Lab Topic 11 Population Genetics I: The Hardy-Weinberg … · 10421 C BC A M P N 263 K/PMS DESIGN SERVICES OF 263 Lab Topic 11 Population Genetics I: The Hardy-Weinberg Theorem Laboratory

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Lab Topic 11

Population Genetics I: The Hardy-Weinberg Theorem

Laboratory Objectives

After completing this lab topic, you should be able to:

1. Explain Hardy-Weinberg equilibrium in terms of allelic and genotypic fre-quencies and relate these to the expression (p � q)2 � p2 � 2pq � q2 � 1.

2. Describe the conditions necessary to maintain Hardy-Weinbergequilibrium.

3. Use the bead model to demonstrate conditions for evolution.

4. Test hypotheses concerning the effects of evolutionary change (migration,mutation, genetic drift by either bottleneck or founder effect, and naturalselection) using a computer model.

Introduction

Charles Darwin’s unique contribution to biology was not that he “discov-ered evolution” but, rather, that he proposed a mechanism for evolutionarychange—natural selection, the differential survival and reproduction ofindividuals in a population. In On the Origin of Species, published in 1859,Darwin described natural selection and provided abundant and convincingevidence in support of evolution, the change in the genetic structure ofpopulations over time. Evolution was accepted as a theory with greatexplanatory power supported by a large and diverse body of evidence.However, at the turn of the century, geneticists and naturalists stilldisagreed about the role of natural selection and the importance of smallvariations in natural populations. How could these variations provide aselective advantage that would result in evolutionary change? It was notuntil evolution and genetics became reconciled with the advent of popula-tion genetics that natural selection became widely accepted.

Ayala (1982) defines evolution as “changes in the genetic constitution ofpopulations.” A population is defined as a group of organisms of the samespecies that occur in the same area and interbreed or share a common genepool, all the alleles at all gene loci of all individuals in the population.The population is considered the basic unit of evolution. The small scalechanges in the genetic structure of populations from generation to generation

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264 Lab Topic 11: Population Genetics I: The Hardy-Weinberg Theorem

is called microevolution. Populations evolve, not individuals. Can youexplain this statement in terms of the process of natural selection?

In 1908, English mathematician G. H. Hardy and German physicianW. Weinberg independently developed models of population genetics thatshowed that the process of heredity by itself did not affect the geneticstructure of a population. The Hardy-Weinberg theorem states that thefrequency of alleles in the population will remain the same from generationto generation. Furthermore, the equilibrium genotypic frequencies will beestablished after one generation of random mating. This theorem is validonly if certain conditions are met:

1. The population is very large.

2. Matings are random.

3. There are no net changes in the gene pool due to mutation; that is, muta-tion from A to a must be equal to mutation from a to A.

4. There is no migration of individuals into and out of the population.

5. There is no selection; all genotypes are equal in reproductive success.

It is estimated, for example, that at the beginning of the 19th century in GreatBritain, more than 95% of the peppered moths were light colored, while lessthan 5% were dark. Only one or two of the dark forms were seen in collec-tions before mid-century. Under Hardy-Weinberg equilibrium, these propor-tions would be maintained in each generation for large, random-breedingpopulations with no change in the mutation rate and migration rate, as longas the environment was relatively stable. The process of heredity would notchange the frequency of the two forms of the moth. Later in this laboratory,you will investigate what happened to these moths as the environmentchanged following the Industrial Revolution.

Basically, the Hardy-Weinberg theorem provides a baseline model in whichgene frequencies do not change and evolution does not occur. By testing thefundamental hypothesis of the Hardy-Weinberg theorem, evolutionistshave investigated the roles of mutation, migration, population size, non-random mating, and natural selection in effecting evolutionary change innatural populations. Although some populations maintain genetic equilib-rium, the exceptions are intriguing to scientists.

Use of the Hardy-Weinberg Theorem

The Hardy-Weinberg theorem provides a mathematical formula forcalculating the frequencies of alleles and genotypes in populations. If webegin with a population with two alleles at a single gene locus—adominant allele, A, and a recessive allele, a—then the frequency of thedominant 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 apopulation, the frequency of the other allele, q, can be determined byusing the formula q � 1 � p.

During sexual reproduction, the frequency of each type of gamete producedis equal to the frequency of the alleles in the population. If the gametes com-bine at random, then the probability of AA in the next generation is p2, andthe probability of aa is q2. The heterozygote can be obtained two ways, witheither parent providing a dominant allele, so the probability would be 2pq.



Lab Topic 11: Population Genetics I: The Hardy-Weinberg Theorem 265

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 AA2pq � frequency of Aa

q2 � frequency of aa

Follow the steps in this example.

1. If alternate alleles of a gene, A and a, occur at equal frequencies, p andq, then during sexual reproduction, 0.5 of all gametes will carry A and0.5 will carry a.

2. Then p � q � 0.5.

3. Once allelic frequencies are known for a population, the genotypicmakeup of the next generation can be predicted from the general equa-tion. In this case,

(0.5A � 0.5a)2 � 0.25AA � 0.5Aa � 0.25aa � 1(p � q)2 � p2 � 2pq � q2 � 1

This represents the results of random mating as shown in Figure 11.1.

