BIO101 Lab 2: Populus: Modeling Natural Selection & Genetic Drift
Pre-Lab Assignment:
Read the lab handout and answer the following questions:
1. What is “relative fitness”? Why does it range between 0 – 100% (0 – 1.0)?
2. What is meant by the “average fitness of a population”?
3. What is meant by “diallelic autosomal locus”?
4. What is a “stable equilibrium”?
5. What does it mean when an allele becomes “fixed” or “lost” from a population?
Background:
Population genetics refers to the most basic processes of evolution, the change in frequencies of alleles within populations. Since alleles may have different effects on the outward appearance of an organism, or phenotype, changes in the frequencies of alleles can result in changes in the appearance of individuals in populations. Changes in allele frequencies within populations are thought to be responsible for most patterns of evolutionary change, when magnified by the accumulation of time.
Modern evolutionary biologists recognize that a number of forces can alter allele frequencies within populations. These include:
· Mutation -- the spontaneous change of one allele into another
· Gene Flow -- the influx/outflow of alleles from/to other populations
· Genetic Drift -- the alteration of allele frequencies via chance
· Selection -- the fact that certain genotypes (combinations of alleles within individuals) have a relatively higher chance of survivorship or fecundity than other genotypes, or higher fitness. It is important to remember that fitness is a combined result of the genotype’s phenotypic expression and the environment.
In the absence of these forces (and in the presence of random mating), the Hardy-Weinberg theorem demonstrates that allele frequencies should remain at equilibrium. This set of computer exercises will focus on how mutation, genetic drift, gene flow, and selection can result in evolutionary change in allele frequencies. In particular, we will consider what characteristics of populations determine which of these forces has the greatest effect.
Lab Exercise:
· Explore, via computer simulations of population genetic models, the factors that influence evolutionary change within populations and that influence evolutionary similarity and divergence among populations.
· Test hypotheses about relationships between microevolution and: (1) aspects of population ecology (e.g., population size, the amount of genetic variation among individuals, and the movement of individuals between populations); and (2) aspects of molecular biology (e.g., mutation rate); and (3) links between organismal and population-level phenomena (e.g., dominance relationships [of fitness] among alleles at a locus).
Overview of software operation
1. Populus is software developed by population biologists at the University of Minnesota. It is distributed free of charge at www.cbs.umn.edu/populus/. It is a Java program, and thus can be run on Windows, Mac OSX or Unix.
2. Populus is a large set of different computerized mathematical models (i.e., simulations of real genetic systems and populations) arranged in menus. Different models are initiated choosing them through the model menu and submenus. Close each model before opening the next to avoid confusion.
3. A description of each model can be found by loading the help document (a pdf file). It is often useful to read these introductions to understand the mathematical bases of the models.
I -- SELECTION
Selection is what we usually think of as the major force causing evolutionary change. Simply put, selection occurs when certain genotypes have higher propensities for survival and/or reproduction than others. These differences are usually defined as fitnesses, the average number of offspring for an individual of each genotype (if an individual doesn't survive, it has zero offspring). In genetic models, fitnesses are usually expressed as relative fitness,
relative fitness = # of offspring for genotype/ # of offspring for most fit genotype
This means that relative fitnesses range between 0 and 1. Consider the following example.
Genotype # of offspring Relative fitness
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AA 18 18/20 = 0.9
Aa 20 20/20 = 1.0
aa 19 16/20 = 0.95
The above is a case of where the heterozygote is higher in fitness than the two homozygotes. What do you predict would happen if both alleles, a and A, were present in a population?
Choose "Natural Selection . . ." from the Model menu. Then, choose "Selection on a Diallelic Autosomal Locus." Alter the genotype fitness to match the above example.
You will be able to view the results for this simulation in three graphs (see Plot Options):
· p (frequency of A) vs. # of generations (t)
· Dp (change in p) vs. p
· Genotype frequencies vs t
· (average fitness of the population) vs. p
1. What happens to the allele frequency of A (p) under these conditions of selection?
Change the initial allele frequency to see if you get the same result.
2. Change the simulation to "six frequencies," which shows what happens at six different starting frequencies simultaneously. Consider the Dp vs. p plot. How can you determine from this figure what (the equilibrium frequency of A) is under these conditions? A stable equilibrium refers to a situation in which allele frequencies, if perturbed from the equilibrium point, return to that same point. If an equilibrium point is unstable, a perturbation will cause allele frequencies to move away from that point, eventually settling at a different equilibrium point. Use this figure to explain why the equilibrium point in this example is stable or unstable.
3. Alter the relative fitnesses of the two homozygotes, keeping WAa = 1. How does this affect the equilibrium frequency of the A allele ()? Experiment with the relative fitnesses of the two homozygotes until you can write a verbal description of their relationship to .
