Ecological Energy Pyramid — 2D Cross-Section of the 10% Trophic Rule

Pyramid Controls

Trophic transfer efficiency η 10%

Producer input E₀ (kcal/m²/yr) 20,000

Trophic levels shown 5

Particle flow speed 1.0×

Live Readouts

Energy reaching top level

Lost as metabolic heat

Max sustainable levels

Energy per Level

How it works

Every trophic transfer loses most of the incoming energy to respiration (metabolic heat), incomplete digestion, and unconsumed biomass. Only a small fraction — the trophic (ecological) efficiency η — passes to the next level. Lindeman's Rule sets η ≈ 10% as a rough ecosystem average (real values range ~5–20% depending on taxa and ecosystem):

E(n) = E₀ · η^n

E₀   = producer energy input (kcal m⁻² yr⁻¹)
η    = trophic transfer efficiency (fraction, e.g. 0.10)
E(n) = energy available at trophic level n

Because loss compounds multiplicatively, a chain of 5 levels at η=10% retains only 0.01% of the original energy (a 10,000× dilution) — which is why food chains rarely exceed four or five levels: beyond that point there is not enough energy left to support a viable population of a new predator.

η slider — sets the fraction of energy that survives each transfer; the pyramid narrows faster at low η and flattens out at high η.
E₀ slider — sets how much energy producers fix at the base (varies hugely by biome: rainforests and estuaries sit near the top of the range, deserts and open ocean near the bottom).
Levels slider — how many trophic levels are rendered; a level whose energy has fallen below the 1 kcal m⁻² yr⁻¹ viability floor is drawn dim and grey.
Rising particles are individually sampled: each one either survives a transfer (green, continues climbing) or is consumed as heat/waste at that boundary (flares orange-red and dissipates) — the aggregate ratio of survivors to losses converges on η exactly as the formula predicts.
The lower chart plots E(n) on a log scale across levels — a straight declining line is the visual signature of the exponential decay E₀·η^n; drag the pyramid to pan, scroll/pinch to zoom.

Energy climbing a level Lost as heat / waste

drag to pan · scroll to zoom

Energy per level (log scale)