A Genetics Study of the Interactions of Malaria and Sickle Cell Anemia

Sickle cell anemia is caused by a mutant form of the gene coding for a subunit of the hemoglobin protein. Consider the dominant (normal) hemoglobin allele, N, and the recessive (sickle cell) allele, S. Persons with sickle cell anemia are born a with homozygous recessive pair, SS, and did not always live to a reproductive age (though life expectancy now averages to be age 40). People with homozygous dominant pair, NN, are not effected by sickle cell, nor are people carrying the heterozygous pair, NS or SN. But heterozygous persons do carry the lethal recessive allele and can potentially pass it on to their children. It is assumed here that children born with sickle cell anemia do not reproduce.

As it turns out, the defective allele that causes sickle cell anemia also helps protect it's carriers from malaria. Having the sickle cell trait (the heterozygous pairing) appears to indicate a partial resistance to malaria. The model seen below is inspired by the paper, "A Study of Malaria and Sickle Cell Anemia: A Hands-on Mathematical Investigation" by Rosalie A. Dance and James T. Sandefur. In it, we assume that

• A fixed percentage of dominant heterozygous individuals die by malaria each generation.
• None of the children born with sickle cell anemia will reproduce.
• People are not aware of carrying the sickle cell trait.
• Reproductive adults in the population at generation n are the only ones who bear children for generation n+1.
• Probabilities of a child in generation n+1 receiving a dominant allele, S, are
  

  q(n+1) = (number of dominant alleles in the reproductive adult population at generation n)/(number of alleles in reproductive adult population at generation n)

• Probabilities of a child in generation n+1 receiving a recessive allele, S, are
  

  q(n+1) = (number of recessive alleles in the reproductive adult population at generation n)/(number of alleles in reproductive adult population at generation n)

The model above was generated from a Stella model using the Stella2Java page at The Shodor Education Foundion, Inc.'s website