The Effect of Changing Hardy Weinberg Conditions on the Coat Color Allele Frequency of Teddy Grahams
(Ursus yummicus)
Content-Based Target:
II. State and explain the five assumptions of the Hardy-Weinberg principle.
Process-Based Targets:
A. Perform calculations using the Hardy-Weinberg principle formulae for determining allele frequency, genotype frequency, and or phenotype frequency for a trait in a population.
B. Perform a chi-square to calculation to determine a p-value in order to assess statistical significance.
Biological evolution is defined as a change in allele frequency within a population. But how do you know if such a change has occurred? What would cause the gene frequency to change?
Background Information
Charles Darwin’s unique contribution to biology was not that he “discovered evolution”. Instead he proposed a mechanism for evolutionary change, known as natural selection. Natural selection describes the differential survival and reproduction of individuals in a population. In his book, On the origin of Species, published in 1859, Darwin described natural selection and provided abundant evidence in support of evolution, the change in populations over time. However, as the turn of the century, geneticists and naturalists still disagreed about the role of selection and the importance of small variations in natural populations. How could these variations provide a selective advantage that would result in evolutionary change? It was not until evolution and genetics became reconciled with the advent of population genetics that natural selection became widely accepted.
A population is defined as a group of organisms of the same species that occur in the same area and interbreed or share a common gene pool. A gene pool is all of the alleles at all gene loci of all the individuals in the population. The population is considered to be the basic unit of evolution. Populations evolve, but individuals do not evolve.
In 1908, English mathematician G.H. Hardy and German Physician W. Weinberg independently developed models of population genetics that showed that the process of heredity by itself did not affect the genetic structure of a population. The Hardy-Weinberg theorem states that the frequency of alleles in a population will remain the same regardless of the starting frequencies. Furthermore, the equilibrium genotypic frequencies will be established after one generation of random mating.
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 2 loci, if 40% of the alleles are A, p would be .40. The rest of the alleles (60%) would be a, and q would equal .6 (p + q = 1). These are referred to as allele frequencies.
The probability of two events happening at the same time is the product of them happening separately. Thus, the chance of an individual in the above population having two A alleles would be (0.6)(0.6) or p2. The chance of an individual in the above population having 2 a alleles is (0.4)(0.4) or q2. The chance of an individual having one of each allele would be 2pq, since the A allele can come from either parent and the a allele could come from either parent. To put that all together, the frequency of the possible diploid combinations of these alleles (AA, Aa, aa) is expressed as:
p2 + 2pq + q2 = 1.
The H-W theorem is valid only if evolution is not occurring and when certain conditions are met:
1. The population is very large. (The effect of chance on changes in allele frequencies is greatly reduced.)
2. Mating is random. (Individuals show no mating preference for a particular phenotype.)
3. There are no net changes in the gene pool due to mutations. (Mutations from A to a are equal to mutations of a to A.)
4. There is no migration of individuals into or out of the population.
5. There is no selection. (All genotypes are equal in reproductive success.)
Basically, the Hardy-Weinberg theorem provides a baseline model in which gene frequencies do not change and evolution does not occur. By testing the fundamental hypothesis of the Hardy Weinberg theorem, evolutionists have investigated the roles of mutation, migration, population size, non-random mating, and natural selection in how they affect evolutionary change in natural populations.
In today’s lab we will be examining evolution quantitatively by using Teddy Grahams (Ursus yummicus). There are a few things you need to know about these box dwelling creatures:
· In Teddy Grahams, there are 3 coat phenotypes: Brown, Honey and Speckled. In order to be a brown bear, you need two alleles for Brown (pp)—one from the mother and one from the father. In order to be Honey colored, you need two Honey colored alleles (qq). However, to be Speckled, you need one of each type of allele (pq). (This is called a co-dominant trait. We will learn more about this later in the semester.)
· Normally, it does not matter what color a bear is. All bears have the same survival and reproductive rate.
· The bears mate once per generation to produce 2 offspring. Adult bears die after mating and are not part of the next generation.
· The bears mate with any other bear. They do not look at the color or any other trait to choose a mate.
DAY 1
Procedure for demonstrating the effects of meeting the Hardy-Weinberg conditions on allele frequencies over 5 generations.
1. Obtain a population of 28 Teddy Grahams: 7 Chocolate, 7 Honey, and 14 Speckled.
2. Using the Hardy-Weinberg equations, calculate the allele frequency of each allele.
(p = chocolate and q = honey) Record data in Data Table 1 for generation 1.
