Laboratory 4 EVOLUTIONARY MECHANISMS & Hardy Weinberg Equilibrium

Transcription

1 Before lab Laboratory 4 EVOLUTIONARY MECHANISMS & Hardy Weinberg Equilibrium Review the mechanisms of evolution and the Hardy-Weinberg principle in your textbook (Freeman Chapter 24, especially section 24.1). Do the web/cd tutorial Read this lab. BRING a CALCULATOR TO LAB Objectives completing this exercise you should be able to: 1. Determine the allele frequencies for a gene in a model population. 2. Calculate observed and expected ratios of genotypes based on Hardy-Weinberg proportions. 3. Test hypotheses about the effect of evolutionary agents (natural selection, gene flow, genetic drift, or mutation) on allele frequencies in a population. 4. Explain why the Hardy-Weinberg principle serves as a null hypothesis. Evaluation 6% 1% Quiz at the beginning of lab 5% Group participation during lab & individual write up due in LAB 5. Timeline 2: :30 Quiz 2: :00 Intro and Exercise 1 3:00 4:30 Exercise 2 (experiments 1, 2, and 3) 4:30 5:00 Discussion of thought questions plus clean up Introduction The Hardy-Weinberg Principle says that heredity itself cannot cause changes in the frequencies of alternate forms of the same gene (alleles). If certain conditions are met, then the proportions of genotypes that make up a population of organisms should remain constant generation after generation according to Hardy- Weinberg equilibrium: Genotype frequencies: p 2 + 2pq + q 2 = 1.0 (for two alleles) If p is the frequency of one allele (A), and q is the frequency of the other allele (a), then Allele frequencies: p + q=1.0 University of Toronto at Mississauga

2 4-2 Evolutionary Mechanisms In nature, however, the frequencies of genes in populations are not static (that is, not unchanging). Natural populations never meet all of the assumptions for Hardy-Weinberg equilibrium. The assumptions for Hardy-Weinberg equilibrium are: 1. The organism in question is diploid. 2. Reproduction is sexual. 3. Mating is random. 4. Population size is very large. 5. Migration is negligible. (i.e., no immigration or emigration occurs) 6. No net changes in the gene pool due to mutation. 7. Natural selection does not affect the locus under consideration (i.e., all genotypes are equally likely to reproduce). Your text lists five conditions which must be met (which cover the same assumptions as listed above): 1. No natural selection at the gene in question. 2. No genetic drift or random allele frequency changes affecting the gene in question. 3. No gene flow. 4. No mutation. 5. Random mating. Be able to explain the Hardy-Weinberg equilibrium and the reason for each condition. Evolution is a process resulting in changes in the genetic makeup of populations through time; therefore, factors that disrupt Hardy-Weinberg equilibrium are referred to as evolutionary agents. In random mating populations, natural selection, gene flow, genetic drift, and mutation can all result in a shift in gene frequencies predicted by the Hardy-Weinberg formula. Nonrandom mating can also result in such changes. The exercises in this lab will demonstrate the effect of these agents on the genetic structure of a simplified model population. If a population is in Hardy-Weinberg equilibrium, then evolution is NOT happening; therefore, the Hardy-Weinberg principle may be called the null hypothesis for evolution. Hypothesis In a large, randomly mating population with no mutation, migration, or selection, the allelic and genotypic frequencies should remain at equilibrium. Prediction If a population is at Hardy-Weinberg equilibrium, then the frequencies of the alleles (represented by beads in this lab) should not change.

3 4-3 Evolutionary Mechanisms Summary of Materials Per student group of 4: plastic dishpan (12" x 7" x 2") 50 large (10-mm diameter) white beads 50 large red/brown beads 50 large pink beads 4,000 small (8-mm diameter) white beads pair of long forceps coarse sieve (9.5-mm) small bowl 2 small paper/opaque plastic bags Exercise 1 Testing Hardy-Weinberg (HW) equilibrium (work in pairs) Materials Plastic/paper bag with 50 beads (mixture of white and red different groups are given a different proportion of red and white beads) Introduction Simulate a population using coloured beads and test whether this population is in HW equilibrium. The bag of beads represents the gene pool for the population; each bead is a single allele (in a single gamete) and the two colours represent the two alleles for that gene in the population. For this simulation we will call red/brown (R) dominant to white (r) Hypothesis: (re-state the Hardy-Weinberg theory) Prediction: Predict the genotype frequencies of the population in future generations (If/then) The code number of the outside of your bag is Count the actual number of alleles in your population: # red/brown beads (alleles) allele frequency of R = # white beads (alleles) allele frequency of r = total # beads How many diploid individuals are represented in this population? Example: diploid individuals; 25 individuals in the population Allele frequency p+q= red allele frequency of R = 35/50 = 0.8 (p) 10 white allele frequency of r = 15/50 = 0.2 (q) total alleles for 25 diploid individuals