4. Enter the following relative fitnesses: WAA = 0.8, WAa = 0.5, and Waa = 1. Describe the result below for p vs. t.
5. Consider the Dp vs. p plot. What are the equilibrium points? Are they stable or unstable equilibria?
6. Consider the vs. p plot. Under these conditions, is always at the maximum value of ? Does natural selection (as in the previous example) always increase the average fitness of the population (from its starting allele frequencies)? Does that mean that the maximum possible average fitness will be attained? Why or why not?
7. Set WAA = 1, WAa = 1 and Waa = 0.7. Choose the single frequency option and set the initial frequency at 0.01. What is ?
Is the deleterious allele eliminated after 200 generations? Explain why Dp is so small when p is close to 1.
Close the simulation.
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II -- GENETIC DRIFT
Choose "Mendelian Genetics . . ." from the Model Menu, and then "Genetic Drift" from the submenu. Read the model description from the help file.
In the last model, we assumed that populations were very large -- in fact, we assumed that they were infinitely large. That was because populations of finite size are subject to a second force of evolution, genetic drift. In order to understand how genetic drift works, we will again look at how the frequency of alleles changes in single populations, but first we will assume that there is no selection acting on these alleles. Looking at such neutral alleles will allow us to see the effects of genetic drift when it alone is acting.
1. Change number of loci to 10, N to 200 and runtime to 100 generations.
Note that the plot shows how drift affects the frequencies of alleles of 10 independent loci (each a different color of line). Note how frequencies may move up or down each generation. Note also that genetic drift will stop when the frequency of the allele is either 0 or 1. This means that one allele has been lost from the population -- in the absence of mutation, an allele lost from a population cannot be recovered. We refer to allele frequencies as reaching fixation at 0 or 1 -- a particular allele is fixed at frequency of 1, and lost at frequency of 0.
Did allele frequencies show any tendency to move up or down?
Note how many alleles fixed at 0 and 1 -- in either case, an allele is lost and thus there is a decrease in genetic variation.
2. Run the simulation again under the same conditions. Did you get the same answer? Explain why or why not.
3. Run the simulation with N=100. Did you get a different answer? Do the simulation again to see if you get a similar answer.
4. Based on these results, you might hypothesize that the larger population size is, the slower alleles are lost due to genetic drift. Test your hypothesis with an experiment. Run simulations 10 times each for population sizes of N = 25, N = 100, and N = 200, taking note each time of the number of alleles fixed or lost after 100 generations. Calculate the mean and standard deviation for each population size. Then determine whether pairs of means are significantly different using an ANOVA (with means comparisons). [You can do this in EXCEL] Record your results on the assignment handout (i.e., the final sheet of this document) and turn in the assignment.
Under what conditions in real populations do you think genetic drift would be most important? Do these conditions occur often?
5. Many species consist of a set of relatively small populations (subpopulations or demes) that are mostly isolated from each other by barriers to migration. Genetic drift would be expected to cause such isolated populations to lose alleles and thus become less genetically diverse. Would you expect the pattern of genetic drift to be exactly the same in each population? What affect will this have on genetic variation among populations of the same species? Make a prediction below, before doing the simulation.
Close the simulation.
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III -- SELECTION AND DRIFT
Choose "Drift and Selection" from the "Mendelian Genetics" menu. Read the introduction to the model in the help document.
In real populations, both selection and genetic drift can occur. But what influences whether genetic drift or selection is the stronger force? Does genetic drift ever overwhelm the force of selection? [Note that the strength of selection is seen in the differences between fitnesses, and the strength of drift is determined by the population size.]
1. Change N = 500, wAA = 0.8, wAa = 1.0, waa = 0.8, and # of generations to 100. What do you expect to occur with these genotype fitnesses? Is your expectation fulfilled?
2. Change N = 250. How is the result different from the last simulation?
3. Change N = 50. How is the result different from the last simulation? Is the allele lost? Repeat the simulation under these conditions several times.
4. Change N = 4. How is the result different from the last simulation? Does the allele frequency reach fixation? Repeat several times.
5. Change N = 500, p = 0.1, wAA = 1, wAa= 1 and waa = 0.9. Do you get a predictable result?
6. Change N = 25 and run several times. What do these simulations suggest can be the effect of small population size on ability of advantageous alleles to sweep to fixation?
Human manipulation of the environment has caused formerly large and widespread habitats (like old-growth temperate forests) to exist in smaller, isolated patches. What do the above simulations suggest about the dangers of habitat fragmentation for species that are specialized to such "habitat islands". Reconsider your answer to the last question in the section II --" Genetic drift" as you formulate your answer.
Names: ______& ______
BIO101L Lab 2
In section II of today's lab, question 4 asks you to perform an experiment to test the idea that the rate of fixation of alleles with genetic drift declines with population size. Use the following table to record your data and test this hypothesis.
Trial / Number of alleles fixed (at six loci) after 100 generationsN = 25 N = 100 N = 200
1
2
3
4
5
6
7
8
9
10
Mean
Standard
Deviation
Is there statistically significant variation in the rate of genetic drift among the three population sizes? Provide your ANOVA p-value.
Explain your conclusion about the relationship between population size and the rate of fixation of alleles by genetic drift.
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