4. The genotypic frequencies in the population are specifically

p2 � frequency of AA � 0.252pq � frequency of Aa � 0.50q2 � frequency of aa � 0.25

5. The allelic frequencies remain p � q � 0.5.

In actual populations the frequencies of alleles are not usually equal. Forexample, in a large random mating population of jimsonweed 4% of thepopulation might be white (a recessive trait), and the frequency of the whiteallele could be calculated as the square root of 0.04.

1. White individuals � q2 � 0.04 (genotypic frequency); therefore,

q � �0.04 � 0.2 (allelic frequency).

2. Since p � q � 1, the frequency of p is (1 � q), or 0.8. So 4% of thepopulation are white, and 20% of the alleles in the gene pool are forwhite flowers and the other 80% are for purple flowers. (Note that youcould not determine the frequency of A by taking the square root of thefrequency of all individuals with purple flowers because you cannotdistinguish the heterozygote and the homozygote for this trait.)

3. The genotypic frequencies of the next generation now can be predictedfrom the general Hardy-Weinberg theorem. First determine the resultsof random mating by completing Figure 11.2 (refer to Figure 11.1).

4. What will be the genotypic frequencies from generation to generation,provided that alleles p and q remain in genetic equilibrium?

AA �

Aa �

aa �

A spermp = 0.5

a spermq = 0.5

AAp2 = 0.25

aApq = 0.25

Aapq = 0.25

aaq2 = 0.25

Sperm

EggsA eggp = 0.5

a eggq = 0.5

Figure 11.1.Random mating in a population atHardy-Weinberg equilibrium. Thecombination of alleles in randomlymating gametes maintains the allelicand genotypic frequency generationafter generation. The gene pool of thepopulation remains constant, and thepopulations do not evolve.

A spermp =

a spermq =

AAp2 =

aApq =

Aapq =

aaq2 =

Sperm

EggsA eggp =

a eggq =

Figure 11.2.Random mating for a population atHardy-Weinberg equilibrium.Complete the mating combinations forpurple and white flowers.




The genetic equilibrium will continue indefinitely if the conditions ofthe Hardy-Weinberg theorem are met. How often in nature do you thinkthese conditions are met? Although natural populations may seldom meetall the conditions, Hardy-Weinberg equilibrium serves as a valuable modelfrom which we can predict genetic changes in populations as a result ofnatural selection or other factors. This allows us to understand quantitativelyand in genetic language how evolution operates at the population level.

Note: Using the square root to obtain the allelic frequency (step 1 above) isonly valid if the population meets the conditions for a population in Hardy-Weinberg equilibrium. Later in the exercise you will use a counting methodto calculate allelic frequencies.

E X E R C I S E 1 1 . 1

Testing Hardy-Weinberg EquilibriumUsing a Bead Model

Materials

plastic or paper bag containing 100 beads of two colors

Introduction

Working in pairs, you will test Hardy-Weinberg equilibrium by simulatinga population using colored beads. The bag of beads represents the genepool for the population. Each bead should be regarded as a single gamete,the two colors representing different alleles of a single gene. Each bagshould contain 100 beads of the two colors in the proportions specified bythe instructor. Record in the spaces provided below the color of the beadsand the initial frequencies for your gene pool.

A � __________ color __________ allelic frequency

a � __________ color __________ allelic frequency

1. How many diploid individuals are represented in this population?

2. What would be the color of the beads for a homozygous dominantindividual?

3. What would be the color of the beads for a homozygous recessiveindividual?

4. What would be the color of the beads for a heterozygous individual?

Hypothesis

State the Hardy-Weinberg theorem in the space provided. This will be yourhypothesis.




Predictions

Predict the genotypic frequencies of the population in future generations(if/then).

Procedure

1. Without looking, randomly remove two beads from the bag. These twobeads represent one diploid individual in the next generation. Recordin the margin of your lab manual the diploid genotype (AA, Aa, or aa)of the individual formed from these two gametes.

2. Return the beads to the bag and shake the bag to reinstate the genepool. By replacing the beads each time, the size of the gene poolremains constant, and the probability of selecting any allele shouldremain equal to its frequency. This procedure is called samplingwith replacement.

3. Repeat steps 1 and 2 (select two beads, record the genotype of the newindividual, and return the beads to the bag) until you have recorded thegenotypes for 50 individuals who will form the next generation of thepopulation.

Results

1. Before calculating the results of your experiment, determine the expectedfrequencies of genotypes and alleles for the population. To do this, usethe original allelic frequencies for the population provided by theinstructor. (Recall that the frequency of A � p, and the frequency ofa � q.) Calculate the expected genotypic frequencies using the Hardy-Weinberg equation p2 � 2pq � q2 � 1. The number of individualsexpected for each genotype can be calculated by multiplying 50 (totalpopulation size) by the expected frequencies. Record these results inTable 11.1.

Table 11.1Expected Genotypic and Allelic Frequencies for the Next GenerationProduced by the Bead Model

ParentPopulations

NewPopulations

AllelicFrequency

Genotypic Number (and Frequency)

AllelicFrequency

A a AA Aa aa A a

( ) ( ) ( )

2. Next, using the results of your experiment, calculate the observed frequenciesin the new population created as you removed beads from the bag. Recordthe number of diploid individuals for each genotype in Table 11.2, andcalculate the frequencies for the three genotypes (AA, Aa, aa). Add the




Table 11.2Observed Genotypic and Allelic Frequencies for the Next GenerationProduced by the Bead Model

ParentPopulations

NewPopulations

AllelicFrequency

Genotypic Number(and Frequency)

AllelicFrequency

A a AA Aa aa A a

( ) ( ) ( )

Table 11.3Chi-Square of Results from the Bead Model

AA Aa aa

Observed value (o)

Expected value (e)

Deviation (o � e) � d

d2

d2/e

Chi-square (χ2) � Σd2/e

numbers of each allele, and calculate the allelic frequencies for A and a.These values are the observed frequencies in the new population. Geno-typic frequencies and allelic frequencies should each equal 1.

