Each trophic level is modelled as a single well-mixed body-burden compartment. A lipophilic contaminant enters an organism directly from water (gills/surface, bioconcentration) and — for consumers — from its diet, and leaves at a first-order elimination rate:
dC_i/dt = k_water,i·C_w + k_diet,i·η·C_(i-1) − k_e,i·C_i
C_i = body-burden concentration at trophic level i (µg/kg)
C_w = contaminant concentration in the water (µg/L)
k_water = direct uptake rate constant (largest for algae, ~0 for top predators)
k_diet = dietary uptake rate constant
η = dietary assimilation efficiency (0–1)
k_e,i = elimination rate, scaled down at higher levels
(bigger, fattier animals clear lipophilic toxins slower)
Each step is integrated exactly for the current source term: C_i(t+Δt) = C_ss + (C_i(t) − C_ss)·e^(−k_e·Δt), with C_ss = source/k_e — the true steady state that level would reach if conditions held constant.
- Biomagnification happens because two things move in opposite directions up the chain: dietary intake concentration rises (level i eats level i−1), while elimination rate falls (larger, higher-fat predators metabolise and excrete the contaminant more slowly). The compounding of both effects is what produces the classic order-of-magnitude jump from plankton to top predator.
- Trophic magnification factor (TMF) is the geometric-mean ratio of concentration between adjacent levels — TMF > 1 means the contaminant is biomagnifying up the web, exactly as observed for real persistent, bioaccumulative, toxic (PBT) substances like methylmercury, PCBs and legacy organochlorine pesticides (DDT).
- Organism colour encodes body-burden concentration on a blue→yellow→red scale, shared across all four levels, so you can watch the same water-borne dose intensify as it climbs the food chain.