Predator-Prey Dynamics
Overview
The Lotka-Volterra equations are among the most famous models in ecology. The logic is deceptively simple: predators eat prey, prey populations crash, then predator populations crash from starvation, and prey bounce back—producing the characteristic cycling pattern that shows up again and again in nature.
Real systems demonstrate these oscillations beautifully. The snowshoe hare and Canada lynx data from Hudson's Bay Company fur records span over a century and show textbook boom-bust cycles with roughly 10-year periodicity. Wolf-elk dynamics in Yellowstone tell a similar story, complicated by the reintroduction of wolves in 1995 and the trophic cascade that followed.
What You'll Do
Set initial population sizes for both predator and prey species, along with intrinsic growth rates, attack rates, and conversion efficiency. Watch the populations cycle on real-time graphs as the simulation runs forward. Introduce perturbations mid-run—a disease outbreak, habitat loss, or a hunting season—and see how the system responds.
You'll also compare your model's predictions to historical data from real predator-prey systems, asking whether the simple Lotka-Volterra framework captures the dynamics you see in the field or whether something more complicated is going on.
Learning Objectives
- Explain the Lotka-Volterra predator-prey model and its core assumptions
- Identify how parameter changes affect cycle amplitude and period
- Compare model output to real population time-series data
- Evaluate the limitations of simple two-species predator-prey models
Background
Alfred Lotka and Vito Volterra independently derived the same pair of coupled differential equations in the 1920s. The prey equation assumes exponential growth in the absence of predators, with a loss term proportional to the product of predator and prey densities. The predator equation assumes exponential decline (starvation) without prey, offset by a gain term that depends on prey consumption and a conversion efficiency parameter.
The model makes several simplifying assumptions: prey have unlimited food, there's no intraspecific competition, predators are specialists, and encounter rates scale linearly with density. None of these hold perfectly in the real world, which is part of what makes this simulation interesting. You can push the model to its breaking point and see exactly where the assumptions fail.
The snowshoe hare / Canada lynx system (Lepus americanus and Lynx canadensis) remains the gold standard for predator-prey cycling. The gray wolf / elk system in Yellowstone provides a more recent and more complex case study, with vegetation feedbacks and multiple prey species complicating the picture.