3. To compare your observed results with those expected, you can use thestatistical test, chi-square. Table 11.3 will assist in the calculation of thechi-square test. Note: To calculate chi-square you must use the actual numberof individuals for each genotype, not the frequencies. See Appendix B for anexplanation of this statistical test.

Degrees of freedom � 2Level of significance, p � 0.05

4. Is your calculated χ2 value greater or smaller than the given χ2 value(Appendix B, Table B.2) for the degrees of freedom and p value for thisproblem?




Discussion

1. What proportion of the population was homozygous dominant?

Homozygous recessive?

Heterozygous?2. Were your observed results consistent with the expected results based

on your statistical analysis? If not, can you suggest an explanation?

3. Compare your results with those of other students. How variable arethe results for each team?

4. Do your results match your predictions for a population at Hardy-Weinberg equilibrium?

What would you expect to happen to the frequencies if you contin-ued this simulation for 25 generations?

Is this population evolving?

Explain your response.

5. Consider each of the conditions for the Hardy-Weinberg model. Doesthis model meet each of those conditions?


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E X E R C I S E 1 1 . 2

Simulation of Evolutionary ChangeUsing the Bead Model

Under the conditions specified by the Hardy-Weinberg model (randommating in a large population, no mutation, no migration, and no selec-tion), the genetic frequencies should not change, and evolution should notoccur. In this exercise, the class will modify each of the conditions and de-termine the effect on genetic frequencies in subsequent generations. Youwill simulate the evolutionary changes that occur when these conditionsare not met.

Working in teams of two or three students, you will simulate two of theexperimental scenarios presented and, using the bead model, determinethe changes in genetic frequencies over several generations. The scenariosinclude the migration of individuals between two populations, alsocalled gene flow; the effects of small population size, called geneticdrift; and examples of natural selection. The effects of mutation takelonger to simulate with the bead model, so you will use computersimulation to consider these in Exercise 11.3. All teams will begin bysimulating the effect of genetic drift, specifically, the bottleneck effect(Experiment A.1). For the second simulation, you can choose to investigatemigration, one of two examples of natural selection, or the founder effect—another example of genetic drift.

The procedure for investigating each of the conditions will follow the generalprocedures described as follows. Before beginning one of the simulationexperiments, be sure you understand the procedures to be used.

Procedure

1. Sampling with Replacement

Unless otherwise instructed, the gene pool size will be 100 beads. Eachnew generation will be formed by randomly choosing 50 diploid individ-uals represented by pairs of beads. After removing each pair of beads(representing the genotype of one individual) from the bag, replace thepair before removing the next set, sampling with replacement. Continueyour simulations for several generations. For example, if the startingpopulation has 50 beads each of A and a (allelic frequency of 0.5), then inthe next generation you might produce the following results:

Number of individuals: 14AA, 24Aa, 12aa

Number of alleles (beads): 28A � 24A, 24a � 24a

Total number of alleles: 100

Frequency of A: 28 �

Frequency of a: 24 �

In this example, the frequency should continue to approximate 0.5 for Aand a.

24 =

48

100= 0.48

24 =

52

100= 0.52




2. Reestablishing a Population with New Allelic Frequencies

In some cases, the number of individuals will decrease as a result of thesimulation. In those cases, return the population to 100 but reestablish thepopulation with new allelic frequencies. For example, if you eliminate byselection all homozygous recessive (aa) individuals in your simulation, thenthe resulting frequencies would be:

Number of individuals: 14AA, 24Aa, 0aa

Number of alleles (beads): 28A � 24A, 24a

Total number of alleles: 76

�

To reestablish a population of 100, then, the number of beads should reflectthese new frequencies. Adjust the number of beads so that A is now 68/100 anda is 32/100. Then continue the next round of the simulation.

If this information is not clear to you, ask for assistance beforebeginning your simulations.

Experiment A. Simulation of Genetic Drift

Materials

plastic or paper bag containing 100 beads, 50 each of two colorsadditional beads as needed

Introduction

Genetic drift is the change in allelic frequencies in small populations as a resultof chance alone. In a small population, combinations of gametes may not berandom, owing to sampling error. (If you toss a coin 500 times, you expectabout a 50:50 ratio of heads to tails; but if you toss the coin only 10 times, theratio may deviate greatly in a small sample owing to chance alone.) Geneticfixation, the loss of all but one possible allele at a gene locus in a population,is a common result of genetic drift in small natural populations. Genetic driftis a significant evolutionary force in situations known as the bottleneck effectand the founder effect. All teams will investigate the bottleneck effect. You maychoose the founder effect (p. 275) for your second simulation.

