Population genetics simulations - answers

NOTES:

1) Your responses will not exactly match those I have given below (things are probably phrased differently and I've probably got spelling errors...). Make sure you understand the overall concepts.

2) The material covered in this exercise may appear on the first lecture and final exam. You may be given a set of parameters (PopGen style) and asked to make and explain a prediction concerning allele frequency change over time (graphically and verbally). Alternatively, you may be given simulation output and asked to interpret it.

3) I have included the appropriate figures (dark line only). These were drawn on a computer to the best of my ability and do not exactly match the output from PopGen. Take notice of the general trends in the figure. If you find these confusing, re-enter the parameters in PopGen and consult the figure produced. Clicking on the figure will open it up in another window (quality is probably better).

KEY:

1) the heterozygote has higher realtive fitness than either homozygote

2) more common to a point

3) maintained at some intermediate frequency

4)

5) hopefully. the frequency of allele A should be 0.5 at equilibrium

6) overdominance alone can maintain genetic diveristy in the population (both alleles are maintained at equilibrium)

note: you can figure out what the stable allele frequencies will be at equilibrium for the case of overdominance alone (selection is the only evolutionary force) as follows:

p* = t / (s + t), where p* is the equilibrium frequency of allele A and wAA = 1 + s, wAa = 1, and waa = 1 + t

In this example, s = -0.1 and t = -0.1. Therefore, p* = 0.5

This is the stable equilibrium point. Regardless of initial allele frequencies, both alleles will be maintained in the population at p = q = 0.5

The same equation is useful for the case of underdominance alone. Remember, the resulting p* gives the unstable equilibrium. Which allele fixes depends on the initial frequency of each allele in the population. If the initial p > p*, p goes to 1. If the initial p < p*, p goes to 0. Consult lecture notes III & IV and Chapter 5 of the text, especially box 5.8.

7) wAA < wAa = waa. Therefore allele A is completely recessive and deleterious

8) less common to a point

9) maintained at a really low frequency but not completely lost

10)

11) hopefully. The frequency of allele A should approach but not reach zero.

12) Complete recessiveness of an allele alone prevents the loss of that allele due to selection alone. Because the heterozygote's relative fitness is equal to the homozygote with both beneficial alleles, the deleterious allele is maintained in the population. Loosely put, the deleterious allele "is hidden" from selection in the heterozygous state.

13) change the realtive fitness values. Remember, relative fitness = 1 - s. The strength of selection is positively related to the rate of spread / loss

14) make wAA > wAa = waa

1: Beneficial recessives increase in frequency, deleterious recessives decrease in frequency

2: Beneficial recessives go to fixation (p = 1), deleterious recessives are not lost because of selection alone

15) neutral

16) neutral

17) more common to a point

18) maintained at an intermediate

19)

20) hopefully. Allele A should be maintained in the population at low frequency

21) Mutation from allele a to allele A introduces allele A into the population. Mutation from allele A to allele a introduces allele a into the population. Because there is no relative fitness advantage to either allele, a mutation balance maintains both alleles in the population at an intermediate frequency

22) As the mutation rates get smaller it takes longer to reach an intermediate frequency. With realistic mutation rates, it doesn't look like much is happening!

23) maintained at an intermediate frequency

24)

25) hopefully. The frequency of allele A should be maintained at an intermediate frequency near 1

26) no. allele A is not rapidly fixed. However, at equilibrium it is closer to a frequency of 1 than before.

27) Possibly. Allele A is rapidly fixed in the population when allele a is partially dominant.

28) A completely recessive allele can be maintained in the population because it is "hidden from selection" in the heterozygous state. The heterozygote does not incur a relative fitness cost because it has one copy of the allele. A partially dominant allele is not "hidden from selection" in the heterozygous state. Because the heterozygote does incur a realtive fitness cost, the allele can be lost from the population.

29) Mutation can prevent the loss of a partially dominant, deleterious allele.

30) Theoretically, yes. Realistically, you'd probably never be able to detect this. If the mutation rate is small, the frequency of allele A in the population is nearly, but not exactly, 1 (e.g., p = 0.99999995).

31) The higher the mutation rate, the lower equilibrium frequency of allele A.

32) This may have been confusing because I accidentally wrote "selection differential" instead of "selection coefficient" (was thinking of future lectures...). The point is that you can use the mutation - selection balance equation to make a prediction about the equilibrium allele frequency and then put the appropriate parameters into PopGen and see if it works. It will. For example, try:

wAA = wAa = 1 and waa = 0.5. Therefore, s = 0.5. If we use a mutation rate of 0.05, the equation predicts a q* of about 0.3. Because we know that p + q = 1, p* must be 0.7. Try plugging these relative fitness values and mutation rate into PopGen and see if the equilibrium frequency of allele A is about 0.7.

33) wAA = wAa < waa

34) less common

35) lost

36)

37) hopefully. The frequency of allele A should be at 1 for a while, then quickly fall to a frequency of 0.

38) The population starts fixed for allele A. Mutation is the only force that can introduce allele a into the population. Once allele a is present, it must be in the homozygous state for selection to drive it to fixation (frequency of allele a = 1, frequency of allele A = 0).

39) The beneficial recessive allele spreads to fixation faster in the population. Mutation is still the only force that can introduce allele a. However, because allele a is partially dominant, selection will begin to drive this allele to fixation when it is in the heterozygous state (allele is not "hidden from seletion").

40) completely recessive

41) beneficial

42) lost (notice this question asks about allele A)

43)

44) hopefully. The frequency of allele A should go to zero.

45) maintained at an intermediate frequency

46)

47) hopefully. the equilibrium frequency of allele A should be somewhere between 0 and 0.5

48) Migration maintained genetic diversity in the population (both alleles are present in the population at equilibrium)

49) Allele A is maintained in the population at a lower frequency at equilibrium.

50) Mutation

51) Mutation and Migration --> creative; Selection --> generally destructive (but remember overdominance)

52) nothing. Allele frequencies should not change

53) Dark line assumes an infinite population size. Therefore the population is in H-W equilibrium. The lighter lines have a population size of 1000. Therefore, each is subject to genetic drift.

54) The lighter lines should diverge more from 0.5 and behave more chaotically as the population size is reduced.

55) When the population size gets smaller, the likelihood that allele A is maintained in the population is decreased. Note: Population size does not affect the likelihood of fixation or loss though.

56) destructive

57) somewhere around 80 or 90 generations

58) No effect on the dark like (remember this assumes infinite population size) but the lighter lines (each individual population) appear more random.

59) genetic drift is a lot stronger than selection. The deleterious allele gets fixed quite often!!!

60) Increasing the degree of dominance of allele A increases the likelihood that allele A will be fixed. Notice that drift can still be stronger than moderate selection!

Final note:

There are equations that predict the equilibrium frequency of an allele in a population given population size, mutation rate, migration rate, and relative fitness values. We are not going to concern ourselves with memorizing all these equations (you can always look them up in your text or another reference book if needed). Focus instead on the concepts and generalities covered in this exercise and lecture