select the species you would like to observe... turtles, humans, etc...
5. Move the “selection against yellow” slider to 100%

6. Click on the “set up” button.             
7. Click on “go.”
8. Monitor the population closely by observing the species and graphs (genotype, phenotype, and allele)
9. Analyze the data after 100 generations and complete the table below.

Case I Ideal Hardy Weinberg Population

 

Number of Each Frequency

Sketch the Graph
(create a legend with different colors)

Initial Data

 Resultant Data

Genotype Frequencies

AA =
Aa =
aa =

AA =
Aa =
aa =

 

Total:

 

 

Phenotype Frequencies

yellow =
blue=

yellow =
blue=

 

Total:

 

 

Allele Frequencies

A=
a=

A=
a=

 

 

Total:

 

 

 

Case II Selection Data Analysis


Question 3.1

How do the new frequencies of p and q compare to the initial frequencies in Case I?



Question 3.2

Predict what would happen to the frequencies of p and q if you simulated another 100 generations.



Question 3.3

In a large population would it be possible to completely eliminate a deleterious recessive allele? Explain.



Question 3.4

What is heterozygote advantage?



Question 3.5

What is the importance of heterozygous genotypes in a population?



4. Hardy Weinberg Practice Problems


Use the Hardy Weinberg equations to answer the following questions

 

p + q = 1

p2 + 2pq + q2 = 1

 

p = frequency of dominant allele

q = frequency of recessive allele

p2 = frequency of homozygous dominant genotype

q2 = frequency of homozygous recessive genotype

2pq = frequency of heterozygous genotype


Question 4.1

In Drosophila the allele for normal length wings is dominant over the allele for vestigial wings. In a population of 1, 000 individuals, 360 show the recessive phenotype. How many individuals would you expect to be homozygous dominant and heterozygous for this trait?



Question 4.2

The allele for unattached earlobes is dominant over the allele for attached earlobes. In a population of 500 individuals, 25% show the recessive phenotype. How many individuals would you expect to be homozygous dominant and heterozygous for this trait?



Question 4.3

The allele for the hair pattern called “widow’s peak” is dominant over the allele for no “widow’s peak.” In a population of 1,000 individuals, 510 show the dominant phenotype. How many individuals would you expect of each of the possible three genotypes for this trait?



Question 4.4

In the United States about 16% of the population is Rh negative. The allele for Rh negative is recessive to the allele for Rh positive. If the student population of a high school in the U.S. is 2,000, how many students would you expect for each of the three possible genotypes?



Question 4.5

In certain African countries 4% of the newborn babies have sickle cell anemia, which is a recessive trait. Out of a random population of 1, 000 newborn babies, how many would you expect for each of the three possible genotypes?



Question 4.6

In a certain population, the dominant PHENOTYPE of a certain trait occurs 91% of the time. What is the frequency of the dominant allele?