Download Word file is HERE - (canvas.brown.edu).

Biology 1410
Problem Set # 1
Evolutionary Genetics
Due Thursday 2/14/2013
Note: This is a two-part exercise: the first part will be done as an out-of-class exercise on
2/4/13, and the second part will be due on 2/14/13. Write up in a Word document, and
Submit on the Assignments link of the BIOL 141 Canvas web page. You must also HAND
IN A HARD COPY in Class Thursday 2/14/13.
POPULATION GENETICS SIMULATIONS USING POPULUS
Accessing Populus
You can download Populus from the Populus Web site
http://www.cbs.umn.edu/populus/installer. There are PC and MacOS versions. If you have
problems, you can use Populus on the PC Clusters in the CIT or Science Library.
Log on to a Cluster PC, locate the Instructional Folder and then All Programs, then Populus.
Click on the icon and it should launch.
Launch Populus You will select different Models from the menu (e.g., Natural Selection).
You will have to 1) Cut and paste some graphs, and 2) answer questions about specific
simulations. Background on the model you run is available by clicking on the Help button (a
PDF file will open). Additional Options and information buttons are at the top of the screen and
provide menus for various display options or file-saving options.
Genetic Drift: Monte Carlo
A warm-up exercise: The Monte Carol simulation of
drift uses a random number generator to mimic the
process of random fluctuation of allele frequencies
from one generation to the next. Choose Model …
Mendelian Genetics … Genetic Drift. The screen
opens under the Monte Carlo option. Set Runtime =
Other: Generations = 50, Population size (N) =
10, leave Number of Loci at 6, and set frequencies
collectively = 0.5. Click View, then on the Output
screen, Click Iterate several times. Do several runs
to convince yourself that drift acts faster at smaller
population sizes. Notice the jaggedness of the lines
(frequency trajectories at separate loci) and how
common it is for loci to reach fixation (p = 1.0) or
loss (p = 0.0). Now quantify this by running 20 simulations at 3 different population sizes and
count the number of events among the 6 loci. For each population size, click Iterate 20 times
and record each outcome:
Population size
20
30
40
# to loss
# to Fixation
# polymorphic
Question 1) Explain how will “selfing” will change these outcomes? Find the Permit Selfing
button, and re-run the simulations to see if your predictions are correct. You can read the Help
file PDF that downloads with Populus for additional information on drift. (3 points: 1data+2ans.)
Biology 1410
Problem Set # 1
Evolutionary Genetics
Due Thursday 2/14/2013
Genetic Drift: Markov Model
The Markov model determines the next generation’s allele or genotype frequencies by
multiplying the current generation by a transition function. For drift, this can be some
proportional loss of variability each generation. Choose Model … Mendelian Genetics …
Genetic Drift and click on the Markov tab. Press View, and then Iterate on the Output screen.
Compare your Output plots to the Buri Experiment in Slide 6 of the 3.1.Drift PowerPoint
lecture. Buri bred 107 populations of fruit flies using 16
individuals per generation, starting at p=0.5. After 19
generations of drift, 30 populations went to p=0.0, and 28
went to p = 1.0. Use this Markov model in Populus to
estimate the effective population size. This is done by
trial and error: Try different population sizes to reconstruct
the Buri data of ~ 27% p=0.0, ~ 27% p = 1.0 after 19
generations (we’ll assume that the same number of
populations went to fixation and to loss). Population Size is
changed by adjusting the values in the screen shown to the
right. To keep the allele frequency at 0.5, set the “Number
of “A” genes per population” equal to the “Population size” (as diploids, this gives 0=0.5), as
shown in the screen shot.
Question 2) Document your estimate: Cut and paste a plot from Populus into your write-up
that shows a genetic drift result similar to that observed by Buri. Screen shot on a Mac: press
[shift-Apple-4] simultaneously, and the mouse arrow becomes a ‘crosshair’. Click and drag over
the desired graph. When you release the mouse, a picture is pasted to your desktop (as ‘picture1’
or ‘picture2’…). In Word, select the Insert menu and select Picture…From file. Navigate to the
desktop, locate picture1, and insert. It should appear in the Word document. (1 point; sum=4)
Question 3) A) Why is the estimate of Effective Population size smaller than 16? B) Identify
two different ‘kinds’ of genetic drift that could account for this effect (hint Lecture 3 notes). (4
points: 2 each; sum = 8)
PART 2. Populus Simulations of Natural Selection
BRING the p’s and q’s of Selection handout (in Lecture Notes folder of Canvas page).
