Every green sphere on the meadow is one unit of prey population; every orange cone is one predator. Their counts are not scripted — they are read straight off a live numerical integration (4th-order Runge-Kutta) of the population equations below, so what you see is the model, not an animation of it.
Logistic growth (prey alone):
dN/dt = r·N·(1 − N/K)
Lotka-Volterra predator-prey (logistic-limited):
dN/dt = r·N·(1 − N/K) − a·N·P
dP/dt = b·a·N·P − m·P
- r — intrinsic prey growth rate. Higher r means faster recovery after a crash, but also stronger overshoot past K.
- K — carrying capacity: the population the meadow can sustain indefinitely with no predator. Prey growth flattens as N approaches K (the dashed ring on the ground marks it).
- a — predation rate: how efficiently a predator finds and removes prey. Raising a crashes the prey population faster and starves predators sooner once prey run low.
- b — conversion efficiency: the fraction of consumed prey biomass a predator turns into its own reproduction.
- m — predator death rate in the absence of food.
Switching to Logistic only doesn't delete the predators — it sets their birth term to zero, so the existing predator population simply starves out at rate m while prey settle onto the logistic curve toward K. Switching back to Predator-Prey re-enables the a·N·P coupling and, if predators haven't fully died out, the classic oscillation resumes.
The coexistence equilibrium is the fixed point where both derivatives are zero: N* = m/(a·b), and P* = r·(1 − N*/K)/a. If N* > K, the predator cannot be sustained by the environment at all — it is shown as "n/a" — and the model instead settles at the pure-prey carrying capacity.
R vs K strategies: species with high r, low investment per offspring (many small, fast-maturing young) thrive when populations are repeatedly crashed by predation or disturbance — they exploit the steep early slope of the logistic curve. Species with low r but efficient resource use crowd toward K and outcompete r-strategists once a population is stable near capacity. Try pushing r high with a strong predator, then low with a weak one, to see both regimes.