1. Bottleneck effect

A bottleneck occurs when a population undergoes a drastic reduction in sizeas a result of chance events (not differential selection), such as a volcanic erup-tion or hurricane. For example, northern elephant seals experienced a bottle-neck when they were hunted almost to extinction with only 20 survivinganimals in the 1890s. In Figure 11.3, the beads pass through a bottleneck,which results in an unpredictable combination of beads that pass to the otherside. These beads would constitute the beginning of the next generation.

Frequency of a: 24 =

24

76= 0.32

24 =

52

76= 0.68Frequency of A: 28




Hypothesis

As your hypothesis, either propose a hypothesis that addresses the bottle-neck effect specifically or state the Hardy-Weinberg theorem.

Prediction

Either predict equilibrium values as a result of Hardy-Weinberg or pre-dict the type of change that you expect to occur in a small population(if/then).

Procedure

1. To investigate the bottleneck effect, establish a starting populationcontaining 50 individuals (how many beads?) with a frequency of0.5 for each allele (Generation 0).

2. Without replacement, randomly select 5 individuals (10% of the pop-ulation), two alleles at a time. This represents a drastic reduction inpopulation size. On a separate sheet of paper, record the genotypesand the number of A and a alleles for the new population.

3. Count the numbers of each genotype and the numbers of each allele.Using these numbers, determine the genotypic frequencies for AA,Aa, and aa and the new allelic frequencies for A (p) and a (q) for thesurviving 5 individuals. These are your observed frequencies. Enterthese frequencies in Table 11.4, Generation 1.

Originalpopulation

Bottleneckingevent

Survivingpopulation

Figure 11.3.The bottleneck effect. The gene poolcan drift by chance when thepopulation is drastically reduced byfactors that act unselectively. Bad luck,not bad genes! The resultingpopulation will have unpredictablecombinations of genes. What hashappened to the amount of variation?




Table 11.4Changes in Allelic and Genotypic Frequencies for Simulations of the Bottleneck Effect, an Example ofGenetic Drift. First, record frequencies based on the observed numbers in your experiment. Then, usingthe observed allelic frequencies, calculate the expected genotypic frequencies.

Generation

Genotypic FrequencyObserved

Allelic FrequencyObserved

Genotypic FrequencyExpected

AA Aa aa A (p) a (q) p2 2pq q2

0 — — — 0.5 0.5 0.25 0.50 0.25

1

2

3

4

5

6

7

8

9

10

4. Using the new observed allelic frequencies, calculate the expected geno-typic frequencies (p2, 2pq, q2). Record these frequencies in Table 11.4,Generation 1.

5. Reestablish the population to 50 individuals using the new allelic frequen-cies (refer to the example in the Procedure on p. 271). Repeat steps 2, 3,and 4. Record your results in the appropriate generation in Table 11.4.

6. Reestablish the gene pool with new frequencies after each generationuntil one of the alleles becomes fixed in the population for severalgenerations.

7. Summarize your results in the Discussion section.

Results

1. How many generations did you simulate?2. Using the graph paper at the end of the lab topic, sketch a graph of the

change in p and q over time. You should have two lines, one for each allele.3. Did one allele go to fixation in that time period? Which allele?

Remember, genetic fixation occurs when the gene pool is composedof only one allele. The others have been eliminated. Did the otherallele ever appear to be going to fixation?




4. Did any of the expected genotypic frequencies go to fixation? If nonedid, why not?

5. Compare results with other teams. Did the same allele go to fixationfor all teams? If not, how many became fixed for A and how manyfor a?

Discussion

1. Compare the pattern of change for p and q. Is there a consistent trendor do the changes suggest chance events? Look at the graphs of otherteams before deciding.

2. Explain your observations of genetic fixation for the replicate simula-tions completed by the class. What would you expect if you simulatedthe bottleneck effect 100 times?

3. How might your results have differed if you had started with differentallelic frequencies, for example, p � 0.2 and q � 0.8?

4. Since only chance events—that is, the effect of small population size—are responsible for the change in gene frequencies, would you say thatevolution has occurred? Explain.

5. Since the 1890s when northern elephant seals were hunted almost toextinction, the populations have increased to 30,000 animals. In a1974 study of genetic variation, scientists found that all elephant sealsare fixed for the same allele at 24 loci. Explain.




On completion of this simulation, choose one or two of theremaining scenarios to investigate. All scenarios should becompleted by at least one team in the laboratory.

2. Founder effect

When a small group of individuals becomes separated from the larger parentpopulation, the allelic frequencies in this small gene pool may be differentfrom those of the original population as a result of chance alone. This occurswhen a group of migrants becomes established in a new area not currentlyinhabited by the species—for instance, the colonization of an island—and istherefore referred to as the founder effect. For example, in 1975, 20 desertbighorn sheep colonized Tiburon Island; by 1999, the population hadincreased to 650 sheep. A comparison with the other populations of thespecies in Arizona showed that the island populations had fewer alleles pergene and overall lower genetic variation due to the small size of the coloniz-ing population and inbreeding.

Hypothesis

As your hypothesis, either propose a hypothesis that addresses foundereffect specifically or state the Hardy-Weinberg theorem.

Prediction

Either predict equilibrium values as a result of Hardy-Weinberg or predictthe type of change that you expect to occur in a small population (if/then).

Procedure

1. To investigate the founder effect, establish a starting population with50 individuals with starting allelic frequencies of your choice. Recordthe frequencies you have selected for Generation 0 in Table 11.5 in theResults section at the end of this exercise.

