Computational Exercise 2.2 – Simulating the Evolution of the G-matrix
© Adam G. Jones & Stevan J. Arnold
The goal of this exercise is to become familiar with a G-matrix simulation program, its strengths, and its
limitations. You should begin by reading the Gmatrix Simulator Home Version Instructions. Next, you
should download the simulator to your desktop and create a handy folder where you can store the
outputs you will generate for this exercise. If you haven’t already downloaded the simulator = Home
Version, you can do so at http://www.bio.tamu.edu/USERS/ajones/GmatrixOnline/gevolving.html
The program should run on any machine running Windows 98, Vista, 7 ,8, and 10 but it will not run on
any other operating system. It will run on Macs and Linux using Wine.
The basic idea of the Simulator is to show the parameters of a two trait G-matrix generation-bygeneration for a specified set of conditions of mutation, drift, and selection. By varying those conditions
and doing numerous runs, you can determine how the G-matrix evolves in response to those conditions.
The Simulator produces both graphic and tabular output. Run the Simulator under some set of
conditions and watch the cartoon that shows the G-matrix eigenvectors and eigenvalues. (Or use the
Sample Output in what follows). In our Exercise today we will pay particular attention to the angle of
the leading eigenvector. Find the column in your output that shows that angle (~G-angle) from
generation to generation. Copy that column into Excel or the graphing program of your choice and
make a graph of the angle as a function of generation. What kind of pattern can you see in this time
series? What does the graph tell you about the stability of the G-matrix?
Today we will explore the conditions that affect both the stability and the evolution of the G-matrix.
The class as a whole will determine whether the angle of the G-matrix evolves in response to the
orientation of the adaptive landscape (AL) and the pattern of pleiotropic mutation . Your group will run
a series of simulations in which you specify orientation of the AL and the pattern of mutation and then
record the resulting G-matrix angle after the simulated populations have achieved mutation-driftselection balance. In each run you will fix the conditions of mutation, population size, and selection
(including AL and mutational pattern) and let each population run for 1000 generations to reach
equilibrium (burn in period). At the end of an additional 1000 generations (experimental generation
period), your program will record the G-matrix angle each generation and then calculate a mean angle
over generations. The Simulator will also do a number of replicate runs under the conditions you
specify. At the end of all the replicate runs, the program will report the mean angle (MEAN = across the
means of individual runs) as well as the standard deviation across runs (STDEV).
The job of your group is to produce a graph of G-matrix angle as a function of the number of elapsed
experimental generations. You will do a total of 5 simulation runs, each time varying the number of
experimental generations over the set of values: 200, 400, 600, 800, 1000. In each simulation run you
will do 10 replicates, focusing on the MEAN and STDEV for the G-matrix angle column. Each group will
use a different set of values for AL orientation and mutational pattern, so that we can combine the
graphs from all the groups at the end of the Exercise. Using your group’s number, consult the following
2
table to see what values you will use for AL orientation and mutational pattern (note: you will use those
same two values in all your runs!).
Group
1
2
3
4
5
6
7
8
9
10
Mutational pattern
( Mut. Corr. = rµ)
0.0
0.0
0.5
0.5
0.9
0.0
0.0
0.5
0.5
0.9
AL orientation
(Stab. Sel. Corr. = rω)
0.0
0.75
0.0
0.75
0.9
0.0
0.75
0.0
0.75
0.9
Because we want to combine the results from all the groups into a single figure, all the group need to
run their simulations using the same basic parameters (i.e., aside from the ones that vary among
groups). Those common values, which you will enter into the Simulator control panel, are listed below:
Parameter Values:
50
Loci
2
Offspring per adult
128
Females in population (Ne=342)
200
Mutations per 1,000,000
2
Traits
varies Experimental generations (from simulation run to simulation run)
5
Mutational variance trait 1 (in hundredths)
49
w2 (trait 1) during stabilizing selection
1000 Initial generations of stab. sel'n
10
Total repetitions
varies Mutational correlation (in hundredths) (according to group number: 0, 50, or 90)
varies Stab. selection correlation (in hundredths) (according to group number: 0, 75, or 90)
49
w2 (trait 2) during stabilizing selection
5
Mutational variance trait 2 (in hundredths)
49
w2 (trait 1) after peak shift
49
w2 (trait 2) after peak shift
varies Selection correlation after shift (hundredths) (according to group number: 0, 75, or 90)
0
Trait 1 optimum shift
0
Trait 2 optimum shift
0
Trait 1 optimum variance
0
Trait 2 optimum variance
1
Interval between calculations of G
1
Generation at which peak shift occurred
3
Peak moves once.
At the bottom of the menu, click the box that says “Move peak once” and the box that says “Begin with
no genetic var.”
At the end of your 5 runs you will have 5 values for MEAN and 5 values for STDEV, a pair for each value
of the number of experimental generations. Email those 10 values to Tyler Heather so that he can make
a combined graph of all the groups’ results: tyler.hether@gmail.com. Include your group number in
your email.
Questions for discussion after the exercise:
 Why do we do simulations to study the stability and evolution of the G-matrix?
 Why are we interested in the orientation of the G-matrix?
 What is the relationship between rµ and the pattern of pleiotropic mutation?
 What is the relationship between rω and the orientation of the adaptive landscape?
 Why might you expect the orientation of the G-matrix to be a compromise between the
orientation of the AL and the pattern of pleiotropic mutation?
 What can we conclude from the combined graph that we have created?
 What besides mutation and selection might affect the orientation of the G-matrix?
 How do our graphed results compare with Figure 3 in Jones et al. (2003)?