Download Introduction to modeling the Hardy

Evolution of Populations
Predicting and Measuring Microevolution
Adaptated from Helen Curtis’ Lab Manual
Laboratory Objectives:
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Explain Hardy-Weinberg equilibrium in terms of allelic and genotypic frequencies and
relate these to the mathematical expression ((p+q)2 = p2 + 2pq + q2
Discuss natural selection and other causes of microevolution as deviations from the
conditions required to maintain the H-W equilibrium.
Understand the effects on allelic frequencies of selection against the homozygous
recessive or other genotypes
Calculate the frequencies of alleles and genotypes in the gene pool of a population using
the H-W formula
Discuss the limitations of this type of model to predict and measure microevolution.
Introduction
Charles Darwin’s unique contribution to biology was not that he “discovered evolution” but, rather, that
he proposed a mechanism for evolutionary change – natural selection, the differential survival and
reproduction of individuals in a population. In On the Origin of Species, published in 1859, Darwin
described natural selection and provided abundant and convincing evidence in support of evolution, the
change in populations over time. Evolution was accepted as a theory with great explanatory power
supported by a large and diverse body of evidence. However, at 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 would these variations provide a selective advantage that would results in
evolutionary change? It was not until evolution and genetics became reconciled with the advents of
populations genetics that natural selection became widely accepted. In addition, there is a great
interest in the role that sexual selection plays in providing advantages/disadvantages to members of a
population.
Ayala (1982) defines evolution as “changes in the genetic constitution of populations”. 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 includes all the alleles at all gene loci (locations) of all individuals in
the population. The population is considered to be the basic unit of evolution. Populations evolve, not
individuals. (1) Can you explain this statement in terms of the process of natural selection?
In 1908, English mathematician GH 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
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The Hardy-Weinberg theorem states that the
frequency of alleles in the population will remain the same regardless
of the starting frequencies. Furthermore, the equilibrium genotypic
frequencies will be established after one generation of random mating.
This theorem is valid only if certain conditions are met:
genetic structure of a population.
1. The population is very large
2. Matings are random.
3. There are no net changes in the gene pool due to mutation.
4. There is no migration of individuals into and out of the population (gene flow)
5. There is not selection pressure; 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, nonrandom
mating and natural selection in effecting evolutionary change in natural populations.
Using the Hardy-Weinberg Theorem
The Hardy-Weinberg theorem provides a mathematical formula for calculating the frequencies of alleles
and genotypes in populations. If we begin with a population at a single gene locus – dominant allele, A,
and a recessive allele, a – then the frequency of the dominant allele is p, and the frequency of the
recessive allele is q. Therefore, p+q = 1. If the frequency of one allele, [p, is known for a population, the
frequency of the other allele, q, can be determined by using the formula q = 1-p.
During sexual reproduction, the frequency of each type of gamete produced is equal to the frequency of
the alleles in the population. If the gametes combine at random, then the probability of AA in the next
generation is p2 , and the probability of aa is q2. The heterozygote can be obtained in two ways, with
either parent providing a dominant allele, so the probability would be 2pq. These genotypic frequencies
can be obtained by multiplying p+q by p+q. The general equation then becomes
(p+q)2 = p2 + 2pq + q2 = 1
To summarize:
p2
= frequency of AA
2pq
= frequency of Aa
2
q2
= frequency of aa
Follow the following steps in this example:
1. If alternate alleles of a gene, A and a, occur at equal frequencies, p and q, then during sexual
reproduction, 0.5 of all gametes (sex cells) will carry A and 0.5 will carry a.
2. 2. Then p = q = 0.5
3. Once allelic frequencies are known for a population, t he genotypic makeup of the next
generation can be predicted from the general equation. In this case,
[0.5(p) + 0.5(q)]2 = 0.25(p2) + 0.50(2pq) + 0.25(q2) = 1
This represents the results of random mating as shown in the following diagram.