2. Without replacement, randomly select 5 individuals, two alleles at a time,to establish a new founder population. On a separate sheet of paper,record the genotypes and the number of A and a alleles for the newpopulation.

3. Calculate the new frequencies for A (p) and a (q) and the genotypicfrequencies for AA (p2), Aa (2pq), and aa (q2) for the founder population,and record this information as Generation 1 in Table 11.5.

4. Reestablish the population to 50 diploid individuals using the new allelicfrequencies. (Refer to the example in the Procedure on p. 271.)




5. Follow the founder population through several generations in the newpopulation. From this point forward, each new generation will be pro-duced by sampling 50 individuals with replacement. After each generation,reestablish the new population based on the new allelic frequencies.Continue until you have sufficient evidence to discuss your results withthe class.

6. Summarize your results in the Discussion section at the end of thisexercise. You will want to compare the founder population with theoriginal population and compare equilibrium frequencies if appropri-ate. Each group will present its results to the class at the end of thelaboratory.

Experiment B. Simulation of Migration: Gene Flow

Materials

2 plastic or paper bags, each containing 100 beads of two colorsadditional beads as needed

Introduction

The migration of individuals between populations results in gene flow. In anatural population, gene flow can be the result of the immigration andemigration of individuals or gametes (for example, pollen movement). Therate and direction of migration and the starting allelic frequencies for thetwo populations can affect the rate of genetic change. In the followingexperiment, the migration rate is equal in the two populations, and the start-ing allelic frequencies differ for the two. Work in teams of four students.

Hypothesis

As your hypothesis, either propose a hypothesis that addresses migrationspecifically or state the Hardy-Weinberg theorem.

Prediction

Either predict equilibrium values as a result of Hardy-Weinberg or predict thetype of change that you expect to observe as a result of migration (if/then).

Procedure

1. To investigate the effects of gene flow on population genetics, establishtwo populations of 100 beads each. Choose different starting allelic fre-quencies for A and a for each population. For example, in Figure 11.4,




Gene flow

Population 1p = 0.9q = 0.1

Population 2p = 0.5q = 0.5

Figure 11.4.Migration. Migration rates areconstant between two populations thatdiffer for starting allelic frequencies.

population 1 might start with 90A and 10a while population 2 mighthave 50 of each allele initially. For comparison, you might choose onepopulation with the same starting frequencies as your population inExercise 11.1. Record the allelic frequencies for each starting popula-tion, Generation 0, in Table 11.5 in the Results section at the end of thisexercise.

2. Select 10 individuals (how many alleles?) from each population, andallow them to migrate to the other population by exchanging beads.Do not sample with replacement in this step.

3. Select 50 individuals from each of these new populations, sampling withreplacement. On a separate sheet of paper, record the genotypes and thenumber of A and a alleles for population 1 and population 2.

4. Calculate the new allelic and genotypic frequencies in the two pop-ulations following migration. Record your results in Table 11.5 inthe Results section. Reestablish each bag based on the new allelicfrequencies.

5. Repeat this procedure (steps 2 to 4) for several generations. In doingthis, you are allowing migration to take place with each generation.Continue until you have a sufficient number to allow you to discussyour results in class successfully.

6. Summarize your results in the Discussion section at the end of thisexercise. Each group will present its results to the class at the end of thelaboratory.

Experiment C. Simulation of Natural Selection

Materials

plastic or paper bag containing 100 beads of two colors additional beadsas needed

Introduction

Natural selection, the differential survival and reproduction of individu-als, was first proposed by Darwin as the mechanism for evolution.Although other factors have since been found to be involved in evolution,selection is still considered an important mechanism. Natural selection is




Figure 11.5.Two color forms of the peppered moth. The dark and light forms of the moth are present in both photographs. Lichens are absent in (a) but present in (b). In which situation would the dark moth have a selective advantage?

based on the observation that individuals with certain heritable traits aremore likely to survive and reproduce than those lacking these advanta-geous traits. Therefore, the proportion of offspring with advantageous traitswill increase in the next generation. The genotypic frequencies will changein the population. Whether traits are advantageous in a population de-pends on the environment and the selective agents (which can includephysical and biological factors). Choose one of the following evolutionaryscenarios to model natural selection in population genetics.

1. Industrial melanism

The peppered moth, Biston betularia, is a speckled moth that sometimesrests on tree trunks during the day, where it avoids predation by blendingwith the bark of trees (an example of cryptic coloration). At the beginningof the 19th century, moth collectors in Great Britain collected almost en-tirely light forms of this moth (light with dark speckles) and only occasion-ally recorded rare dark forms (Figure 11.5). With the advent of theIndustrial Revolution and increased pollution the tree bark darkened,lichens died, and the frequency of the dark moth increased dramatically inindustrialized areas. However, in rural areas, the light moth continued tooccur in high frequencies. (This is an example of the relative nature of se-lective advantage, depending on the environment.)

Color is controlled by a single gene with two allelic forms, dark andlight. Pigment production is dominant (A), and the lack of pigment isrecessive (a). The light moth would be aa, but the dark form could beeither AA or Aa.

Hypothesis

As your hypothesis, either propose a hypothesis that addresses naturalselection occurring in polluted environments specifically or state theHardy-Weinberg theorem.

a. b.




