Testing the 2nd Model

Figure 10 shows the simulated behavior of the second model starting with the same set of initial conditions used in the introductory model. The populations still reach dynamic equilibrium in around eight years, and we still see a total of around 200 adults. But the mix of blacks and whites is much different than before. Figure 6 shows around 175 blacks and only 22 whites.

We now have an 8:1 ratio of blacks to whites even though both the blacks and whites are exposed to the same loss fractions in the preadult stage and in the adult stage of their life cycle. The 8:1 ratio of blacks to whites arises from the random mating and the dominance of the melanic (M) allele.

Figure 6. Simulated behavior of the second moth model.

Discussion: Room for Improvement

The second model does a good job in combining the population life cycle of the two moth populations with the genetics sector. We are now able to simulate the differences in the relative size of the populations due to their genetic differences. In this first test, we observe an 8:1 ratio of blacks moths to white moths. The 8:1 ratio is a logical result of the assumptions adopted so far. But we face three problems with this model:

First, the 8:1 ratio does not agree with observations from the era prior to industrialization. The black moths were certainly not 8 times more prevalent than the white moths. Indeed, the black moths were quite rare in the era prior to industrialization.

The second problem is closely related to the first -- this model does not deal with concealment and bird predation. In its present form, we are not in a position to simulate industrial melanism.

Finally, the model relies on probabilities derived from the assumption that the two genotypes of the melanic phenotype are equally frequent. A more general approach would involve a model with each genotype simulated explicitly.

The collection of exercises challenges you to expand and improve the model to deal with these problems.