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 Q’ 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
(R = 0.9, T = 0.1, S = 0.1) and a society in tropics where carrying a sickle cell allele makes people less
likely to die from malaria (R = .2, T = 0.1, S = 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 bb genotype are sterile (cannot reproduce)?
The precise mechanism by which sickle cell trait imparts resistance to malaria is unknown. Malaria
parasites multiply within red blood cells. Red blood cells in trait-carrier individuals are mostly normal,
but can become sickled in low-oxigen condition. It seems that infestation of a cell may create low-oxigen
conditions and effectively destroy the cell.
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