For the first two questions you will use the web based program Web Popgen (https://www.radford.edu/~rsheehy/Gen_flash/popgen/) to explore some aspects of population genetics .
(1) (15 marks)
Heterozygous advantage. Let wAA = 0.4, wAa = 0.6, waa = 0.3.
(a) Give the relative viabilities if we put wAa = 1.0 (round to two decimal places):
wAA = _ wAa = 1.0 waa = _
(b) Using these viabilities give the predicted equilibrium allele frequency p* using the appropriate equation from the equation sheet.
(c) Starting from an initial frequency p(A) = 0.1, what is the final equilibrium frequency? Also if you now start from p(A) = 0.9, what is the result?
(d) Either copy a plot from Web Popgen or draw a rough figure showing the gene frequency trajectories for both cases, i.e. starting from p = 0.1, and p = 0.9.
(e) Calculate the mean population fitness, , at the starting gene frequencies (p = 0.1 and p = 0.9 ) and at the gene frequency equilibrium (p*)you calculated in part (ii). Note: find the equation for in the notes and use that; it is not on the equation sheet. Therefore what happens to the mean population fitness, , in both cases, as the gene frequencies change from the initial frequencies of 0.1 and 0.9 (i.e. does increase, decrease, not change,etc.)?
(2) (10 marks)
In this question you will explore the balance between genetic drift and selection. In the lecture we introduced the equation s < 1/Ne, which says that if s is small relative to population size then drift will predominate.
You will model selection against a recessive allele with s = 0.01, which means setting WAA = WAa = 1, and Waa = 0.99. Use Web Popgen.
For each population size run the simulation 50 times. Each time start with a population with p = q = 0.5. You can run a maximum of 10 populations at a time. You can vary the number of generations according to population size for clarity.Record the result from each run – as either A or a fixed, and use the total over 50 runs.
Fill in the following table:
Observed number of populations with: Expected number of populations with:
N 1/N A fixed a fixed A fixed a fixed
(a) Give the expected number of populations fixed for the A and a alleles.
Use the equation s < 1/N to deduce what you would expect.
(b) How do the observed numbers differ, or not, from the expected?
What are the reasons for any differences?
(3) (10 marks)
One thousand individuals were typed for two traits determined by two different autosomal loci, each with two alleles (A and a; B and b) with the following the two-locus genotype numbers:
BB Bb bb Total AA 36 48 16 100 Aa 72 96 32 200 aa 252 336 112 700 Total 360 480 160 1000
(i) Determine if each locus is at a single-locus Hardy–Weinberg equilibrium (you do not have to do a statistical test; determine this by eye).
(ii) If not,what would the genotype frequencies be at each locus considered separately?
(iii) What are the expected frequencies of the nine different two locus genotypes?
Put these in the Table below:
f(AABB) = f(AABb) = f(AAbb) =
f(AaBB) = f(AaBb) = f(Aabb) =
f(aaBB) = f(aaBb) = f(aabb) =