Given this table of genotypes and average absolute fitnesses: Genotype AA Aa aa Mean # offspring 35 60 30 Compute s, the selection coefficient against AA homozygotes and t, the selection coefficient against aa homozygotes (hint: you need to compute the relative fitnesses to get these) In excel (or by hand on graph paper), draw a graph of this fitness relationship with p (frequency of A) on the X axis and population mean fitness (w-bar) on the Y axis. This can be done by filling in this table using this formula for mean fitness (assuming Hardy-Weinberg proportions) w-bar = wAA*p2 + wAa*2*p*q + waa*q2 where: the w's are the relative fitnesses of the genotypes, p is the frequency of A and q is the frequency of a and filling in this table: p (freq. of A) w-bar (mean fitness) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 Screen capture the graph image and insert it into this word document. If you draw the graph manually, scan it as a .jpg image and insert the image into this word file. Compute the equilibrium value using the formula p* = t/(s+t). Make sure this answer agrees with your graph and your insight on where the equilibrium should be given the relative fitnesses of the two homozygotes, as discussed in the video lecture.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Given this table of genotypes and average absolute fitnesses:
|
Genotype |
AA |
Aa |
aa |
|
Mean # offspring |
35 |
60 |
30 |
- Compute s, the selection coefficient against AA homozygotes and t, the selection coefficient against aa homozygotes (hint: you need to compute the relative fitnesses to get these)
- In excel (or by hand on graph paper), draw a graph of this fitness relationship with p (frequency of A) on the X axis and population mean fitness (w-bar) on the Y axis. This can be done by filling in this table using this formula for mean fitness (assuming Hardy-Weinberg proportions)
w-bar = wAA*p2 + wAa*2*p*q + waa*q2
where: the w's are the relative fitnesses of the genotypes, p is the frequency of A and q is the frequency of a
and filling in this table:
|
p (freq. of A) |
w-bar (mean fitness) |
|
0.00 |
|
|
0.05 |
|
|
0.10 |
|
|
0.15 |
|
|
0.20 |
|
|
0.25 |
|
|
0.30 |
|
|
0.35 |
|
|
0.40 |
|
|
0.45 |
|
|
0.50 |
|
|
0.55 |
|
|
0.60 |
|
|
0.65 |
|
|
0.70 |
|
|
0.75 |
|
|
0.80 |
|
|
0.85 |
|
|
0.90 |
|
|
0.95 |
|
|
1.00 |
|
Screen capture the graph image and insert it into this word document. If you draw the graph manually, scan it as a .jpg image and insert the image into this word file.
- Compute the equilibrium value using the formula p* = t/(s+t). Make sure this answer agrees with your graph and your insight on where the equilibrium should be given the relative fitnesses of the two homozygotes, as discussed in the video lecture.
Step by step
Solved in 5 steps with 2 images
