Producers grow logistically: dN/dt = r·N·(1 − N/K) with carrying capacity K set by sunlight/rainfall. Consumers gain energy via a Holling type II functional response (saturating at high prey density) and lose it to metabolism and competition, so populations cycle — the classic predator–prey oscillation you can see in the chart. A prey-refuge term (prey at low density are hard to find) is what keeps the webs from collapsing — the same stabilising mechanism ecologists saw in Huffaker's 1958 mite experiments. Trophic transfer uses the ~10% rule (adjustable 5–20%): each level keeps only the captured fraction, so an apex predator needs a huge biomass of prey beneath it. Removing a species removes a link: you can trigger mesopredator release (mid-level predator booms after top predator removal) or a trophic cascade right here — try the apex predators and watch them wipe out competitors that shared their prey.