4 4-4 Evolutionary Mechanisms Expected genotype frequency p 2 + 2pq + q 2 = 1.0 (0.8) 2 + 2(0.8x0.2) + (0.2) 2 = = 1 Homozygous red = 0.64 or 16 individuals in a population of 25 Heterozygous = 0.32 or 8 individuals Homozygous white = 0.04 or 1 individual Expected phenotype frequency red = 0.96 or 24 individuals in a population of 25 White 0.04 or 1 individual Procedure 1. Without looking, randomly remove two beads from the bag. These two beads represent one diploid individual in the next generation. Record the genotype in Table 1a. 2. Return the beads to the bag, shake before selecting two more beads. Why? (see explanation below- sampling with replacement ) 3. Continue steps 1 & 2 until you have recorded the genotypes for 20 individuals. Results 1. Determine the expected frequencies of alleles and genotypes for the population from the original allele frequency: [see sample calculations above] Expected allele frequencies: p + q=1.0 p (freq of R) = q (freq of r) = Expected genotype frequencies ( p 2 + 2pq + q 2 = 1.0 (for two alleles)) and the expected number of individuals of each genotype. [use the number you counted above] Expected freq RR Rr rr # individuals RR Rr rr 2. Calculate the observed frequencies from the observed number of individuals of each genotype obtained from your experiment. # individuals RR Rr rr Observed freq RR Rr rr 3. To determine whether the observed frequencies were consistent with what was expected,use the Chi-Square statistical test. (See sample calculation in Table 3a)

5 4-5 Evolutionary Mechanisms Table Ia The # of individuals with the three genotypes after one generation comparing the observed versus expected # of individuals # RR #Rr #rr Observed (o) Expected (e) Deviation (o-e)= d d 2 d 2/ /e Chi-square = sum d 2/ /e Discussion 4. Do the results of your statistical analysis suggest that the frequencies of genotypes in your population are significantly different from expected? 5. Were your results consistent with your hypothesis and prediction? 6. What would you expect to happen to the frequencies if you continued the simulation for 25 generations? 7. Is this population evolving? Explain your answer. 8. How does this simulation meet the conditions for the population to be in HW equilibrium? Answer yes or no for each condition: Random mating ; Large population ; no gene flow ; no selection Sample data, calculations, and discussion: Table Ib Example for 50 individuals randomly selected with an initial allele frequency or p=q # RR #Rr #rr Observed (o) Expected (e) Deviation (o-e)= d d d 2/ /e Chi-square = sum d 2/ /e 1.55 (degrees of freedom = 2 because 3 genotypes -1 = 2), level of significance p=0.05) NOT Significant Table Ic Critical values for the χ 2 - distribution Degrees Level of probability of freedom Discussion: The observed results are consistent with the expected results. The data support the hypothesis; the observed distribution is not significant from expected under the Hardy-Weinberg theory. Any minor differences can be attributed to change of sampling error. (This population is not

6 4-6 Evolutionary Mechanisms evolving.) Sampling with replacement By replacing the beads each time after sampling, the size of the gene pool stays the same and the probability of selecting any allele should remain equal to its frequency. Exercise 2 Simulating Evolutionary Change (work in teams of 3-4) Under the conditions specified by the HW-model, the allele frequencies should not change, and evolution should not occur. In this exercise, you will modify each of the conditions to determine the effect on allele and genotype frequencies in subsequent generations using the bead model. The General Model The populations you will be working with are composed of coloured beads representing individuals as follows: White beads are homozygous for the white allele (C W C W ). Red beads are homozygous for the red allele (C R C R ) Pink beads are heterozygotes (C W C R ). These beads exist in "ponds" that are represented by plastic dishpans filled with smaller beads. The smaller beads can be strained to retrieve all the "individuals" that make up the model population. When the individuals are recovered, the frequencies of the colour alleles can be determined using the Hardy-Weinberg formula. The alleles in our population are codominant. Thus, each white bead contains two white alleles; each pink bead, one white and one red; and each red bead, two red alleles. The total number of colour alleles in a population of twenty individuals is forty. If such a population contains five white beads and ten pink beads, the frequency of the white allele is: p = (2 x 5) + 10 = Because p + q = 1.0, the frequency of the red allele (q) must also be 0.5 if there are only two colour alleles in this population. Experiment 1 Natural Selection by simulated predation Natural selection disturbs Hardy-Weinberg equilibrium by discriminating between individuals with respect to their ability to produce young. Those individuals that survive and reproduce will perpetuate more of their genes in the population. These individuals are said to exhibit greater fitness than those who leave no offspring or fewer offspring. We will model the effect of natural selection by simulating predation on our population. 1. The initial population: ten large white beads, ten large red beads twenty large pink beads Put into a dishpan filled with small white beads (to a depth of at least 5 cm). 2. One student is the predator. the beads are mixed, the predator searches the pond and

