Niche Overlap & Competitive Exclusion Simulator (2D)

Niche Geometry

Niche spacing Δ 1.20

Niche width w 0.80

Growth rate r 0.80

Carrying capacity K 100

Simulation speed 1.0×

Populations (N / K)

System State

Species surviving

5 / 5

Sim time

0.0

Adjacent niche overlap α (MacArthur–Levins)

How it works

Five species share a single continuous resource axis (e.g. seed size, beak depth). Each species i has a Gaussian resource-utilization curve centred at c_i with breadth w, spaced Δ apart. Their populations N_i follow the Lotka–Volterra competition model:

dN_i/dt = r · N_i · (1 − (Σ_j α_ij N_j) / K)

The competition coefficient α_ij between two species is the overlap of their resource-utilization curves — the MacArthur–Levins formula for equal-width Gaussians:

α_ij = exp( −(c_i − c_j)² / (4w²) ),  α_ii = 1

Niche spacing Δ — how far apart species' resource preferences sit. Wider spacing means less overlap.
Niche width w — how broad each species' diet/habitat tolerance is. A broad generalist overlaps more with its neighbours.
Growth rate r — how fast populations respond to competitive pressure.
Carrying capacity K — the resource ceiling every species is measured against; raising it lifts every equilibrium population proportionally.

This is Gause's competitive exclusion principle: when niche overlap α is high relative to spacing (Δ small or w large), one species drives its neighbours to N≈0. When Δ/w is large enough, α drops and all five species stably coexist at N≈K. The top panel is each species' fixed utilization curve; the middle bar row is the combined resource demand U(x) actually drawn from the environment, colour-blended by who is drawing it; the bottom bars are the live populations. Drag the view left/right or scroll to zoom the resource axis across all three panels.

Species A Species B Species C Species D Species E

drag to pan · scroll to zoom