Quadratic Function Applications

The Biology Project > Biomath > Quadratic Functions > Applications > Population Genetics

Quadratic Functions Applications

Population Genetics

Problem 6 - Find the frequency of the A allele that corresponds to a given mean fitness.

light form of peppered moth

The light (top) and melanic (bottom) forms of the pepper moth (Biston betularia). Photo credit: © Ian Kimber - http://ukmoths.org.uk.

Peppered moths (Biston betularia) have two different forms: a dark (melanic) form and a light (typical) form. The dark allele (M) is completely dominant to the light allele (m). This means that individuals with genotypes MM or Mm will both be dark and thus will appear the same. Peppered moths are a well-studied population genetic example because the frequency of the dark form rose dramatically during the mid-20th century in areas of England that were polluted. This phenomenon is known as industrial melanism. It was hypothesized that the dark form had a selective advantage, and were thus favored in polluted areas because the dark moths were cryptic and less prone to predation.

Suppose that genotypes MM and Mm have fitness values of 1 (i.e. w₁₁ = 1.00 andw₁₂ = 1.00), and genotype mm has fitness value 0.5 (i.e. w₂₂ = 0.50) in a particular area. Let p represent the frequency of M allele and q represent the frequency of m allele. Using the equation for mean fitness,

what value of p corresponds to = 0.80?

A.	p = 1.65
B.	p = 0.84
C.	p = 0.37
D.	p = 0.98
E.	p = 0.27
F.	p = 0.72

This is the final question on population genetics.

The Biology Project > Biomath > Quadratic Functions > Applications > Population Genetics

The Biology Project
Department of Biochemistry and Molecular Biophysics
The University of Arizona
July 2006
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