This is a spatially-resolved mechanistic light-competition model (after Kropff & Spitters, 1991), independently computed cell-by-cell across a 48×48 top-down field grid — a different mathematical approach from the 3D companion sim, which drives its visuals from the empirical Cousens (1985) hyperbola directly. Here the yield-loss number instead emerges from simulating daily canopy growth and light capture:
LAI_c(t), LAI_w(t) — leaf area index, logistic growth
gated by planting density / emergence day
I_tot = I0·(1 − e^(−k·(LAI_c+LAI_w))) Beer's law
share_c = LAI_c·e^(β·h_c) / (LAI_c·e^(β·h_c) + LAI_w·e^(β·h_w))
→ taller canopy overtops and disproportionately
captures light (β sets the overtopping strength)
dB_c/dt = RUE_c · I_tot · share_c (Monteith 1977 RUE growth)
B_c = ∫ dB_c/dt dt over the season, per grid cell
- Weed patchiness: real fields are weedy in patches, not uniformly — the mean density you set is redistributed across several random clusters, and yield loss is the field-wide average of a per-cell simulation, so denser patches lose more locally.
- Emergence timing shifts weed canopy growth earlier or later relative to the crop, changing when weeds first compete for the height-weighted light share — the mechanistic version of Cousens' empirical "critical period" effect.
- Crop planting density raises the crop's maximum leaf area index, closing the canopy faster and capturing a larger light share before weeds can establish — a real density-compensation effect.
- Herbicide/mechanical control scales local weed leaf-area growth down directly, rather than a simple density discount.
The field map shows the actual canopy composition: green cells are crop-dominated, amber are weed-dominated, brightness tracks canopy closure (1 − e−LAI). Whichever canopy is currently taller renders on top, matching what an aerial photo of real overtopping would show.