Under Model choose "Natural selection", then “Selection on a Diallelic Autosomal locus”
You will be presented with a menu for changing various conditions of the simulation. Start with
p vs. t (allele frequency vs. time), the Fitness option (input fitnesses rather than selection
coefficients), and six-frequency option (simultaneously runs six different simulations with
different starting frequencies). Set the fitnesses to the values listed below. Set the number of
generations to 300 (you can change this for different strengths of selection to let the simulation
approach equilibrium). When you run the simulation (by clicking the View button), a graph will
appear. Different graphs can be plotted by clicking the appropriate button (e.g., genotype
frequency vs. time (generations); ∆p vs. p; wbar vs. time). Run the simulation for each of the
following conditions (two different sets of values for each general condition). Click the buttons
to view the different graphs: ∆p vs. gene frequency (p); wbar vs. gene frequency (p) plots.
The Help menu describes how to zoom the screen or place a grid on the graphs. Run each of the
Biology 1410
Problem Set # 1
Evolutionary Genetics
Due Thursday 2/14/2013
conditions below, and understand the graphs of p vs. t and wbar vs. gene frequency so that you
can compare the shapes of the plots for each condition. You will have to hand in some of the
graphs with descriptions of each conditions (see below). When you have run them all, answer
the questions below. NOTE: Populus on the Mac OS may not let you enter 3 different fitness
values, so you may have to use a Cluster PC.
Condition
Run
wAA
wAa
waa
Selection against
a recessive genotype
1A
1B
0.9
0.5
1
1
1
1
Selection with codominance
2A
2B
0.9
0.6
0.95
0.8
1
1
Selection with overdominance
3A
3B
0.9
0.4
1
1
0.8
0.6
Do This: Cut and paste the graphs for p vs. t and for wbar vs. gene frequency for runs 1A and
1B, 3A and 3B above. Provide a one-sentence description of the difference between each pair of
graphs 1A-B, 2A-B, 3A-B, 4A-B, but you only need to show graphs 1A, 1B, 3A, 3B in the writeup. Note for PC users, in the Graph window, click on the File icon and a picture is copied to the
clipboard for pasting. Resize these graphs to reduce paper waste.
Question 4) Why do the runs 1B, 2B, 3B, 4B take fewer generations to reach equilibrium than
runs 1A, 2A, 3A, 4A? (1 points: sum=9)
Using your graphs of the Wbar vs. gene frequency (p) plots for each run (‘Adaptive Topography’
plots), explain the following facts:
Question 5) For runs 1A, 1B why does the graph reach a maximum at one extreme allele
frequency, while in graph 3A, 3B, the maximum is between 0 and 1? Answer this for #1 Runs vs.
the #3 runs. (2 points, sum=11)
Question 6) Why is the adaptive topography line curved in case of dominance / recessive, but
linear in case of co-dominance? (4 points, 2 each explanation; sum = 15).
Part 3. Interaction of Drift and Selection
Choose Model … Mendelian Genetics … Drift and Selection. You will do four separate simulations,
two each under two different modes of selection: Set Population Size = 10; Initial frequency = .5;
Generations = 200. Set the genotypic fitnesses as:
Co dominance (2 simulations)
Over dominance (2 simulations)
Genotype
Simulation #1
#2
#3
#4
wAA
1.00 1.0
0.98 0.4
wAa
0.99 0.8
1.00 1.0
waa
0.98 0.6
0.96 0.3
Biology 1410
Problem Set # 1
Evolutionary Genetics
Due Thursday 2/14/2013
For each simulation, press View 10 times (10 different runs) and for each run record 1) the number
losses (line hits the x-axis [same as fixation of "a" allele]), 2) the number of fixations (line hits the top of
screen [same as fixation of the "A" allele]). Record your results in the table below, and determine the
mean number of generations to fixation or loss under each simulation. OK, it sounds boring, but
remember: repetition is the mother of learning. (For the write-up, you can cut and paste table into a new
Word document; this problem set can be obtained on the course web page).
Simulation #1
Loss Fixed
Mean
=
Simulation #2
Simulation #3
Simulation #4
Gener. Loss Fixed Gener. Loss Fixed Gener. Loss Fixed Gener.
Mean
=
Mean
=
Mean
=
Question 7) Does the “A” allele always get fixed?; WHY? (1 point, sum = 16)
Question 8) Does heterozygote advantage (overdominance) guarantee that both alleles will be
maintained in the population? WHY? (1 point, sum=17)
Question 9) Population genetics theory tells us that evolution is “neutral” when the product of
(effective population size) x ( selection coefficient) </= 1.0. Explain based on the results from
runs 1-4 above, and with reference to Gillespie, page 94. (3 points, sum=20).