Forest Cross-Section Lab: Canopy Light, Mycorrhizal Carbon Network, Deer Browsing and Soil Nitrogen

A slice through a mixed oak and spruce forest. Leaves share the light (Beer–Lambert), fungi trade soil nitrogen for sugar and link the trees, deer eat the understory and the seedlings, and litter feeds the soil. Change one thing and watch the forest answer over decades.

Educational model. Nine plants in a 150 m² plot stand for a whole forest; all rates are illustrative and tuned for a stable mature stand, not fitted to a site. Carbon sharing through fungal networks is real but its size and benefit are debated — here it is a simple source–sink exchange. See “The science”.

Scenario

Environment

Soil fungi

With the network off, plants keep the tax they would have paid to the fungi, but lose both the easier nitrogen uptake and the sugar sharing.

Deer

Live readout

The plants

Network flux: sugar moving through the fungus, positive = received (kg C per year).

Big trees (kg C)

Young trees (kg C)

Understory and deer

Soil nitrogen and fungus

Experiment: does the network keep shaded seedlings alive?

Runs three 40-year forests from the same start: network on, network off, and network on after the old oak is felled. Reports the mean biomass of the four young trees. Network off lets shaded seedlings starve; felling the mother tree also removes their sugar donor but floods the floor with light.

Experiment: how many deer is too many?

Runs 40-year forests at four hunting/predation rates and reports the equilibrium deer density, understory and young-tree biomass.

Independent numerical checks

Also run in Node: node src/check.js (adds the 40-year network-on versus network-off runs).

Controls

Drag / one finger: orbit; wheel / pinch: zoom. Cross-section, Canopy and Soil network move the camera.
Gold dots in the soil are sugar moving along fungal threads from sugar-rich to sugar-poor plants; blue dots are nutrients arriving at the roots.
Speed sets how many model years pass per second.

The science

Light. Each plant has leaf area LA = 0.45 B^0.8 (m², deciduous oaks only in leaf from April to October) and height h = 1.9 B^0.3 (m), with B the structural carbon in kg C [illustrative allometry]. A plant sees the light that survives the leaves of all taller plants: I = I₀ exp(−k Σ LA_above / A), k = 0.5 (leaf-angle factor for randomly oriented leaves), A = 150 m². This is the Beer–Lambert law; the page checks it against a Monte-Carlo ray cast through random flat leaves.

Photosynthesis. P = P_max LA I/(I + I_k) f_W s(t) with a saturating light response, soil-moisture factor f_W = W/(W+0.2) and a seasonal factor s(t). Oaks have a higher P_max; spruce is more shade tolerant (smaller I_k).

Sugar, growth and nitrogen. Each plant has a sugar pool S. dS/dt = P − tax − G − R + F. Growth G = k_g S f_N is limited by soil nitrogen through f_N = N/(N + K_eff); 70 % of G becomes wood, 30 % is growth respiration. Maintenance respiration R = r₀ B^0.75 (metabolic scaling) is paid from S; a plant whose sugar runs out starves. Wood turns over at 0.6 % per year into litter.

Mycorrhizal fungi. Each plant pays a share φ of its photosynthate to the fungus (biomass M). The more fungus, the better the nitrogen uptake: K_eff = K_N/(1 + β M/(M+M_ref)). The fungus also links plants: sugar moves between plants i and j by F_i = κ Σ_j A_ij(c_j − c_i), with c = S/(B + b₀) and A_ij = exp(−|x_i − x_j|/6 m). This conserves carbon exactly (what one plant loses another gains) and, on a complete graph, relaxes the concentrations to their mean at rate nκ/(B + b₀), which the page verifies. Whether real networks move enough carbon to matter for seedlings is still debated; this term is a simple stand-in [model].

Soil. Litter decomposes at k_d f_W releasing CO₂ and nitrogen (C:N 40), plus atmospheric deposition; plants take up nitrogen in proportion to growth (C:N 40). Soil moisture W is rain minus evapotranspiration (proportional to leaf area) minus drainage.

Understory and deer. A Rosenzweig–MacArthur pair: understory U grows logistically with the light that reaches the floor, dU/dt = r U (1 − U/K) I_g/(I_g+0.12) − aUD/(1 + a h U), and deer D grow on what they eat and die or are hunted: dD/dt = e a U D/(1 + a h U) − (m + hunt) D. At equilibrium (without the light factor) U* = m/(a(e − m h)); large K destabilises it into boom-and-bust cycles (the paradox of enrichment). Deer also browse young trees: loss = b D exp(−h_tree/1.2 m) B, so tall trees escape.

Carbon budget. The code tracks cumulative photosynthesis, respiration (plants, fungus, decomposition) and browsing; wood + sugar + fungus + litter must change by exactly the difference. The page checks this closure.

Not modelled. Individual tree positions beyond one transect, seed dispersal, fire, pests, nitrogen fixation, temperature, wolves or other predators (only a hunting rate), and real species parameters. The image of the soil network is schematic: the x-ray roots and threads are drawn on the cut face. Not affiliated with any organisation.