Biological Control vs. Pesticide: Pest Population Dynamics

Interventions

Spray selectivity 40% targeted

Pest resistance to spray: 0%

Field Conditions

Pest reproduction rate r 0.25 / s

Population & Yield

Aphids (pest)

Ladybugs (biocontrol)

Crop yield: 100%Damage: 0%

Time elapsed

0.0 s

Sprays applied

How it works

Pest and biocontrol populations follow a Lotka-Volterra predator-prey model with logistic pest growth and density-limited predator mortality:

dP/dt = r·P·(1 - P/K) - a·P·Q
dQ/dt = b·a·P·Q - d·Q - c·Q²/Qcap

P = aphid population, Q = ladybug population, K = field carrying capacity, a = predation (attack) rate, b = prey-to-predator conversion efficiency, d = predator death rate, and the c·Q² term caps predator crowding.

Release Ladybugs — adds biocontrol agents (Q) directly; a slow, self-sustaining, chemical-free response that depends on predators finding enough prey to persist.
Spray Pesticide — an instant kill pulse on both populations. The selectivity slider sets how targeted the spray is: 0% is broad-spectrum (kills pests and beneficials almost equally, wiping out biocontrol along with the outbreak), 100% is a narrow-spectrum/targeted product (kills mostly pests, sparing ladybugs).
Resistance — every spray nudges the pest population toward resistance, permanently reducing that spray's future kill efficiency, exactly as repeated blanket spraying selects for resistant genotypes in the field.
Crop damage integrates pest population above an economic injury threshold over time; yield is 100% minus accumulated damage.

This is the same trade-off real Integrated Pest Management (IPM) programs weigh: biological control is slower and self-limiting but sustainable and resistance-free, while pesticides act fast but degrade over-sprayed and can collapse the natural enemies that would otherwise keep a pest in check.

Crop plants Aphids (pest) Ladybugs (biocontrol)

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Agriculture Pest Control Simulation