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

Quadratic Functions Applications

Population Genetics

Problem 5- Find the frequency of the A allele that will maximize the mean fitness of a population.

Suppose there is a gene locus with two alleles, A and S, and suppose further that there is natural selection at this locus. In particular, the fitness values of genotypes AA, AS, and SS are w11, w12, and w22, respectively. If we let p and q represent the frequencies of the A and S alleles, respectively, we define the mean fitness of the population as follows,

Red blood cells from a patient with sickle cell anemia. Photo credit: Courtsey: National Institute of Health.

Overdominance occurs when the heterozygous genotype is most fit. In areas where malaria is prevalent, the genetic disease sickle cell anemia is an example of overdominance, where either homozygote is less fit than the heterozygote. In particular, sickle cell anemia carriers (AS genotypes) have increased resistance to malaria. Individuals affected with sickle anemia (SS genotypes) have high mortality, and individuals that are unaffected (AA genotypes) have no additional resistance to malaria. The fitness values of the three genotypes have been estimated as: w11 = 0.76, w12 = 1.0 and w22 = 0.20 [1].

 

Recall that the Hardy- Weinberg Law states that after one generation of random mating, the frequencies of the three genotypes in the population are given by:

fAA = p2,

fAa = 2pq,

faa = q2.

Using these fitness values and the equation for mean fitness , what value of p maximizes mean fitness?

A.

 

 p = 0.77

B.

 

 p = 1.00

C.

 

 p = 0.50

D.

 

 p = 1.65
E. p = 0.23
F. p = 0.89

[1] Allison, A.C. 1956. The sickle-cell and hemoglobin C genes in some African populations. Ann. Hum. Genet. 21: 67-89.

 

 

 

  

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

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

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