Mechanisms of Evolutionary Change - Case Studies in Evolution | Exercises Evolutionary biology

Part II: Mechanisms of Evolutionary Change

Case Studies in Evolution

MIGRATION AND GENETIC DRIFT AS MECHANISMS OF EVOLUTION

by Jon C. Herron, University of Washington

Introduction

This case study will help you develop an intuition about how migration and genetic drift cause evolution.

You will use a software simulation of an evolving population to analyze examples discussed in Chapter 7,

and to answer a variety questions concerning changes in the frequencies of alleles. Once you are familiar

with the simulation program, you can use it to answer questions of your own. For example, How often does

a mildly deleterious allele drift to fixation in populations of different sizes?

To complete the case study you will need the application program AlleleA1. You can download AlleleA1

from the Evolutionary Analysis website. Versions are provided that run under MacOS and Windows.

AlleleA1 simulates evolution at a single locus in an ideal population. The locus has 2 alleles: A1 and A2.

AlleleA1 allows you to enter parameters controlling selection, mutation, migration, drift, and inbreeding.

The program then plots a graph showing the frequency of allele A1 over time. Each generation's frequency

is calculated from the previous generation's frequency, according to the equations described in Chapters 6

and 7.

AlleleA1 is easy to use. Small boxes in the lower portion of the AlleleA1 window allow you to enter and

change the parameters for the simulation. The tool palette has buttons that allow you to run the simulation,

clear the graph, reset all parameters to their default values, print your graph, and quit. More details on using

AlleleA1 can be found in the manual, available both as a separate PDF file and online, under the Help

menu, while you are running AlleleA1.

Exercises

Hardy-Weinberg equilibrium

1. If you have not used AlleleA1 before, play with it for a bit to see how it works. Then restore all

parameters to their default settings. The default settings encompass initial frequencies of 0.5 for both

alleles, and the assumptions of no selection, no mutation, no migration, no genetic drift, and random

mating. Run the simulation to verify that under these conditions the allele frequencies do not change. Try

different values for the starting frequency of allele A1. Does your experimentation verify that any starting

frequencies for A1 and A2 are in equilibrium so long as there is no selection, no mutation, no migration, and

no drift?

Migration as a mechanism of evolution

2. AlleleA1 uses the one-island model of migration described on pages 234-237 of the text. The simulation

tracks the frequency of allele A1 in an island population. The parameter called Fraction of migrants each

generation determines the number of individuals that move from the mainland to the island every

generation, as a fraction of the island population. For example, setting the parameter to 0.1 means that each

generation ten percent of the individuals in the island population are new arrivals from the mainland. The

parameter called Frequency of A1 in the source pop'n determines the frequency of allele A1 on the mainland

(and thus among each generation's migrants).

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Part II: Mechanisms of Evolutionary Change Case Studies in Evolution MIGRATION AND GENETIC DRIFT AS MECHANISMS OF EVOLUTION by Jon C. Herron, University of Washington Introduction This case study will help you develop an intuition about how migration and genetic drift cause evolution. You will use a software simulation of an evolving population to analyze examples discussed in Chapter 7, and to answer a variety questions concerning changes in the frequencies of alleles. Once you are familiar with the simulation program, you can use it to answer questions of your own. For example, How often does a mildly deleterious allele drift to fixation in populations of different sizes? To complete the case study you will need the application program AlleleA1. You can download AlleleA from the Evolutionary Analysis website. Versions are provided that run under MacOS and Windows. AlleleA1 simulates evolution at a single locus in an ideal population. The locus has 2 alleles: A 1 and A 2. AlleleA1 allows you to enter parameters controlling selection, mutation, migration, drift, and inbreeding. The program then plots a graph showing the frequency of allele A 1 over time. Each generation's frequency is calculated from the previous generation's frequency, according to the equations described in Chapters 6 and 7. AlleleA1 is easy to use. Small boxes in the lower portion of the AlleleA1 window allow you to enter and change the parameters for the simulation. The tool palette has buttons that allow you to run the simulation, clear the graph, reset all parameters to their default values, print your graph, and quit. More details on using AlleleA1 can be found in the manual, available both as a separate PDF file and online, under the Help menu, while you are running AlleleA1. Exercises Hardy-Weinberg equilibrium

