Advanced Exercises with the Genetics Model
Two exercises are provided for student with special interest
in genetics. They challenge you to expand the generality of the genetics
model by treating each genotype in an explicit manner.
1. Simulate Three Genotypes with Stocks
The existing model assigns one stock to the black phenotype and a second
stock to the white phenotype. This approach is easy to understand when thinking
about the color of the moths, but it may be confusing when we think about
the genotypes. Revise the model to make the genotypes explicit. There are
three genotypes, each of which must be simulated by assigning stocks to
the preadult phase and the adult phase:
the mm genotype corresponds to the white moths;
the MM and Mm genotypes corresponds to the black moths.
Revise the genetics sector to simulate random matings among the three populations
and introduce a new set of probabilities to keep track of the three types
of broods. Now, run the new model with the soot index at zero. Do the MM
blacks turn out to comprise 50% of the black population (as assumed in the
previous model--the mondel in the 4th introductory exercise)? How do the
ratios of black to white moths compare with the previous model? Run the
model with the soot index increasing over time. How do the results compare
with the previous model?
2. Simulate Six Genotypes with Stocks
The previous models concentrate on white (typical) moths and black (melanic)
moths, but there is a third phenotype: the darkly mottled insularia (M').
The insularia (M') is dominant to the typical; the melanic (M) is dominant
to both of the other alleles. Expand the previous model to keep track of
the insularia population. You will now have six genotypes, so you will need
six pairs of stocks to keep track of each genotype in the preadult and adult
phases. The phenotype populations may be calculated as converters:
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