Introductory Exercises with the Genetics Model

Seven introductory exercises have been designed for students begining their study of genetics. The exercises are organized around the challenge of simulating industrial melanism with relatively minor changes in the existing model.

1. Build and Verify
Build the second model and verify that it generates the behavior shown in Figure 6.

2. Predation Losses Depend on the Soot Index
Introduce a soot index , a model input which will range from 0 to 1. Set the index to 0 to represent conditions prior to industrial development; a value of 1 represents the highly polluted conditions shown in Figure 1. Then define separate loss fractions from bird predation as shown below

white_moth_bird_loss_fr = GRAPH(Soot_Index)
(0.00, 0.1), (0.25, 0.3), (0.5, 0.5), (0.75, 0.7), (1.00, 0.9)

black_moth_bird_loss_fr = GRAPH(Soot_Index)
(0.00, 0.9), (0.25, 0.7), (0.5, 0.5), (0.75, 0.3), (1.00, 0.1)

With the soot index at zero, the white moths are well concealed, so they are exposed to only 10% losses from birds. The blacks, on the other hand, would be highly visible, and they are exposed to 90% losses. If the index moves to 1.0, the opposite extreme, the whites become much more visible to the birds and are exposed to 90% losses. With the index at 1.0, the blacks would be well concealed and experience only 10% losses. Notice that the graphs set the losses for both black and white moths at 50% if the index is at the intermediate value of 0.5.

3. Verify that the White Moths Dominate Under Clean Conditions

Run the new model with the soot index set to zero. The simulation should show the combination of white and black moths reaching dynamic equilibrium with approximately 200 adults (as in the previous examples). But the low loss fraction of the white moths will allow them to predominate. Your simulation should show a ratio of approximately 10:1 in favor of the whites.

4. Simulating Industrial Melanism

Now run the new model over 480 months to simulate a four decade period in which urban pollution gradually changes the soot index from 0 to 1. Turn in a time graph of the size of the black and white adult populations over the 480 month period. Does the model simulate industrial melanism?

5. Range of Possible Results

Review Kettlewell's (1973, p. 135) frequency map of the Biston betularia and its two melanics at 83 locations in Britain. It shows that melanics totally dominated in some cities (especially in the midlands), but they were entirely absent in other areas (like northern Scotland). Suppose we were to assume that the only important difference between these areas is the soot index. Is the model from the previous exercise capable of showing this wide range of population results due entirely to changes in the soot index?

6. Sensitivity to the Bird Loss Fractions

The bird loss fractions from exercise #2 change from 10% to 90% in a simple, linear manner. Review the information on bird predation from field observations (Kettlewell 1973) or from visibility experiments (Weaver and Hedrick 1995, p. 425). Then change the graph functions based on what you learn and repeat the simulation from exercise #4 to learn the importance of your change in the loss fractions.

7. Sensitivity to the Mix of Homozygotes and Heterozygotes

The probabilities in the previous exercises are based on the assumption that the black phenotype is comprised of a 50/50 mix of homozygotes (MM) and heterozygotes (Mm). Change the probabilities to reflect a situation with 25% homozygotes, and repeat the simulation in exercise #4. Then change the probabilities to represent a population with 75% homozygotes, and repeat the simulation. Is the simulated pattern of melanism altered in a significant manner?