Introduction to the Modeling and Analysis of Complex Systems

19.4. ECOLOGICAL AND EVOLUTIONARY MODELS 455returnelse: # if there are rabbits nearbyif random() < rf:agents.append(cp.copy(ag))def update_one_unit_time():global agentst = 0.while t < 1.:t += 1. / len(agents)update()import pycxsimulatorpycxsimulator.GUI().start(func=[initialize, observe, update_one_unit_time])A typical simulation result is shown in Figure 19.5. The tiny blue dots represent preyindividuals, while the larger red circles represent predators. As you see in the figure,the interplay between prey and predators produces very dynamic spatial patterns, whichsomewhat resemble the patterns seen in the host-pathogen CA model discussed in Section11.5. The prey population grows to form clusters (clouds of tiny blue dots), but if theyare infested by predators, the predators also grow rapidly to consume the prey, leavinga deserted empty space behind. As a result, the system as a whole begins to show dynamicwaves of prey followed by predators. It is clear that spatial distributions of thosespecies are highly heterogeneous. While we observe the periodic wax and wane of thesespecies, as predicted in the equation-based predator-prey models, the ABM version generatesfar more complex dynamics that involve spatial locality and stochasticity. One couldargue that the results obtained from this ABM version would be more realistic than thoseobtained from purely equation-based models.We can further modify the simulator code of the predator-prey ABM so that it outputsthe time series plot of prey and predator populations next to the visualization of the agents’positions. This can be done in a fairly simple revision: We just need to create lists to storetime series of prey and predator populations, and then revise the observe function tocount them, append the results to the lists, and visualize the lists as time series plots.Here are the updated initialize and observe functions:Code 19.18: predator-prey-abm-with-plot.pydef initialize():global agents, rdata, fdata