If you have not used AlleleA1 before, play with it for a bit to see how it works. Then restore all parameters to their default settings. The default settings encompass initial frequencies of 0.5 for both alleles, and the assumptions of no selection, no mutation, no migration, no genetic drift, and random mating. Run the simulation to verify that under these conditions the allele frequencies do not change. Try different values for the starting frequency of allele A 1. Does your experimentation verify that any starting frequencies for A 1 and A 2 are in equilibrium so long as there is no selection, no mutation, no migration, and no drift? Migration as a mechanism of evolution
AlleleA1 uses the one-island model of migration described on pages 234-237 of the text. The simulation tracks the frequency of allele A 1 in an island population. The parameter called Fraction of migrants each generation determines the number of individuals that move from the mainland to the island every generation, as a fraction of the island population. For example, setting the parameter to 0.1 means that each generation ten percent of the individuals in the island population are new arrivals from the mainland. The parameter called Frequency of A 1 in the source pop'n determines the frequency of allele A 1 on the mainland (and thus among each generation's migrants).

a) Click on the Reset button to restore all parameters to their default values. Predict what will happen when you set the fraction of migrants each generation to 0.01 and the frequency of A 1 in the source population to 0.8. Then set the parameters to these values and run the simulation. If your prediction was not correct, try to explain the difference between what you expected and what actually happened. G eneration Fr eq u en cy of

A

lle le

A

Prediction: G eneration Fr eq u en cy of

A

lle le

A

What actually happened: Explanation: b) Leave the frequency of A 1 in the source population at 0.8, and try setting the fraction of migrants each generation to 0.05, then 0.1. c) Try several different values for the both the fraction of migrants and the frequency of allele A 1 in the source population. d) Based on your experiences in parts a, b, and c, summarize what migration from the mainland does to the frequency of A 1 on the island. How long does it take for migration to exert its influence? How effective is migration as a mechanism of evolution? Migration and selection

Imagine that allele A 1 is deleterious for individuals living on the island, such that the fitnesses of genotypes A 1 A 1 , A 1 A 2 , and A 2 A 2 are 0.9, 0.95, and 1. a) If there is no migration, what is the frequency of A 1 after 500 generations? Why? b) In accord with what you saw in part a, set the starting frequency of A 1 to 0. Remember that this is the frequency in the island population. Now imagine that although it is deleterious on the island, allele A 1 is beneficial on the mainland, such that A 1 is fixed in the source population (that is, its frequency is equal to 1). What is the island frequency of A 1 after 500 generations if the fraction of migrants each generation is 0.0001? 0.001? 0.01? 0.1? Fraction of migrants Ending frequency of A 1 0. 0. 0. 0. c) In the scenario you investigated in part b, how high does the migration rate have to be for migration to overwhelm selection in controlling the frequency of A 1 on the island? If selection against A 1 on the island were stronger than we assumed in this example, would migration be less likely to overwhelm it?

Conservation biologists generally consider genetic diversity to be a good thing. That is, populations are more likely to escape extinction if there are several alleles present for each gene. a) What does drift do to the genetic diversity in a population as the population nears extinction? b) Reset all parameters to their default values. Note that the starting frequencies for alleles A 1 and A 2 are 0.5. Roughly how big does the population have to be for the chances to be reasonably good that both alleles will persist for 500 generations? The random fixation of alleles
You have seen that when genetic drift is the only evolutionary force at work in a population—when there is no selection, no mutation, and no migration—the frequencies of alleles in the population wander between 0 and 1. If we track a particular allele for long enough, its frequency will eventually hit one boundary or the other. That is, sooner or later the allele will drift to loss or fixation. Investigate the effect of an allele’s initial frequency on the probability that its ultimate fate will be fixation versus loss. a) Reset all parameters to their default values, and set the population size to 100. Pick an initial frequency for A 1 , and set the starting frequency parameter in AlleleA1 accordingly. Then run the simulation 100 times. Record your results in the grid below. There are 100 squares in the grid. If A 1 drifts to fixation in a particular run, write a 1 in one of the squares on the grid. If A 1 drifts to loss, write a 0 in one of the squares. If a run ends with A 1 still at a frequency between 0 and 1, disregard the run and continue with the experiment. After 100 runs in which A 1 drifted to fixation or loss, count the 1’s on your grid to determine the percentage of runs in which A 1 drifted to fixation. Starting frequency of allele A 1 : Percentage of runs in which allele A 1 drifted to fixation: Final frequencies for 100 runs:

Final frequency of allele A 1 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

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u m b er o f^ ru ns 5 10 15 20 25 b) Repeat the experiment you performed in part a, but use a starting frequency for A 1 that is substantially different from the one you used before. Record your results in the grid below. Starting frequency of allele A 1 : Percentage of runs in which allele A 1 drifted to fixation: Final frequencies for 100 runs: c) Based on your experiments in parts a and b, can you use the starting frequency of an allele to predict the probability that the allele will eventually drift to fixation? Compare your conclusion to the analysis in Box 7.3 on page 248.

