Year 0Sun 0 W/m²GPP 0 MJ/m²/yrLost as heat 0 % of GPPHerbivore transfer 0 %—FPS 0

Drag to orbit, wheel or pinch to zoom. Yellow packets: sunlight absorbed by plants. Green: plants eaten by herbivores. Orange: herbivores eaten by carnivores. Brown: dead matter and droppings going to the decomposers (mushrooms). Red-orange plumes rising: heat, the energy that is lost at every step. The slabs on the right are the pyramid of the chosen quantity.

Meadow Energy Flow: Sunlight to Decomposers, Trophic Efficiency and the Biomass Pyramid

Follow one year of sunlight through a meadow: how much plants capture, how little each step up the food chain keeps, and where the rest goes as heat. Why is the pyramid usually narrow at the top, and when does it flip?

Events

Sunlight and plants

Herbivores

Carnivores

Decomposers

Time

Pyramid

Pyramid of

Logarithmic widths (4 decades)

Live readouts

Stocks approaching the steady state

Missions

Predict: with a flat 10 % transfer at every step, how much carnivore production (MJ/m²/yr) does this meadow's NPP support?

Multiply the NPP by 0.1 twice, then compare with the efficiencies the sliders actually give.

Experiments

Each button solves the steady state for several values (closed form, same model) and reports NPP, herbivore and carnivore production, the carnivore/herbivore production ratio and the herbivore/plant biomass ratio.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom; three camera views.
Presets set every efficiency together. Sliders act at once; the ecosystem relaxes toward the new steady state shown in the readouts. Events perturb the running meadow.
Time scale is simulated years per real second.

The science

Light to GPP. Gross primary production GPP = S · 0.45 · f_abs · ε: annual mean sunlight S (1 W m⁻² for a year is 31.56 MJ m⁻²), the photosynthetically active share 0.45, canopy absorption f_abs and light-use efficiency ε (typically 1 to 2 % in grassland, here a few tenths to 3 %). Plants burn a share r_a of GPP in their own respiration; the rest is net primary production, NPP = (1 − r_a) GPP.

Compartments. Plants P, herbivores H, carnivores C and dead organic matter D, in MJ m⁻² of energy. Ingestion is donor-controlled: herbivores eat a fixed share g_H of the plant stock per year, carnivores a share g_C of the herbivore stock. Of what is eaten, a fraction a is assimilated (the rest is egested to detritus) and a fraction p of the assimilated energy becomes new tissue; the remainder a (1 − p) · intake is respired as heat. dP/dt = NPP − g_HP − m_PP, dH/dt = a_Hp_Hg_HP − g_CH − m_HH, dC/dt = a_Cp_Cg_CH − m_CC, dD/dt = (inflows) − k_DD, and decomposers respire all detritus energy as heat at rate k_DD.

Conservation. At any moment d(P+H+C+D)/dt = GPP − (all respiration), and at steady state GPP equals total heat loss: nothing is created, the energy only leaves as heat (the second law). Both are verified numerically below.

Transfer efficiency (Lindeman). Production of one level over the previous level at steady state is CE × AE × PE: the share consumed, assimilated and turned into tissue. The popular "10 % rule" is an average; cold-blooded animals (p ≈ 0.3 to 0.5) pass on more, warm-blooded animals (p ≈ 0.01 to 0.05) far less because they spend most of their intake on body heat.

Pyramids. The energy (production) pyramid can never invert, but the biomass pyramid can: where plants (phytoplankton) turn over fast, a small stock supports a larger stock of long-lived consumers; try the ocean preset. Steady state in closed form: P* = NPP/(g_H+m_P), H* = a_Hp_Hg_HP*/(m_H+g_C), C* = a_Cp_Cg_CH*/m_C.

Simplifications. Linear donor-controlled feeding (no predator-prey oscillations, no saturation), one species per level, constant annual mean light, no seasons, no nutrient limits, no energy export. All default numbers are illustrative typical values, not measurements of any site; spot-check them before quoting. Animals drawn are scaled from the stocks relative to the default meadow. Assets built with Blender; scene by Three.js.