PROBLEM SET 8
SIMULATION OF MICROEVOLUTIONARY PROCESSES
The purposes of this assignment are to study the effect of selection and/or
mutation on a large randomly mating population and the possible effect of population size
on variation of gene frequencies in small populations.
PART I: Effects of micro-evolutionary forces on genotype frequencies. You will create
a spreadsheet model to explore the effects of selection and mutation on genetic structure
of populations. Assume a trait is controlled by two alleles (a and A) at an autosomal
locus with the initial gene frequency of "a" being r and that of "A" being (1-r); W1, W2,
and W3 are the relative fitness values for aa, aA , and AA genotypes; and m is the forward
mutation rate of A to a and n is the reverse mutation rate of a to A. The initial allele
frequency of a is obtained from genotype frequencies:
T
rS
2
where S is the frequency of aa, T the frequency of Aa, and U the frequency of AA.
Selection and mutation act on the allele frequency of the next generation as follows:
TW2
 SW1
2
rG1 
 (1  m  n)  m
W
where
W  SW1  TW2  UW3
The genotype frequencies in the next generation assume random mating:
S G 1  rG21
TG 1  2rG 1 (1  rG 1 )
U G 1  (1  rG 1 ) 2
Your spreadsheet model should calculate the initial gene frequency of “a” from the initial
genotype frequencies. Set the relative fitness values of the three genotypes (W1, W2, and
W3), and the mutation rates (m and n) as constants. The spreadsheet should show
genotype and frequency of the “a” allele from at least 100 generations.
1. Show that your predicted genotype frequencies will achieve Hardy-Weinberg
equilibrium in one generation in the absence of selection and mutation.
2. Show the effect of variation in genotype fitness on allele and genotype frequencies.
At a minimum, obtain results for W W2>W1 and W2>W3 and for W3<W2 and W3<W1
or W1<W2 and W1<W3. What is the effect of mutation on the steady-state obtained?
3. Assuming that W1=0 and both W2 and W3 are 1, show that the ultimate steady-state
frequency of allele “a” is a function of the mutation rates. Find this function.
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PART II. Random genetic drift. Random genetic drift can be simulated by using a
Monte-Carlo approach. You will create a second model (using Visual Basic) that
simulates effects of random mating in finite populations. For each individual, you first
randomly select a genotype for each parent and then the allele contributed by each parent.
The sampling is repeated for each individual in the population for as many generations as
desired. The following six assumptions will facilitate model building:
1. The model describes only single locus, 2 allele genetics systems, (i.e. three genotypes,
aa, Aa, and AA, with frequencies of S, T, and U;
2. No selection occurs;
3. Genotypes of the next generation are determined only by the genotypes of the present
generation;
4. Number of offspring per generation is constant;
5. Mating is random; and
6. Genotype frequencies are equal for males and females;
Let N be the number of offspring per generation. The number of parents is thus 2N. For
2N random numbers, determine the genotype by the following convention:
For random number R, if R is equal or less than S, then the genotype is aa. If R is less
than S+T, then the genotype is aA. Otherwise the genotype is AA for a heterozygote
parent (aA), another random number must be selected to choose the allele. If R is less
than 0.5 then the allele is A.
The Visual Basic model should accept variable population size and should
continue until either 100 generations have elapsed or the frequency of “a” reaches 0 or 1.
Plot frequency of the "a" allele with time for population sizes of 10, 20 and 30
individuals. Repeat the drift simulation three times to find the average time required for
fixation to occur as a function of generation size. Finally create a plot of average time to
fixation versus population size for a range of sizes of 10 to 100 individuals.
SUBMIT:
1. An Excel file with:
Models for Part I and II and their outputs (10 points).
Two plots: One plot of the allele frequencies under genetic drift and a second plot
of time to fixation as a function of generation size (10 points).
3. A discussion of the relative effects of micro-evolutionary forces and genetic drift on
variation in genetic structure of populations. The discussion must include reference to the
required analyses (1 to 3) in Part I. (20 points).
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