3. Mix all of your bears together and randomly place them into couples. It is best to do this with your eyes closed to ensure true random mating.
4. Allow your bears to mate and produce offspring. In order for them to do so, follow these rules which follow the rules of heredity:
a. If both bears in a couple are either both chocolate or both Honey, then the 2 offspring they produce will both be the same color as the parents.
b. If one bear is speckled and the other is either chocolate or honey, then one offspring will be Speckled and the other will be the color of the other parent.
c. If one bear is honey and one is chocolate, all offspring will be speckled.
d. If both bears are speckled, use the cards at your table to determine the offspring. Each parent has a p allele and a q allele. For each offspring produced, pick a card from each parent. If both alleles chosen are q, the offspring is honey. If both alleles are p, then the offspring is chocolate. If one allele is pa n the other is q, the offspring is speckled.
5. For each couple, produce 2 offspring. Use your bag of extra bears to get the types you need. Put extra bears back in the bag. You should end up with 28 bears for the 2nd generation. Record the numbers of each type in the data table, and repeat steps 1-5 until the data table is completed.
6. Once 5 generations have passed, calculate your allele frequencies in Table 1. Note—To find the frequency of the p allele:
a. Multiply the number of chocolate bears by 2 and add the number of speckled bears.
b. Divide “a” answer by 56 total alleles in the population since each bear has 2 alleles
6. State a null hypothesis for a Chi Square Test comparing the initial and final allele frequencies.______
______
______
______
8. Perform a Chi Square test to determine whether the final allele frequencies are statistically the same or different from the initial gene frequencies. Use Table 2 to help you.
Data Table 1
Number of Chocolate, Speckled and Honey Bears each Generation, Along with Allele Frequencies over 5 Generations When All Hardy Weinberg Conditions are Met
Generation / # of chocolate Bears (pp) / # of speckled Bears (pq) / # ofhoney
Bears (qq) / # of chocolate (p) alleles / # of honey (q) alleles / Frequency of
chocolate (p) allele / Frequency of
honey (q) allele
1
2
3
4
5
Data Table 2
Chi Square test for the 5th Generation when all Hardy Weinberg Conditions Have Been Met
Alleles in the Population / # of Observed alleles after 5 generations / # of Expected alleles after 5 generations / (O - E)2 / E / Sum (O-E)2/E / P Valuep allele
q allele
Use the following chart to determine the p-value. Look at Table #2 to help determine degrees of freedom!
Questions:
1. What can you conclude about the allele frequency after 5 generations of random mating when the Hardy-Weinberg conditions are met? Explain.
2. Do you support or reject the null hypothesis? Explain.
DAY 2: Procedure for Testing the Effect of Changing a Hardy Weinberg condition on Allele Frequency Change.
1. You will use the basic procedure above to determine what effect changing one of the Hardy Weinberg conditions has on the allele frequencies after 5 generations of mating.
2. Your teacher will assign you one of the following conditions to test:
a. Population size: decrease or increase the total number of bears.
b. Non-Random Mating: Set rules for mating or look during paring process.
c. Mutation: Change the expected phenotype of offspring
d. Migration: add or remove bears after each generation.
e. Selective pressure: Select against 1 phenotype (color)
3. You are to indicate changes/additions to the DAY 1 procedure based on your H-W violation.
4. Generate both a null hypothesis & experimental hypothesis to predict the effect of the H-W violation on the allele frequency.
5. Make a list of constants and explain how they will be kept the same for comparison of data between day 1 & 2 experiments
6. Make 2 data tables to record results & calculations for experiment.
7. Use Chi Square to analyze whether or not changing your assigned condition did indeed cause a change in allele frequency after 5 generations.
8. Briefly present experimental design, data, data analysis, and conclusion(s) to the class.
9. Each group will create a Google Doc. Please be sure to SHARE the google doc with all group members and your teacher! You can use the google doc to help you with your presentation.
a. Hypothesis
· Null Hypothesis
· Experimental Hypothesis
b. Procedure
· Briefly state & describe changes made to “DAY 1” procedure step(s) and or state & explain procedure steps you added & where steps were inserted
· State & explain how you kept all other variables constant for comparison of results between DAY 1 and DAY 2 experiments
c. Data Tables
· Use models of tables provided in this lab handout & create your own; TITLE BOTH TABLES
d. Statements explaining data
· Describe initial & final allele frequencies
· State Chi-Square value
· State degrees of freedom
· State p-value
e. Conclusion using data and based on the result of the Chi Square test
· Did you support or refute null hypothesis & experimental hypothesis?
· Explain why hypotheses were supported or refuted?
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