Prediction

Either predict equilibrium values as a result of the Hardy-Weinberg theoremor predict the type of change that you expect to observe as a result of natu-ral selection in the polluted environment (if/then).

Procedure

1. To investigate the effect of natural selection on the frequency of lightand dark moths, establish a population of 50 individuals with allelicfrequencies of light (a) � 0.9 and dark (A) � 0.1. Record the frequen-cies of the starting population, Generation 0, in Table 11.5 in theResults section at the end of this exercise.

2. Determine the genotypes and phenotypes of the population by selecting50 individuals, two alleles at a time, by sampling with replacement (seeProcedure, p. 270). On a separate sheet of paper, record the genotypesand phenotypes of each individual.

Now, assume that pollution has become a significant factor and that inthis new population 50% of the light moths but only 10% of the darkmoths are eaten. How many light moths must you eliminate from yourstarting population of 50 individuals? How many dark moths? Canselection distinguish dark moths with AA and Aa genotypes? How willyou decide which dark moths to remove? Remove the appropriatenumber of individuals of each phenotype.

3. Calculate new allelic frequencies for the remaining population.Reestablish the population with these new allelic frequencies for the100 alleles. (Refer to the Procedure on p. 271.) Record the newfrequencies in Table 11.5 in the Results section.

4. Continue the selection procedure, recording the frequencies, for severalgenerations until you have sufficient evidence to discuss your resultswith the class.

5. Summarize your results in the Discussion section at the end of thisexercise. Each group will present its results to the class at the end ofthe laboratory.

2. Sickle-cell disease

Sickle-cell disease is caused by a mutant allele (Hb�), which, in thehomozygous condition, in the past was often fatal to people at quite youngages. The mutation causes the formation of abnormal, sickle-shaped redblood cells that clog vessels, cause organ damage, and are inefficient trans-porters of oxygen (Figure 11.6). Individuals who are heterozygous(Hb�Hb�) have the sickle-cell trait (a mild form of the disease), which is notfatal. Scientists were surprised to find a high frequency of the Hb� allele inpopulations in Africa until they determined that heterozygous individuals




Figure 11.6.Effects of the sickle-cell allele.(a) Normal red blood cells are disk-shaped. (b) The jagged shape of sickled cells causes them to pile up and clog small blood vessels. (c) The results include damage to a large number of organs. In thehomozygous condition, sickle-celldisease can be fatal.

have a selective advantage in resisting malaria. Although the homozygouscondition may be lethal, the heterozygotes are under both a positive and anegative selection force. In malarial countries in tropical Africa, the het-erozygotes are at an advantage compared to either homozygote.

Impairedmental

functionHeart failure Rheumatism Abdominal

pain

Weaknessand fatigue

Poor physicaldevelopment

Pneumonia Paralysis Kidneyfailure

Increase in amountof bone marrow

Dilationof heart

Anemia

Lungdamage

Braindamage

Kidneydamage

Heartdamage

Muscle andjoint damage

Gastrointestinaltract damage

Local failures in blood supply

Collection of sicklecells in the spleen

Clumping of cells andinterference withblood circulation

Rapid destructionof sickle cells

Overactivity ofbone marrow

Sickling of red blood cells

Abnormal hemoglobin

Homozygousrecessive

individuals

Skulldeformation

Enlargement,then fibrosis

of spleen

a. b.

c.




Hypothesis

As your hypothesis, either propose a hypothesis that addresses naturalselection in tropical Africa specifically or state the Hardy-Weinbergtheorem.

Prediction

Either predict equilibrium values as a result of the Hardy-Weinberg theoremor predict the type of change that you expect to observe as a result of natu-ral selection in tropical Africa (if/then).

Procedure

1. To investigate the role of selection under conditions of heterozygoteadvantage, establish a population of 50 individuals with allelic fre-quencies of 0.5 for both alleles. Record the frequencies of the startingpopulation, Generation 0, in Table 11.5 in the Results section at theend of this exercise.

For our model, assume that the selection force on each genotype is

Hb�Hb�: 30% die of malaria

Hb�Hb�: 10% die of malaria

Hb�Hb�: 100% die of sickle-cell disease

2. Determine the genotypes and phenotypes of the population by selecting50 individuals, two alleles at a time, by sampling with replacement (seeProcedure, p. 270). On a separate sheet of paper, record the 50 individ-uals. Select against each genotype by eliminating individuals accordingto the percent mortality shown above. How many Hb�Hb� must beremoved? How many Hb�Hb�? How many Hb�Hb�? Remove theappropriate number of beads for each color.

3. Calculate new allelic and genotypic frequencies based on the survivors,and reestablish the population using these new frequencies. (Refer tothe procedure on p. 271 if necessary.) Record your new frequencies inTable 11.5 in the Results section.

4. Continue the selection procedure, recording frequencies, for severalgenerations, until you have sufficient evidence for your discussionin class.

5. Summarize your results in the Discussion section. Each group will pres-ent its results to the class at the end of the laboratory.




Results and Discussion for Selected Simulation

Results

Each team will record the results of its chosen experiment in Table 11.5.Modify the table to match the information you need to record for yoursimulation. Use the margins to expand the table or make additional notes.

Discussion

In preparation for presenting your results to the class, answer the followingquestions about your chosen simulation. Choose one team member to makethe presentation, which should be organized in the format of a scientific paper.

