Plants feed herbivores, and herbivores feed predators. Change the weather or the animals and watch how everyone is affected.
Run a three-level food chain. Change temperature, rainfall, soil nutrients and populations to see trophic cascades, collapses and cycles.
Explore a Rosenzweig-MacArthur style food chain with saturating feeding rates: top-down and bottom-up control, extinction thresholds and the paradox of enrichment.
Simplified model, not a forecast
Start from a scenario
Predators10.2, steady
Herbivores20.0, steady
Plants67.5, steady
Bars show the average over the last quarter of the run. Plant capacity in these conditions: 96; plant growth rate: 94% of its best.
In the model: Plants, herbivores and predators hold steady: predators keep herbivores in check, and herbivores keep plants below their limit.
In real ecosystems: Real communities are never perfectly still. Weather, disease and many other species keep populations changing, which this model leaves out.
Over 80 years: predators settle at a steady level near 10.2; herbivores settle at a steady level near 20.0; plants settle at a steady level near 67.5.
Sometimes the animals at the top decide what happens below them: fewer predators can mean more plant-eaters and fewer plants. Other times the bottom decides: less rain means fewer plants, and less food for everyone above.
In top-down control, predators limit herbivores, which lets plants thrive; removing the predators can set off a trophic cascade. In bottom-up control, the amount of plant growth, set by climate and soil, limits every level above it.
Top-down effects propagate through consumer-resource links as trophic cascades, while bottom-up effects follow from primary productivity. Because energy is lost at every transfer, low productivity can leave too little energy to sustain a top level at all.
Ecologist Robert Paine removed a predatory sea star from rocky shores and found that the number of species there fell. He later coined the term keystone species for predators with such large effects.Source: Paine, 1966Source: Paine, 1969 Comparing Aleutian islands with and without sea otters showed that otters control plant-eating invertebrates; where otters were missing, grazing increased and kelp beds were destroyed.Source: Estes & Palmisano, 1974
Debated: did wolves restore Yellowstone?
Wolves were returned to Yellowstone in the 1990s, and a 2012 review described trophic cascades in the park over the first 15 years.Source: Ripple & Beschta, 2012 A 20-year field experiment published in 2024 concluded that restoring large carnivores had not restored willow communities along streams on the park's northern range, where the earlier loss of beavers also mattered.Source: Hobbs et al., 2024
Plants (P), herbivores (H) and predators (C) change each year according to these equations, solved numerically in your browser:
dP/dt = r·P·(1 − P/K) − f₁(P)·H dH/dt = e₁·f₁(P)·H − m₁·H − q₁·H² − f₂(H)·C dC/dt = e₂·f₂(H)·C − m₂·C f₁(P) = a₁·P / (b₁ + P) f₂(H) = a₂·H / (b₂ + H)
The feeding rates f₁ and f₂ level off when food is plentiful (a Holling type II response).Source: Holling, 1959 The plant growth rate falls off on either side of an illustrative best temperature of 22 °C. A population that drops below 0.01 is treated as gone, because real populations cannot recover from a fraction of an individual.
| Symbol | Meaning | Value |
|---|---|---|
| r | Plant growth rate at the best temperature (per year) | 2 × temperature factor |
| K | Plant carrying capacity | 160 × nutrients × rain ÷ (rain + 600 mm) |
| a₁, b₁ | Herbivore maximum feeding rate and half-saturation | 3, 40 |
| e₁, m₁ | Herbivore conversion efficiency and loss rate | 0.3, 0.3 |
| q₁ | Herbivore crowding | 0.003 |
| a₂, b₂ | Predator maximum feeding rate and half-saturation | 0.8, 20 |
| e₂, m₂ | Predator conversion efficiency and loss rate | 0.5, 0.2 |
Every constant was chosen so the scenarios show clear, typical behaviors. None was measured from a real ecosystem.
Knowledge check
Knowledge check
The explanations on this page are our own summaries of these sources. Follow a link to read the original; if anything here disagrees with it, the original wins. How we choose and check sources.
Krebs CJ, Boonstra R, Boutin S, et al. (2001). BioScience 51:25-35.
Real population cycles involve food, predators and more; simple two-species models leave much out.
Hastings A, Powell T (1991). Ecology 72(3):896-903.
A three-level food chain model of the same form as our Ecosystem Simulator: logistic plants and saturating feeding rates.
Estes JA, Palmisano JF (1974). Science 185:1058-1060.
Paine RT (1966). The American Naturalist 100:65-75.
Removing a predatory sea star from rocky shores reduced the number of species present.
Ripple WJ, Beschta RL (2012). Biological Conservation 145:205-213.
Hobbs NT, Johnston DB, Marshall KN, et al. (2024). Ecological Monographs 94.
Field experiments questioning how fully wolf reintroduction restored Yellowstone's streamside vegetation.
OpenStax (2018). OpenStax, Rice University.
Free introductory college textbook.
Licence: CC BY-NC-SA 4.0 (linked, not reused)
Rosenzweig ML (1971). Science 171:385-387.
In some models, adding resources makes predator-prey cycles larger and less stable.
Rosenzweig ML, MacArthur RH (1963). The American Naturalist 97:209-223.
Volterra V (1926). Nature 118:558-560.
One of the founding mathematical models of predator-prey cycles.
Holling CS (1959). The Canadian Entomologist 91:385-398.
Introduced the functional response: how a predator's feeding rate saturates as prey become abundant.
Paine RT (1969). The American Naturalist 103:91-93.
Introduced the term keystone species.