Download Lab 02 – Selection and mutation Introduction Mathematical models

Lab 02 – Selection and mutation
Introduction
Mathematical models and computer simulations are important tools in biology. Such
approaches range from simple (like the ones you will be using to explore evolution, here)
to complex. Here, we would like you to use computer simulations how mutation, migration
and selection affect allele frequencies, and hence the evolution of a population.
Please download Allele A1 from this site:
http://faculty.washington.edu/herronjc/SoftwareFolder/AlleleA1.html
AlleleA1 allows you to view the allele and genotype frequencies at the end of a simulation.
It also models one population at a time - if you need to see the results of several
simulations, you will need to press “run” several times, use “auto” graph lines and “reset” or
“clear” to return to starting conditions. Using tab will move you between the input boxes.
You can change the y axis to show alleles and genotype frequencies. You can also change
the scale on the x axis. Use the program to answer the questions below.
In Windows, you can use a few tricks to copy the image from your simulations to a
document file:
1. Click on the active window
2. Press ALT + PrtScrn (alt printscreen)
3. Place cursor in document
4. press CTRL + V.
This is the approach used to copy the images above.
(I don’t have an apple mac, but here are online instructions you can try
http://still-scripts.com/mac-os-x/how-to-create-or-take-a-screen-shot-or-screen-caputrewith-your-apple-computer/)
Questions
1. Hardy-Weinberg Equilibrium
1. After investigating the simulation program to see
how it works, enter the default settings given in the
image to the right. 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 are in equilibrium so long as there is no
selection, no mutation, no migration, and no drift?
(2pts)
Yes – an allele is maintained at a constant frequency when no evolutionary force acts on it.
2. Relative fitness
There are three boxes that let you set the fitness values for the three genotypes. The fitness
values allow you to play with the effects of selection (that is, differences between the
genotypes in survival or reproduction). Setting the values to 1, 0.8, and 0.2, for example, is
equivalent to specifying that for every 100 individuals of genotype A1A1 that survive to
reproduce, 80 individuals of genotype A1A2 survive, and 20 individuals of genotype A2A2
survive.
a. Predict what will happen if you set the fitness values of A1A1, A1A2, and A2A2 to 1, 0.8,
and 0.2, respectively. Then run the simulation with several runs. Was your prediction
correct? Please explain. (2pts)
I personally was surprised at how fast selection acts.
The population is at maximum genetic diversity at an
allele frequency of 0.5. Therefore, all genotypes are
present and there is a high opportunity for selection
b. Now set the initial frequency of allele A1 to 0.01, and the fitness values to 1, 1, and 0.99.
What happens when you run the simulation? Why? Now try fitness values of 1, 1, and 0.95.
Can you explain the difference? (3pts)
Despite a relatively small difference
in fitness, the second scenario
(green: 1,1,0) increases faster. This
is because the frequency of
heterozygotes increases faster in
the population. Since both
heterozygotes and A1A1
homozygotes are favored, there is
more opportunity for selection.
3. Selection on recessive and dominant alleles.
Restore all parameters to their default values, then set the initial frequency of allele A1 to
0.01.
a. Predict what will happen when you try fitness values of 1, 1, and 0.9, then check your
prediction. Now predict what will happen when you try fitness values of 1, 0.9 and 0.9, and
check your prediction. Were your predictions correct? Please fully explain the results (you
can run the two different scenarios on the graphs). (4pts)
blue = 1, 1, 0.9, purple = 1.0, 0.9, 0.9
In the purple scenario, both A1A2 and A2A2
are equally unfit. A1 can only form
heterozygotes when it is at low frequency.
Therefore, there is little opportunity for
selection.
In contrast in the blue scenario both A1A1
and A1A2 are equally fit. As soon as A1A2
appear, they are selected for, increase in
frequency, and then more homozygotes
appear.
b. In Question 3a, when was allele A1 dominant (with respect to fitness) and when was it
recessive? (2pts)
In scenario 1, A1 was dominant
In scenario 2, A1 was recessive, because the heterozygote had the same phenotype as the
homozygote A2A2
c. Which of the following will increase in frequency more rapidly when favored by
selection: a rare recessive allele, or a rare dominant allele? Why? (Try running various
combinations of initial frequencies and fitness values in AlleleA1) (2pts)
A rare dominant allele. As soon as it starts forming heterozygotes, it will be favored by
selection.
d. Which rises to a frequency of 1.0 more rapidly under selection: a common recessive
allele, or a common dominant allele? Why? (3pts)
green = dominant, blue =
recessive
A common recessive allele. If
A1 is dominant, it will always
dominate A2. Therefore, at
high frequencies of A1, A2
will always appear as a
heterozygote – and “hide
out” in this form. It is difficult
to remove it from the
population.
Question 4. Selection in captive populations.