1. Which of the conditions that are necessary for Hardy-Weinberg equi-librium were met?

Table 11.5Changes in Allelic and Genotypic Frequencies for Simulations Selected in Exercise 11.2. Calculateexpected frequencies based on the actual observed numbers in your experiment.

Experiment ________________________ Simulation of ________________________________________

Generation

Allelic Frequency Genotypic Frequency

p q p2 2pq q2

0

1

2

3

4

5

6

7

8

9

10




2. Which condition was changed?

3. Briefly describe the scenario that your team simulated.

4. What were your predicted results?

5. How many generations did you simulate?

6. Sketch a graph of the change in p and q over time. You should have twolines, one for each frequency.

7. Describe the changes in allelic frequencies p and q over time. Did yourresults match your predictions? Explain.

8. Describe the changes in the genotypic frequencies.

9. Compare your final allelic and genotypic frequencies with those of thestarting population.




10. If you can, formulate a general summary statement or conclusion.

11. Would you expect your results to be the same if you had chosen differ-ent starting allelic frequencies? Explain.

12. Critique your experimental design and outline your next simulation.

Be prepared to take notes, sketch graphs, and ask questions during the stu-dent presentations. You are responsible for understanding and answeringquestions for all conditions simulated in the laboratory.

E X E R C I S E 1 1 . 3

Open-Inquiry Computer Simulation of Evolution

Simulations involving only a few generations are fairly easy with the beadmodel, but this model is too cumbersome to obtain information about long-term changes or to combine two or more factors. Computer simulationswill allow you to model 50 or 100 generations quickly or to do a series ofsimulations changing one factor and comparing the results. As with any sci-entific investigation, design your experiment to test a hypothesis and makepredictions before you begin.

Several computer simulation programs are available; the instructor willdemonstrate the software. From the following suggestions or your ownideas, pursue one of the factors in more detail or several in combination.Consult with your instructor before beginning your simulations. Be pre-pared to present your results in the next lab period in either oral or writtenform. Follow the procedures provided with the simulation program.

Mutation

Evolution can occur only when there is variation in a population, and theultimate source for that variation is mutation. The mutation rate at mostgene loci is actually very small (1 � 10�5 per gamete per generation), and




the forward and backward rates of mutation are seldom at equilibrium.Evolutionary change as a result of mutation alone would occur very slowly,thus requiring many generations of simulation. Changes in this conditionare best considered using a computer simulation that easily handles thelengthy process. Do not simulate this condition using the bead model.

Other Suggestions for Computer Simulations

1. The migration between natural populations seldom occurs at thesame rate in both directions. Devise a model to simulate differentmigration rates between two populations. Compare your results withthe bead model.

2. How does the probability of genetic fixation differ for populations thathave different starting allelic frequencies? Simulate genetic drift using avariety of allelic frequencies.

3. How large must a population be to avoid genetic drift?4. Devise a model to simulate selection for recessive and lethal traits.

Then, using the same starting allelic frequencies, select against thedominant lethals. Compare rate of change of allelic frequency as aresult of lethality for dominant and recessive traits.

5. Mutation alone has only small effects on evolution over long periods oftime. Using realistic rates of mutation, compare the evolutionarychange for mutation alone with simulations that combine mutation andnatural selection.

6. Combine factors (usually two at a time). For example, combinemutation and natural selection, using realistic estimates of mutationrates. Combine genetic drift and migration. Compare your results tosimulations of each condition alone.

Reviewing Your Knowledge

1. Define and provide examples of the following terms: evolution, population,gene pool, gene flow, genetic drift, bottleneck effect, founder effect, naturalselection, genetic fixation, genotypic frequency, allelic frequency, and model.

2. State the five conditions necessary for Hardy-Weinberg equilibrium.

3. Describe how gene flow, genetic drift, and natural selection bring aboutevolution.

4. In a population of 100 rock pink plants, 84 individuals have red flowerswhile 16 have white flowers. Assume that white petals are inherited as arecessive trait (a) and red petals as a dominant trait (A). What are thefrequencies p and q? In the next generation, what will be the equilibriumgenotypic frequencies?




5. Migration occurs at a constant rate between two populations of fieldmice. In one population, 65% of the population are white; in the otherpopulation, only 15% are white. What would you expect to happen tothe allelic frequencies of these two populations over time?

6. Explain the difference between evolution and natural selection. Use anexample to illustrate your answer.

Applying Your Knowledge

1. Pingelap is a tiny island in the Pacific Ocean that is part of the Feder-ated States of Micronesia. In 1774, a typhoon devastated the island andof the 500 people who inhabited the island only 20 survived. One malesurvivor was heterozygous for a rare type of congenital colorblindness.After four generations a number of children were born with completecolorblindness and hypersensitivity to light due to defective cones(achromatopsia). The islands remained isolated for over 150 years.Now there are about 3,000 Pingelap descendants, including those on anearby island and a small town on a third island. The frequency ofindividuals who are homozygous recessive and have the disease is5% and another 30% are heterozygous carriers. This compares to theaverage of 1% carriers for the human population at large. Explain theconditions that are responsible for these differences in genetic frequen-cies for the Pingelap population and the general human population.

