Our model of the delayed auxotrophy system, which acted via thymineless death, first defined a mean number of plasmids in each bacterium and distributed plasmids across the initial population of bacteria according to a standard deviation from this mean value. With each division, a time step that was defined to be one day, some plasmids were lost, with a probability defined in the model. When a bacterium had zero remaining plasmids, it was considered “dead” and removed from the count of total bacteria. Because we did not have time to experimentally determine initial plasmid number and rate of plasmid loss, sensitivity analysis was performed for these values within ranges determined from literature values. The rate of plasmid loss was varied between 0.001% and 50% loss per division, giving the first plot seen above. As the rate of plasmid loss increased, the peak number of bacteria decreased and rate at which the bacterial population decreased rose, as shown by the steeper downward slope after the peak with higher rates of plasmid loss. The initial plasmid number was varied between 40 and 80 plasmids per bacterium, with a standard deviation of 10, giving the second plot shown above. As the initial plasmid number increased, the peak number of bacteria increased and the rate of decrease in the bacterial population decreased.

This model illustrates the relationship between the E.coli population and the zebra mussel population. It utilizes a system of differential equations to calculate zebra mussel population as a function of initial zebra mussel population, zebra mussel growth rate, and rate of zebra mussel death due to the bacteria, which is a function of the total number of bacteria, itself a function of our first model, the delayed auxotrophy system. The value of zebra mussel growth rate was determined from literature values, and the initial population of zebra mussels was taken to be 1000. In the first plot illustrates the general relationship between the changing population of E.coli and the changing population of zebra mussels, for a zebra mussel death rate due to bacteria of 0.00005. However, as we did not have time to experimentally determine the values of this death rate constant, we instead performed sensitivity analysis using a range death rate values. This sensitivity analysis is shown in the second plot, with the large orange peak representing the bacterial population, and the smaller peaks representing the changing zebra mussel population for death rate due to bacteria values ranging from 0.00001 to 0.0005. For smaller death rates, the zebra mussel population decreased more slowly and began to rebound at long times, while for larger death rates, the zebra mussel population decreased more quickly and reached lower values before the bacterial population began to decline, which in turn resulted in a smaller incidence of rebounding zebra mussel population.