Eggs
A egg; p = 0.5
A sperm;
p = 0.5
a sperm;
q = 0.5
a egg; q = 0.5
AA
Aa
P2 = 0.25
pq = 0.25
Aa
aa
pq = 0.25
q2 = 0.25
4. The genotypic frequencies in the population are specifically
p2
= frequency of AA = 0.25
2pq
= frequency of Aa = 0.50
q2
= frequency of aa = 0.25
5. The allelic frequencies remain p = q = 0.5
The frequency of alleles is not usually equal. For example, 4% of a population might be albinos (a
recessive trait), and the frequency of the albino allele could be calculated as the square root of 0.04.
1. Albino individuals = q2 = 0.04 (genotypic frequency); therefore, q = square rot of 0.04 = 0.2
(allelic frequency).
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2. Since p+q = 1, the frequency of p is (1-q), or 0.8. So 4% of the population are albinos, and 20%
of the alleles in the gene pool are for albinism and the other 80% are for normal pigmentation.
(2)Why can you not determine the frequency of A directly?
3. The genotypic frequencies of the next generation now can be predicted from the general H-W
theorem. First determine the results on random mating by completing the following figure.
Eggs
A egg; p =
A sperm; p =
a sperm; q =
a egg; q =
AA
Aa
P2 =
pq =
Aa
aa
pq =
q2 =
4. What will be the genotypic frequencies from generation to generation, provided that alleles p
and q remain in genetic equilibrium?
p2
= frequency of AA =
2pq
= frequency of Aa =
q2
= frequency of aa =
The genetic equilibrium will continue indefinitely if the conditions of the H-W theorem are met. (3) How
often in nature do you think these conditions are met?
Laboratory Procedures
Part I – Testing the Hardy-Weinberg Equilibrium Using a Bean Model
Introduction
Using two different color beads(or beans) and working in pairs, you will simulate a population in a
Hardy-Weinberg equilibrium. The bag of beads represents the gene pool for the population. Each bean
should be regarded as a single gamete, the two colors representing different alleles of a single gene.
Each bag should contain 100 beads. You and your partner decide the proportion of red and white
beans. Record the initial allelic frequencies below
A = red color; __________ = allelic frequency
a = white color; ________ = allelic frequency
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Discussion:
1. How many diploid individuals are represented?
2. What would be the color of the beads for a homozygous dominant individual?
3. What would be the color of the beads for a homozygous recessive individual?
4. What would be the color of the beads for a heterozygous individual?
Hypothesis: Write your hypothesis in your lab journal.
Prediction: Beneath your hypothesis, predict the genotypic frequencies of the population in future
generations.
Experimental Design Questions: (You need only to complete these for Part I)
Control?
DV/IV?
Extraneous factors eliminated?
What is being measured?
Repeat data/verify results?
Procedure:
1. Without looking, randomly remove two beads from the g=bag. These two beans represent one
diploid individual in the next generation. Record the number of diploid genotypes randomly
selected in your data chart until all 50 individuals are selected.
2. Record the observed genotypic and allelic frequencies for the Parent generation. The sum of
the allelic frequency and the genotypic frequencies should equal 1.
Parent Population
Allelic Frequencies
A
a
Genotypic Frequencies
AA
Aa
aa
3. Return all the beans to the bag and shake the bad to reinstate the gene pool. By replacing the
beans each time, the size of the gene pool remains constant the probability of selecting any
allele should remain equal to its frequency. This procedure is called “sampling with
replacement”.
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4. To determine the expected frequencies for the population, use the original allelic frequencies
from your Parent population.
A
Expected F1
Expected F1
Allelic Frequencies F1
Genotypic Frequencies
a
AA
Aa
aa
Discussion:
1. How did the expected and observed allelic and genotypic frequencies of the F1 generation
compare to the Parent frequencies? Homozygous dominant? Homozygous recessive?
Heterozygous?
2. Were the observed results consistent with the expected results? Why? Why not?
3. Compare your results with those of other teams. How variable are the results for each team?
4. Do your results match your predictions for a population in H-W equilibrium?
5. What would you expect to happen to the frequencies if you continued this simulation for 25
generations?
6. Is this population evolving? Explain.
7. Considering each of the conditions for the H-W theorem, does this model meet each of the
conditions? Discuss the limitations of this model.
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