Predator-Prey Oscillations in a Cellular Automaton of Huffaker's Mite Experiment

Predator-prey interactions are commonly modeled using the Lotka-Volterra ordinary differential equations, producing intertwined predator and prey population oscillations.Scientists have attempted to reproduce these oscillations, such as Carl Huffaker and his 1958 experiment with mites and oranges.However, Huffaker was only able to produce sustained oscillations after adjusting his system's spatial factors.Particularly, increased space per orange and increased mite dispersal have a significant impact on achieving predator-prey oscillations.To address and confirm this result, we developed a cellular automaton model of Huffaker's mite experiment.We simplified his system to fit automata criteria, created rules to govern mite dynamics, tested model parameters relating to mite lifetime and fertility, and increased patches per orange and mite dispersal by wooden posts to determine the conditions for successful oscillations.The results of our simulations show that increasing prey dispersal and the number of patches available per orange is sufficient for producing lasting oscillations in our model.Secondarily, we concluded that a certain disparity between reproduction and lifetime parameters for the predators and prey is sufficient for oscillations as well.In conclusion, spatial complexity must be considered when attempting to achieve predator-prey oscillations experimentally.