BIOL 2040 Lecture Notes - Lecture 7: Allele Frequency, Aviary, Warfarin
27 Apr 2018
School
Department
Course
Professor
Lecture 7 - Evolutionary Change at the DNA Level
February 6, 2018
5:46 PM
Sample question:
The 'A' allele is dominant, and produces a phenotype which allows rats to be resistant against
warfarin. The 'a' allele is a recessive gene, and it is not resistant against warfarin.
Frequency
W (fitness)
AA
0.5
0.8
Aa
0.4
1
aa
0.1
0.3
What is the allele frequency? Is the population in HWE (Hardy-Weinberg equilibrium)? What is the
mean fitness? What is the equilibrium frequency of the A allele?
Allele frequency: f[AA] + (1/2)f[Aa] = 0.5 + (1/2)(0.4) = 0.7 = p
q = 0.3
Is the population in HWE?
p2 = 0.72 = 0.49
2pq = 2(0.7)(0.3) = 2 x 0.21 = 0.42
q2 = 0.32 = 0.09
These values are pretty close to HWE, so we can consider it that the population is in
HWE.
What is the mean fitness (W-bar)?
W
Product (frequency x W)
AA
0.8
= 1 - t, t = 0.2
0.4
Aa
1
0.4
aa
0.3
= 1 - s, s = 0.7
0.03
0.83 = W-bar (mean fitness)
p* = equilibrium allele frequency of A
= s/(s+t) = 0.7/(0.7 + 0.2) = 0.7/0.9 = 0.7778
There is a stronger selection against the 'a' allele than the 'A' allele. It makes sense that the 'A'
allele would have a higher allele frequency at equilibrium.
Kettlewell's Experiments
• Are Pepper moths cryptic? How well is the camouflage?
o He placed a moth on a tree, walked away and recorded the distance when he couldn't see it
anymore. He repeated this many times with both morphs, in both polluted and unpolluted
sites.
o He could see the typica (light version) most of the time in polluted areas, but rarely saw the
carbonaria (dark version) in polluted areas.
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o He couldn't see the typica at all in unpolluted areas, and saw the dark version most of the
time in unpolluted areas.
• Do birds eat moths? Do they eat moths selectively?
o If birds ate them selectively:
• Camouflaged moths were less likely to be eaten - better chance of survival
• Non-camouflaged moths would be instantly picked off
o Both forms of moths were released into an aviary - all moths on the wrong background
(exposed/visible) were eaten, while 45% of the moths on the correct background
(camouflaged) were eaten
• Mark-release recapture
o Recapture rate is seen as fitness level - if they get recaptured, they survived
o Polluted area:
• More percentages of dark forms were recaptured
o Unpolluted area:
• More percentages of light forms were recaptured
• A fair amount of work was put in to measure selection, and then to implement the theory.
• Scientific criticism
o Do moths rest of tree trunks?
• If oths do’t aturally rest o tree truks (if it's ot their natural environment), they
are over-exposed to predation
• But Kettlewell used the same method in both forests (polluted and unpolluted) so any
over-estimation of predation would be the same - qualitative difference remains
Effects of Migration: Geographical Clines
• Objection: proportions of melanics never reached 100%
• Observation: male moths fly more than 2.5km each night - migration!
• Mark and recapture areas were set up around the areas where the moths were placed back onto
trees
• If it was selection alone, allele frequency of dark form is higher than selection+migration
o Migration homogenizes allele frequencies (brings the them closer to 0.5)
o Selection diverges the populations
Decline of Melanism Following Population Control
• Decrease in pollution resulted in dark forms decreasing - light forms become more common
• Using migration rates and fitness, we can model and estimate the decline of dark forms - it
matches closely with the actual observable decline
Summary
• Short version is oversimplified - details reveal more complexity (in the real world, all four
evolutionary forces operate)
• Variation existed before selection
o Likely a mutation-selection balance
• Variation is heritable
o Experimental crosses reveal that it's one single gene, but with multiple alleles
• Selection drove allele frequency change
o Many mark recapture experiments match
o Theoretical calculations predicts accurately
o Changes are seen over time
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