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Forces of evolution
Handed out: September 23
Due: October 5

Tools: Population genetics & evolution simulation - Populus java computer program, version 5.4
& PopG computer program

Populus: Download site and installation instructions at the University of Minnesota located here. (.jar files available for PC, Mac, Linux-Unix)
Make sure you have checked for java compatibility according to the instructions on that page.
A PDF file of instructions for all modules is downloaded with the program.
Check with us if you need to run the program on Athena workstations rather than your own computer.

PopG: Download site and installation instructions at the University of Washington located here.

This lab will allow you to explore the impact of various forces on allele dynamics.
Here we will present an overview of the laboratory, along with some introductory questions. This is followed by a link to a pdf file for the full laboratory itself.

The rest of the lab: using Populus (part 2a) and PopG (part 2b)

1. Start Populus by double-clicking on the Populus icon as per the type of machine you are using.
2. Click in the Model box in the left side of the menu bar; select autosomal selection (i.e., no sex, we're British).
3. In Plot Options, keep p vs t; later, you can change this to examine shifts in genotype frequencies.  p is, of course, the frequency of the model A1 allele. 
4. In the “Fitness/Selection Coefficients” box, make sure the “fitness” tab is selected.  Later, you can select the “selection” tab, in which you examine the effects of different selection coefficients s.
5. Set genotype fitnesses according to the hypothesis you wish to test (see below).
6. Under “Initial Conditions” highlight the button for “Six Initial Frequencies" (or however many you want).
7. Now you are ready to run a simulation:  Click on the “View” button (green arrows).   The following graph should appear:
   

   Each color represents the predicted change in the frequency of allele “A” over 200 generations, given different starting frequencies.  Note that the model predicts that A will become the only allele eventually (at equilibrium) no matter what the starting frequency. Using options at the top of the graph screen, you can save your results to a new file. You can save the graph as a picture, or you can save a text file with the data used to generate the graph. (Tip: On a Macintosh, it appears that is easiest to save a graph file as a pdf by using the Print menu, rather than saving it as a jpeg file. Savingjpegs appears to work fine on Windows and Linux.) Be careful to note where you save files.
   
   Also, you should take notes on the important predictions of each run of the model. For example, if you reduce the heterozygote Aa and aa homozygote fitnesses, how does the time to reach equilibrium change?

Using PopG
PopG limits itself to a one-locus, 2 allele model, but lets one investigate all the interactions between selection, migration, mutation, and drift (by specifying the population size). Please follow the instructions on the same web page as the installation instructions. You will either execute the popg file in a terminal window (on Linux); or click or double-click the PopG icon (on a Macintosh or Windows). This will pull up a menu where where you can start a new run of 100 generations at a time, after specifying fitnesses, mutation rates, migration rates, and initial frequency of the A allele. We will not be using PopG until Part 2b of this lab.

Part 2a: Populus warmup exercises

Question 1. If an allele is lethat but recessive, how fast can selection remove it from a population?
For this question, you should set aa fitness to zero, and AA and Aa fitness to 1.0.
   -Run the program, and determine the number of generations to fixation for A.
   -You may want to use “Options” on the graph menu to set up a grid.
   -Record the number of generations as a function of starting frequency for A.
   -(If you can find an analytic relationship using the equations from the text/notes, so much the better, but confirm your analytic formula with a simulation.)
    -Report your results in the form of a short table.

Question 2. How is the rate of elimination of a deleterious allele affected by the selection coefficient s?
For this question, you will need to vary aa fitness (fitness = 1 – s).
    -Choose a single starting frequency.
    -Run the simulation and note the time to fixation.
    -Reset the simulation for a different fitness, and note the new time to fixation.
    -You will need to set up a table with a column for aa fitness and a column for the corresponding time to fixation.
An Excel graph would be a good way to present this relationship.

Question 3. How can we calculate fitness values and selection coefficients from real data?
Remember that selection does not act on a gene in isolation. Locus A has two alleles A and a and three genotypes.  We can calculate fitness and the force of selection on these genotypes- the selection coefficients.

Step 1. The most fit genotype is always set as 1.  Suppose AA is most fit. The less fit genotypes are calculated as proportions of the most fit genotype. The s values are "selection coefficients" but often we shall just use the ratios directly, these are the relative fitnesses.

Step 2. You superimpose this calculation on the Hardy-Weinberg frequencies to compute the frequency after selection.

Genotype	AA	Aa	aa
Frequency before selection	p2	2pq	q2
Proportional contribution to next generation	p2 W11	2pq W12	q2 W22

Step 3. Calculating selection coefficients from empirical data. You assume that the frequency before selection is in H-W equillibrium. The "proportional contribution to next generation" is what is observed.

Genotype	AA	Aa	aa
Frequency before selection	0.25	0.50	0.25
Proportional contribution to next generation	0.35	0.48	0.17
Relative survival value	0.35/0.25 = 1.4	0.48/0.58=0.96	0.17/0.25=0.68
Relative fitness value	1.4/1.4 = 1.0	0.96/1.4=0.70	0.68/1.4=0.40
Selection coefficient	1-1 = 0	1-0.7 = 0.3	1- 0.4 = 0.6

Step 4. Calculating fitness values & selection coefficients from real data: Applying Step 3 to actual field data.
Biston betulia, the peppered moth, and its response to industrial melanism (aka 'smoke from British factories') is the classical result on natural selection observed the wild studied by Kettlewell (1959).  To test his hypothesis that there was selection favoring darker colored moths that could more readily hide on the pollution-darkened bark of trees, he did mark-recapture experiments in a polluted wood. He released 154 carbonaria (the melanic form) and 65 typica (lighter) moths for a total of 218. Note that the carbonaria form occurs if the genotype is either CC or Cc (i.e., C is a dominant allele). The lighter moths only occur if the genotype is cc.
Kettlewell recaptured 82 carbonaria and 16 typica. From this data you can calculate the selection coefficients, as follows. We give you the first 5 rows of the data table. You are to calculate the numbers that go in the last two rows: first relative fitness, and then the selection coefficients. Relative fitness, w, is just the survival ratios amongst all the types (so we normalize the value to 1.0 for the highest surviving type). The selection coefficient, s, is computed as in the table above.

Question 3 (finally): With the fitness values that you just computed that presumably favor the carbonaria form, how long, in terms of # of moth generations, would it take to change the frequency of carbonaria observed in an unpolluted wood at 2%, to the 87% frequency Kettlewell observed in a polluted wood? Note that the Populus model uses a continuous simulation, but, obviously the moth populations are discrete, so you'll have to reconcile this difference.

References: Kettlewell, H. B. D. 1959.  Darwin's missing evidence. Scientific American 200 (8): 48-53.
If you'd like to read the debate about Kettlewell's experiments (not entirely accurate, in my view, as usual for Wikipedia), see the Wikipedia entry here.

Part 2: The forces of evolution - selection, mutation, migration, and drift - Populus and Popgen exercises.
OK, with your computer muscles all warmed up, please now proceed to Part 2b, of the laboratory, a more extensive exploration of the interaction between different evolutionary forces, in the pdf document here.