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:
  • The black (melanic) population would be based on the MM, MM' and Mm genotypes.
  • The molted (insularia) population would be comprised of the M'M' and M'm genotypes.
  • The white (typical) population is the mm genotype.

Be sure to assign a separate loss fraction to the darkly mottled insularia as a function of the soot index. Also, adopt predation assumptions that are suitable for a moth whose coloring is intermediate between the melanic and typical moths. Run the new model with the soot index increasing over time. How do the new results compare with the results from the model with only three genotypes?