7 4-7 Evolutionary Mechanisms removes as many prey items (large beads) as possible in 30 seconds. In order to more closely model the handling time required by real predators, you must search for and remove beads with a pair of long forceps. 3. Because some of the large beads are cryptically coloured (they blend into the environment), the proportions of beads taken may not reflect the original proportions. Sift the pond with the sieve, count the number of large white, pink, and red beads, and record the totals in Table 1. Use these counts to calculate the frequencies of the white (p) and red (q) alleles remaining in the population after selection and record them in Table 2. For example, if five white, eight pink, and eight red beads remain, the frequency of the white allele is: p = (2 x 5) + 8 = Using the new values for allele frequencies, calculate genotype frequencies for homozygous white (p 2 ), heterozygous pink (2pq), and homozygous red (q 2 ) individuals, and record them in Table 2. For example, if p now equals 0.43, the frequency of homozygous white individuals is: p 2 = (0.43) 2 = 0.18 Assuming that fifty individuals comprise the next generation, calculate the number of white, pink, and red individuals needed to create the population of a new pond and record these numbers in Table 5.1. For example, if p 2 = 0.18, the number of white beads is: Using these numbers, construct a new pond. p 2 x 50 = 0.18 x 50 = Repeat steps 2 4 for three more rounds. Stop when Tables 1 and 2 are filled in completely. A different student should be the predator in each round. When you are finished, plot the frequency of the red allele over time in Figure1. Thought Question 1 How would the gene frequencies change, if you started with small red beads as a background?

8 4-8 Evolutionary Mechanisms Table 1 Counts of large beads before and after four rounds of simulated predation (Part B). Beads White Pink Red Total Initial Population Before Second Population Before 50 Third Population Before 50 Fourth Population Before 50 Table 2 Allele and genotype frequencies due to selection by simulated predation. Population p q p 2 2pq q 2 Initial population First Second Third Fourth

9 4-9 Evolutionary Mechanisms Frequency of red allele ( q ) Time (in generations) Figure 1 Effects of predation on allele frequencies. Selection that favors one extreme phenotype over the other and causes allele frequencies to change in a predictable direction is known as directional selection. When selection favors an intermediate phenotype rather than one at the extremes, it is known as stabilizing selection. Selection that operates against the intermediate phenotype and favors the extreme ones is called disruptive selection. It is important to realize that selection operates on the entire phenotype so that the overall fitness of an organism is based on the result of interactions of thousands of genes. The model presented here is very simple. Occasionally simple genetic differences like the one you have modeled are critical to the survival of different phenotypes Thought Question 2 If two identical populations were in different environments (such as in our red and white ponds), how would the frequency of the colour genes in each pond compare after a large number of generations? As two populations become genetically different through time (divergence), individuals from these populations may lose the ability to interbreed (=reproductive isolation). If this happens, two species form from one ancestral species. This process is called speciation. Results & Discussion working draft for your assignment due in Lab 5 Experiment 1 Natural selection by predation 1. State your hypothesis: 2. State your prediction: 3. Which of the conditions necessary for Hardy-Weinberg equilibrium were met?

10 4-10 Evolutionary Mechanisms 4. Which condition (s) changed? 5. Describe the changes in allele frequencies of p and q over time and compare the end frequencies to starting frequencies. 6. Describe the changes in genotype frequencies and compare the end frequencies to starting frequencies. Experiment 2 Natural Selection and Gene Flow (migration) The frequencies of alleles in a population also change if new organisms immigrate and interbreed, or when old breeding members emigrate. Gene flow due to migration may be a powerful force in evolution. To demonstrate its effect: 1. Establish an initial population as in Experiment 1 Step Begin selection as before, except in this part of the exercise add five new red beads to each generation before the new allele frequencies are determined. These beads represent migrants from a population where the red allele confers greater fitness. Record the counts before and after predation (with the five new red beads added) in Table 3 and the frequencies of alleles in Table For each generation, record in Table 5 the frequencies of the red allele obtained with both selection and migration. Thought Question 3 How does migration influence the effectiveness of selection in this example? Some level of gene flow is necessary to keep local populations of the same species from becoming more and more different from each other. Things that serve as barriers to gene flow may accelerate the production of new species. Migration may also introduce new genes into a population and produce new genetic combinations. Imagine the result of a black allele being introduced into our model population and the new heterozygotes (perhaps gray and dark red) it would produce.