Three daughters of the male survivor on Pingelap, who were carriers forcolorblindness, moved to the nearby island of Mokil. This new islandwas even smaller and had fewer people. How would this event changethe frequency of the colorblindess in the Mokil population? Is this anexample of founder effect or bottleneck? Explain.

A number of Pingelap citizens were transplanted to a small town on yeta third larger island, the capital of this island group. What factors do




1950 1960 1970 1980 1990 2000

1.0

0.8

0.0

Freq

uenc

y of

dar

k m

oths

Year

Frequency of peppered moth, dark form,in northwestern England (After Cook, 2003).

you think affected the frequency of colorblindness on this island?Would you expect the frequency of the colorblind allele to be the sameon this island as it is on Pingelap? Explain.

2. Cystic fibrosis (CF) is caused by a genetic mutation resulting in defectiveproteins in secretory cells, mainly in the epithelial lining of the respiratorytract. The one in every 2,000 Caucasian babies who has the disease ishomozygous for the recessive mutant. Although medical treatment is be-coming more effective, in the past most children with CF died before theirteens. About 20 Caucasians in 2,000 are carriers of the trait, having onemutant and one normal allele, but they do not develop the disease. Accord-ing to rules of population genetics, the frequency of the homozygous reces-sive genotype should be rarer than it is. What is one possible explanationfor the unusually high frequency of this allele in Caucasian populations?

3. In the figure below, the frequency of dark forms of the peppered mothis shown for populations in northwestern England. Describe thechanges in dark moth frequency from 1970 to 2000.




Do these populations appear to be in Hardy-Weinberg equilibrium?Explain.

Using these results for the peppered moth, describe the roles of geneticvariation and natural selection in evolutionary change.

Student Media: BioFlix, Activities, Investigations, and Videoswww.masteringbiology.com (select Study Area)

BioFlix—Ch. 23: Mechanisms of Evolution (Animation)Activities—Ch. 23: Causes of Evolutionary ChangeInvestigations—Ch. 22: How Do Environmental Changes Affect a Population? What Are the Patterns of Antibiotic

Resistance?Ch. 23: How Can Frequency of Alleles Be Calculated? Biology Labs OnLine: Population Genetics Lab:Background, Assignments 1, 2, 4, 5, 6, 7; Evolution Lab

Videos—Ch. 22: Discovery Videos: Charles Darwin

References

Some parts of this lab topic were modified from J. C. Glase, 1993, “A Laboratory on Population Genet-ics and Evolution: A Physical Model and ComputerSimulation,” pages 29–41, in Tested Studies for LaboratoryTeaching, Volume 7/8 (C. A. Goldman and P. L. Hauta,Editors). Proceedings of the 7th and 8th Workshop/Conference of the Association for Biology LaboratoryEducation (ABLE), 187 pages. Used by permission.

Ayala, F. J. Population and Evolutionary Genetics: APrimer. Menlo Park, CA: Benjamin Cummings, 1982.

Cook, L. M. “The Rise and Fall of the Carbonaria Formof the Peppered Moth.” The Quarterly Review of Biology,2003, vol. 78(4), pp. 399–417.

Futuyama, D. Evolution, 2nd ed. Sunderland, MA: Sin-auer Associates, 2009.

Halliburton, R. Introduction to Population Genetics. SanFrancisco, CA: Benjamin Cummings, 2004.

Hardy, G. H. “Mendelian Proportions in a Mixed Pop-ulation.” Science (July 10, 1908) pp. 49–50. In this

interesting early application of the “Hardy-WeinbergTheorem,” this letter written by Hardy to the editorof Science refutes a report that dominant charactersincrease in frequency over time.

Hedrick, P. W., G. Gutierrez-Espeleta, and R. Lee.“Founder Effect in an Island Population of BighornSheep.” Molecular Ecology, 2001, vol. 10(4), pp. 851–857.

Heitz, J. and C. Giffen. Practicing Biology: A StudentWorkbook, 4th ed. San Francisco, CA: BenjaminCummings, 2010. Chapter 23 provides a guide tosolving population genetics problems and practiceproblems.

Price, F. and V. Vaughn. “Evolve,” BioQuest LibraryOnline. http://www.bioquest.org/BQLibrary/library_result.php (software available to download).

Sundin, O. H., J. Yang, Y. Li, D. Zhu, J. Hurd, T. Mitchell, E. Silva, and I. Maumenee. “Genetic Basisof Total Colourblindness Among the Pingelapese Is-landers.” Nature Genetics, 2000, vol. 25, pp. 289–293.




Websites

Issues in Evolution, American Institutes of BiologicalSciences, provides resources, interviews, and issues:http://www.actionbioscience.org/evolution/

Library of resources at PBS Evolution website: http://www.pbs.org/wgbh/evolution/library/index.html

Malaria movie showing sickle cell and malaria. Impor-tance of mutation: http://www.pbs.org/wgbh/evolution/library/01/2/l_012_02.html

Resources for evolution and population genetics. Searchfor population genetics: http://www.pbs.org/wgbh/evolution/library/index.html

Simulation software and resources for populationbiology: http://www.cbs.umn.edu/populus/ http://dorakmt.tripod.com/evolution/popgen.html

Video of Endler’s work on guppies: http://www.pbs.org/wgbh/evolution/sex/guppy/index.html

Video of toxic newt and garter snake—evolutionaryarms race: http://www.pbs.org/wgbh/evolution/library/01/3/l_013_07.html





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