Population Genetics
The following exercises in population genetics are designed to lead you through evolutionary experiments with a Medelian trait. The first parts examine fundamental concepts; the other parts use a simulation of the Hardy-Weinberg equilibrium and show how allelic frequencies are affected by varying genotype survival rates, initial allele percentage, and population size. This assignment is due Wednesday, October 11th,in lecture.
Fundamentals
Parts A-C below are intended to help you test your understanding of the fundamentals of the Hardy Weinberg equilibrium and do not require that you make any computer runs. However, as the computer simulation will use + and &endash; to represent the two different alleles instead of the normal A and a we will do the same for these problems. Note that either the + allele or the &endash; allele can be dominant and that the phenotype we are considering is survival
A. Calculating Genotypic and Allelic Frequencies
Calculate the number (not the frequency!) of each genotype in a population of 1000 individuals in Hardy-Weinberg equilibrium with an A allele frequency of 0.2; write the number of each genotype in the spaces below:
Consider an initial population of 200 AA individuals, 460 Aa individuals, and 340 aa individuals.
a. What are the frequencies of the alleles?
b. Given the allele frequencies you calculated above, determine the numbers of each of the genotypes you would expect if the population were in Hardy-Weinberg equilibrium:
c. Is the population in Hardy-Weinberg equilibrium? __________
B. Determining Dominance
The tables below show some different possible genotypic survival rates. Survival rates are measured in terms of the percent of each genotype surviving from birth (or hatching, germinating) to reproductive age.
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In which of the tables is A dominant for survival rate? a. b. c. d. e. f.
In which of the tables is A recessive for survival rates? a. b. c. d. e. f.
In which of the tables is there heterozygous advantage (Aa is the most advantageous geneotype) for survival rate? a. b. c. d. e. f.
In which of the tables do the alleles show incomplete dominance for survival rates? a. b. c. d. e. f.
Evolution of Mendelian Traits
In the following excercises you will investigate the effects of different evolutionary forces on the evolution of a virtual population. The trait being examined is a classical mendelian trait and the simulator will randomly mate individuals and produce progeny using the rules for mendelian inheritance. As the mating and production of progeny are random, you may wish to make several runs with each set of parameters. Note that there is to be no gene flow or differential reproductive success, nor will you need to change parameters during a run.
C. Time needed to establish Hardy-Weinberg equilibrium.
A population in obvious disequilibrium would be one
consisting entirely of heterozygotes. There are other ways
to set up such an out-of-equilibrium population, can you
describe another one?
On the basis of what you know, it would be reasonable to
predict that a population would reach Hardy Weinberg
equilibrium in one generation. More specifically: the allele
and genotype frequencies would remain stable from generation
to generation, and within one generation the genotype
frequencies would approximate p2 for AA, 2pq for Aa, and
q2 for aa. Can
you think of a situation where a population is in
disequilibrium, but does not reach the Hardy Weinberg
equilibrium after one generation of random mating?
D. Neutral Genetic Drift.
For the following exercises you will use population genetics simulators at the University of Conneticut. At their web page you determine the starting parameters for the simulation and a computer program simulates what would happen in a real population from one generation to the next. For the genetic drift simulator the parameters that you can control are the population size (N:), the initial p allele frequency (p:) [the frequency of the a allele q, is 1 - p], and the number of generations (Generations:) that you want the simulation to run. When all of the parameters are set you click on the "Start" button and the computer runs the simulation and returns a graph of the A allele frequency after each generation, number of generations is on the x axis and p is plotted on the y axis. Go to the University of Conneticut Population Genetics Simulator (http://137.99.27.45/simulations/drift.html) [if you're using Netscape on a Mac you'll have to use this version, http://137.99.27.45/simulations/jdk1.0/drift.html and you may need to hide and then reveal the window to see the results - Internet Explorer works OK on Macs] now and run the default simulation, p = 0.5, N = 50, generations = 100. What was the final allele frequency? (read it off of the graph) _________
Go back to the simulator and run the same simulation again (the new graph will be a different color). Did you get the same result? __________
Go back to the simulator run it three more times. Look at the five graphs that are produced. Are they very different or are they all the same?
Why do you think you got this result?
Go back to the simulator, change the population size to 250 and run five simulations again. Is there a difference between this result and what you found with the smaller population?
Explain this result.
E. Natural Selection
As natural selection is the evolutionary force that produces adaptation, let's look at the effect of selection on the allele frequencies. First we will investigate the effect of increasing the strength of selection on the evolution of an advantageous, dominant allele.
Prediction: Do you expect that evolution (that is, change in allele and genotype frequencies) proceeds more rapidly when the selection is stronger (differences in survival between the genotypes are larger)?
Weak selection for a dominant trait:
For natural selection you have to determine the "fitness" of each genotype. In this simulation, w11 is the fitness of the AA genotype, w12 is the fitness of the Aa genotype and w22 is the fitness of the aa genotype. Larger numbers mean a genotype is more fit, relative to the ohter genotypes. Go to the Natural Selection simulation (http://137.99.27.45/simulations/selection.html; again use this alternate version, http://137.99.27.45/simulations/jdk1.0/selection.html, if you are using Netscape and a Mac) and set the parameters of the simulation to the following: p: 0.1; w11: 1.2; w12: 1.2; and w22: 1.1 (weak selection against the aa genotype)
How many generations did it take for the A allele frequency to reach 50%?_____ What is it after 100 generations?________
Describe the pattern of change of the A allele
frequency (straight line up at a steep angle, exponential,
etc.)
Strong selection for a dominant trait:
Set the parameters of the simulation to the following: p: 0.1; w11: 1.2; w12: 1.2; and w22: 0.8 (strong selection against the aa genotype)
How many generations did it take for the A allele frequency to reach 50%?_____ What is it after 100 generations?________
Describe the pattern of change of the A allele
frequency relative to the first experiment (weak
selection)
Why do you think the deleterious recessive allele is
still there, even when the selection against the allele is
very strong?
The effect of dominance on the evolution of an advantageous allele.
Prediction: Do you think that a dominant allele
that is strongly selected for would reach 100% faster than a
recessive allele that is strongly selected for? Why?
Strong selection for a recessive trait:
Set the parameters of the simulation to the following: p: 0.1; w11: 1.2; w12: 0.8; and w22: 0.8 (strong selection for the AA genotype, only - as if A was recessive and was only expressed in homozygotes)
How many generations did it take for the A allele frequency to reach 50%?_____ What is it after 100 generations?________
Describe the pattern of change of the A allele
frequency
Compare this result to the one you got with the strong
selection for a dominant trait. Was your prediction about
the effect of dominance on the rate of evolution correct?
Why or why not?
The effect of population size on the evolution of an advantageous allele (drift + selection)?
Selection for a trait in a small population:
Set the parameters of the Selection and Genetic Drift Simulation (or the alternate version for Mac Netscape users - Selection and Genetic Drift Simulation (http://137.99.27.45/simulations/jdk1.0/selection-drift.html)) to the following: p = 0.01, N = 250, generations = 100 and run it 5 times. The selection is already preset to favor the A allele.
Are the results of the different runs similar or very different?
What do you think is going on here? What happens if
you reduce the population to N = 50?.
Bell CSU Chico Library
This document is copyright of Jeff Bell
Last Update: Friday, October 6, 2000