11 4-11 Evolutionary Mechanisms Table 3 Counts of large beads before and after four rounds of simulated predation with gene flow. Beads White Pink Red Total Initial Population Before Second Population Before 50 Third Population Before 50 Fourth Population Before 50 Table 4 Allele and genotype frequencies due to selection by simulated predation with addition of gene flow. Population p q p 2 2pq q 2 Initial population First Second Third Fourth

12 4-12 Evolutionary Mechanisms Table 5 Frequency of red allele due to selection and migration. Generation Selection Alone (Experiment 1) Selection and migration (Experiment 2) 1 q = q = 2 q = q = 3 q = q = 4 q = q = Experiment 2: Natural selection with gene flow (migration) working draft 7. State your hypothesis: 8. State your prediction: 9. Which of the conditions necessary for Hardy-Weinberg equilibrium were met? 10. Which condition (s) changed? 11. Describe the changes in allele frequencies of p and q over time and compare the end frequencies to starting frequencies. 12. Describe the changes in genotype frequencies and compare the end frequencies to starting frequencies.

13 4-13 Evolutionary Mechanisms Experiment 3 Natural Selection with Genetic Drift (founder or bottleneck effect) Chance is another factor that affects the kind of gametes in a population that are involved in fertilization. As a result, shifts in gene frequencies can occur between generations just because of the random aspects of fertilization. This phenomenon is known as genetic drift. In this portion of the experiment, we will simulate genetic drift. 1. Establish an initial population as in Experiment 1 Step l. 2. One student in the group should, without looking, place his or her hand in the bowl and choose ten large beads at random. 3. Record the allele frequencies in Table 6 that would result from the ten individuals you have chosen. Table 6 Allele frequencies produced by genetic drift. Expected frequencies Actual Frequencies (n = 10) Actual Frequencies (n = 30) p = 0.5 p = p = q = 0.5 q = q = Thought Question 4 If the individuals you selected were the only individuals to reproduce in this generation, what would be the effect on allele frequencies compared to those initially present in the population? 4. Now replace the ten beads you removed in step 2. Select beads at random again, but this time select thirty beads. 5. Calculate the allele frequencies from the thirty beads and record these frequencies in Table 6. Thought Question 5 How do these frequencies for 30 individuals compare to those generated in step 3 for 10 individuals? Generally, the larger the breeding population, the smaller the sampling effect that we call genetic drift. In small populations, genetic drift can cause fluctuations in gene frequencies that are great enough to eliminate an allele from a population, such that p becomes 0.0 and the other allele becomes fixed (q = 1.0). Genetic variation in such a population is reduced. Populations that become very small may lose much of their genetic variation. This is known as a bottleneck effect. Another way in which chance affects allele frequencies in a population is when new populations are established by migrants from old populations.

14 4-14 Evolutionary Mechanisms 6. To model this effect, choose at random six individuals from an initial population as in Part B1 to represent the migrants. 7. Move these individuals to a new unoccupied pond. It is not necessary to actually set up a new pond for this demonstration; just use your imagination. 8. Now calculate the allele frequencies in the new pond and record them in Table 7. Table 7 Allele frequencies in a founder population. Initial Population Founder Population p = 0.5 p = q = 0.5 q = Thought Question 7 How do they compare with the frequencies that were characteristic of the pond from which these migrants came? The genetic makeup in future generations in the new population will more closely resemble the six migrants than the population from which the migrants came. This effect is known as the founder effect. The founder effect may not be an entirely random process because organisms that migrate from a population may be genetically different from the rest of the population to begin with. For example, if wing length in a population of insects is variable, one might expect insects with longer wings to be better at founding new populations because they may be carried farther by winds. Experiment 3 natural selection and genetic drift (founder and bottleneck) working draft 13. State your hypothesis: 14. State your prediction: 15. Which of the conditions necessary for Hardy-Weinberg equilibrium were met?

15 4-15 Evolutionary Mechanisms 16. Which condition (s) changed? 17. Describe the changes in allele frequencies of p and q over time and compare the end frequencies to starting frequencies. 18. Describe the changes in genotype frequencies and compare the end frequencies to starting frequencies. Review of Chi-square χ 2 test The chi-square (χ 2 pronounced kye-square) test is one way to test an hypothesis in an experiment in which the data collected are frequency data, rather than continuous data ( t -test). Genetic and behavioural experiments often measure the frequency of occurrence of events; for instance, an experimenter may want to compare the number of animals responding to some stimulus to the number of animals that did not respond. Note that the χ 2 ; analysis uses raw data only, not percentages or proportions. The χ 2 formula is χ 2 = Table 6. Critical values for the χ 2 - distribution Degrees Level of probability of freedom (observed - expected) expected