Math 4600, Homework 10
1. In the model for random genetic drift in a population of bacteria, consider the case when each cell has
4 plasmids. In the original cells we introduce half of the plasmids of type P and half of the plasmid of type
Q, so p02 = 1. Iterate to find what will be the distribution of plasmids in the population after 50 generations.
This phenomenon was first observed experimentally and it was hypothesized that the plasmids interact so
that they cannot be picked up into the same cell. Your result shows that the separation of plasmid types
can happen simply as a result of random plasmid transfer.
2. In the sickle cell anemia model, consider 2 different situations: a society with strong genetic counseling
(γ = 0.9, α = 0.1, β = 0.1) and a society in tropics where carrying a sickle cell allele makes people less likely
to die from malaria (γ = .2, α = 0.1, β = 0.4 and also see below).
a) Explain why this choice of parameters fits the word description of each society
b) What will happen to disease in each population in the long run (use cobwebbing by hand)?
c) How will the model change if individuals with hh genotype are sterile (cannot reproduce)?
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