Reread An Experimental Study on Random Fixation and Loss of Heterozygosity on pages 249-252. Peter Buri (1956) followed the frequency of the bw^75 allele for 19 generations in 107 populations of fruit flies. Buri maintained each population at a size of just 16 individuals, which caused the populations to evolve rapidly by genetic drift. Use AlleleA1 to simulate Buri's experiment. a) Reset all parameters to their default values, then set the population size to 16 and the number of generations to 20. Run the simulation 50 times. After each run, round the final frequency of A 1 to the nearest 0.05, and fill in a box on the grid at right above the resulting value. As the number of runs you have completed grows, stack the filled boxes on top of each other so that they form a histogram, like this: After completing 50 runs, compare your histogram to the one from generation 19 of Buri's experiment, at the bottom of Figure 7. on page 250. How well did your simulated experiment "predict" the results of Buri's actual experiment? Can you explain the difference between the shape of your graph and the shape of Buri's?

a) Set the graph line color to black, and run the simulation once with the population size set to infinite. How long does it take for allele A 1 to be created by mutation and carried by natural selection to fixation? b) Now set the graph line mode to multiple, the graph line color to red, and the population size to 10. Run the simulation several times. What typically happens? c) Set the graph line color to orange and the population size to 100. Run the simulation several times. What typically happens? d) Set the graph line color to green and the population size to 1000. Run the simulation several times. What typically happens? e) Finally, set the graph line color to blue and the population size to 10000. Run the simulation two or three times. What typically happens? f) How large does a population have to be before a mildly advangateous allele will become fixed as rapidly as it would in a population of infinite size? How strongly does the answer depend on the strength of selection and the mutation rate? Drift, selection, migration, and genetic diversity

In question 7, we noted that conservation biologists consider genetic diversity to be a good thing, and found that genetic drift can reduce genetic diversity and potentially hasten the extinction of small populations. We now revisit these issues by investigating a particular scenario in more detail. Imagine that allele A 1 is maintained in a population by heterozygote advantage, with the fitnesses of genotypes A 1 A 1 , A 1 A 2 , and A 2 A 2 equal to 0.2, 1.0, and 0.8. a) What is the equilibrium frequency of A 1 in an ideal population? (You can answer this question either by using the formula derived in Box 6.7 on pages 208-209, or by using AlleleA1.) b) Once the frequency of allele A 1 has reached its equilibrium value, what are the frequencies of the three genotypes? (You can answer this question either by using the Hardy-Weinberg equilibrium principle, or by using AlleleA1.) c) Once the frequency of allele A 1 has reached its equilibrium value, what is the mean fitness of the population? (To calculate the mean fitness, multiply the fitness of each genotype by its frequency, then sum the results; see Box 6 .3 on page 194 ). d) Using AlleleA1, first reset all parameters to their default values. Then set the starting frequency of A 1 to 0.2, the fitnesses of A 1 A 1 , A 1 A 2 , and A 2 A 2 to 0.2, 1.0, and 0.8, and the population size to 20. Run the simulation several times. What usually happens? e) After A 1 has been lost due to genetic drift, what is the mean fitness of the population? By how much has drift reduced the mean fitness? If this effect were multiplied across several loci, could drift substantially increase the chance that our small population will go extinct? Why or why not? f) Use AlleleA1 to investigate the effect of introducing a single migrant individual into our small population each generation, where the migrant comes from a large population in which the frequency of A 1 is 0.2. (What value for the Fraction of migrants each generation parameter reflects a single individual joining a population of 20?) Could the introduction of migrants maintain enough genetic diversity in the population to ameliorate the effects of genetic drift? Compare the scenario you have investigated in this question to the case of the Florida panther discussed at the beginning and end of Chapter 7.

Literature Cited Buri, P. 1956. Gene frequency in small populations of mutant Drosophila. Evolution 10:367–402. King, R.B., and R. Lawson. 1995. Color-pattern variation in Lake Erie water snakes: The role of gene flow. Evolution 49:885–896.

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