The most appropriate choice for describing a real-world simulation that calculates the population of caterpillars on trees over the course of a specific year would be a simulation.
Simulations are used to model complex systems and can incorporate various factors like growth rates, food availability, and environmental conditions affecting caterpillar populations over time.
If the calculation is done at discrete time intervals (e.g., every month), then calling it a discrete model could also be appropriate, but in the context of your question referring to a simulation of the population over time, simulation is the best fit.