Pacific oysters are introduced from Japan into the Pacific Northwest, where they are
extensively cultured in aquaculture.
Figure 1. Pacific oyster families were
raised in a hatchery, allowed to settle
on cultch and then outplanted in the
marine environment. After a year,
the offspring were sampled and
genotyped. The results report the
relative proportions of offspring
genotypes at a locus scored in
individual Pacific oyster families (112), for which there is a significant
departure (p<0.05) from classical
Mendelian segregation ratios. The
far-right bar labeled “Exp.,” which shows expected genotypes and their Mendelian
proportions.
a. Examine Figure 4, and please explain the results. (3pts)
The AA genotype is at lower frequency than expected in each of the families. Therefore,
there must be selection against this genotype.
b. B is dominant over A. A has a very high frequency in the population, 0.1. Assume that
hatchery conditions allow all larvae to survive. What is the frequency of AA individuals in
the population at this stage? If the hatchery had a population of 1000 individuals, how
many would be AA? (2pts)
Under Hardy-Weinberg:
AA = p2 = 0.12=0.01 therefore, 10 individuals in 1000 will be AA
c. Hatchery managers decide that AA individuals are reducing productivity in their culture
operations and thus reducing their profit margin. If all AA individuals were removed from
the larval population, what would be the fitness values of the three genotypes? Please
explain. (3pts)
AA = 0 AB = 1 BB = 1
The hatchery is allowing the heterozygotes to survive, therefore, they are carriers of the A
allele.
d. Use Allele A1 to predict the long-term effect of active removal on the frequency of the A
allele. Please explain your results. Is removal a viable strategy over a 20 year period, given
that oysters typically reach market size in 30 months and reproduce every three years?
(3pts)
It is highly unlikely that this allele
will be lost over this time frame – the
allele is “hiding out” in the
heterozygote.
e. What else could be done to eliminate the A allele?
Would this be a viable approach? Use a simulation to
illustrate your conclusions. (3pts)
You could also remove the heterozygotes, if you
were able to detect the allele.
However, you might be reducing the genetic
diversity at other loci and cause inbreeding.
5. Selection on homozygotes and heterozygotes
The marine copepod Tisbe reticulata (a small free swimming marine crustacean) was
raised under crowded conditions. T. reticulata has one gene with two alleles, V and M.
Heterozygotes VM have greater survival and more offspring than both homozygotes.
a. The allele V has a population frequency of 0.1. What do
you predict will be the frequency of the allele after 500
generations? Perform a simulation and show whether
your prediction is correct. (2pts)
Neither allele is preferred in the population over the long
term
b. Please explain you results. Toggle between allele and
genotype frequencies. (3pts)
If the genotype A1A2 is the most fit, then it is maintained at a
maximum at an allele frequency of 0.5. In this extreme
scenario, the two homozygotes are selected against as soon as
they appear.
6. Mutation as a mechanism of evolution
There are 2 boxes in AlleleA1's window that let you play with the mutation rate. One
controls the rate at which copies of A1 turn into A2’s; a mutation rate of 0.001 means that
each generation one out of every thousand A1’s turns into an A2. The other box controls the
mutation rate in the other direction. Note that the mutation rate should be a number
between 0 and 1 (why?). If you enter a number outside this range you will get weird
behavior. Return all parameters to their default values, then set the mutation rates to
0.0001 and 0. Predict what will happen.
Were you correct? For any real gene a mutation rate of 0.0001 would be extraordinarily
high. How effective is mutation, by itself, as a force of evolution? (3pts)
The frequency of A1 declines
over time (green).
In a real case scenario (blue),
mutation would not be a
significant force on its own.
7. Mutation-selection balance
Re-examine the case of allele A in oyster populations. Let’s assume that it is caused by a
recessive loss-of-function mutation.
a. Using AlleleA1, return all parameters to their default values. Let A2 represent the normal
allele B, and let A1 represent the loss-of-function allele A. Estimate that the fitness of
affected individuals is about 0.1. Set the fitness values to 0.1, 1, and 1. What is the
frequency of the knockout allele A after 500 generations? Why? (2pts)
The frequency is 0.00222. The allele is
being carried in the heterozygote.
b. The actual frequency of knockout alleles for A in populations is about 0.01. One
hypothesis for the maintenance of this frequency is that new knockout alleles are
continuously created by mutation. With fitness values of 0.1, 1, and 1, how high does the
mutation rate from A2 to A1 need to be to achieve an equilibrium frequency of 0.01 for
allele A? (2pts)
mutation rate = 0.0001
c. The actual mutation rate in gene has been measured. It is high-- about
0.00011. Do you think a balance between mutation and selection is an adequate
explanation for the persistence of knockout alleles at a frequency of 0.01? Pease explain.
(2pts)
Yes – the simulation shows that the allele is being maintained in the population at this level