Ecological Interaction Types Simulator

Interaction Type

Parameters

Interaction strength β 0.40

Species A growth rate r_A 0.80

Species B growth rate r_B 0.80

Live Readouts

Species A Species B

Population A

100

Population B

100

dA/dt

0.0

dB/dt

0.0

Simulated time

0.0 yr

How it works

Every pairwise ecological relationship can be written as a generalized logistic-competition model for two population densities A and B:

dA/dt = rA·A·(1 - A/K) + sA·β·A·B
dB/dt = rB·B·(1 - B/K) + sB·β·A·B

The first term is ordinary logistic growth toward carrying capacity K. The second term is the interaction: β is its strength (this simulator's slider) and sA, sB are its signs, which are exactly what distinguish the five textbook interaction types:

Competition (−/−) — sA=−1, sB=−1. Both species suppress each other's growth (shared limiting resource); strong β drives one toward competitive exclusion.
Predation (+/−) — sA=+1 (A is predator/consumer), sB=−1 (B is prey). Produces the classic Lotka–Volterra oscillation between the two populations.
Mutualism (+/+) — sA=+1, sB=+1. Each species' presence raises the other's growth (e.g. pollinator/plant); both settle above their solo carrying capacity.
Commensalism (+/0) — sA=+1, sB=0. Species A benefits from B's presence while B is statistically unaffected (e.g. an epiphyte on a tree).
Parasitism (+/−, mild) — sA=+1, sB=−1 but the harm to B is damped (×0.35) and A's own growth is capped, modelling a parasite that drains its host without normally killing it outright, unlike a predator.

The equations are integrated with a clamped explicit Euler step (dt capped so the model can't blow up on a slow frame), and each population is rendered as a swarm of instanced spheres in the 3D arena — instance count tracks A and B directly, so the visual density is the population.

Type: Competition

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