The pest index N follows logistic growth suppressed by a Holling type‑II functional response from the predator (beneficial insect) index P; the predator responds numerically to available prey and decays naturally:
dN/dt = rN(1 − N/K) − aPN / (1 + haN)
dP/dt = baPN / (1 + haN) − mP + I(habitat)
loss/day ∝ k·N (accumulated over the season)
r = intrinsic pest growth rate, K = carrying capacity, a = attack rate, h = handling time, b = predator conversion efficiency, m = predator death rate, and I(habitat) is a steady immigration of beneficial insects that scales with the habitat slider — hedgerows, flower strips and reduced broad-spectrum spraying all raise it in real IPM practice.
- No spraying — biological control is the only regulator; a high habitat value can hold N below damaging levels on its own, low habitat lets pests escape predator control (a predator-prey outbreak).
- Calendar spray — a pesticide application every 14 days regardless of pest pressure, which also knocks back the predator population and can trigger pest resurgence.
- IPM — spray at threshold — the field is only sprayed once N crosses the Economic Threshold (ET), the pest density at which the cost of damage first exceeds the cost of control; this is the actual decision rule used in real integrated pest management.
- Each spray kills ~70% of N and ~30% of P instantly and costs $30/ha, deducted from the season's net revenue.
- Drag the field map to pan, scroll/pinch to zoom — the lower panel plots N(t) and P(t) against the ET line as the season progresses.