The dark disc at the bottom is the environmental reservoir — soil, sediment or water carrying a long-lived ("existential") pollutant such as a PFAS compound. Emissions feed it continuously; unlike ordinary pollutants it barely breaks down, so its half-life is measured in decades, not days. Above it sit four trophic levels — plankton, small fish, big fish and an apex predator/bird — each one absorbing pollutant from the level below it faster than its own body can excrete it. That imbalance is biomagnification: concentration roughly multiplies at every step up the food chain, so the apex predator can end up carrying a load orders of magnitude higher than the water it swims in ever had.
dC_env/dt = emission − ln(2)/half-life · C_env
target(level i) = level(i−1) · biomagnification
level(i) → target(i) (lagged by the organism's own turnover)
- Emission rate — how much pollutant enters the environment each simulated year; the reservoir's long-run level is emission × half-life ÷ ln(2), so persistence multiplies a source that would otherwise look small.
- Environmental half-life — how many years it takes the reservoir to lose half its load with emissions switched off; forever-chemical half-lives can run into decades, versus days or weeks for an ordinary contaminant.
- Biomagnification / step — the multiplier applied at each trophic transfer; a value near 1 means no magnification, values above ~3 approximate what's measured for real persistent organic pollutants moving up aquatic food chains.
- Time speed — how many simulated years pass per real second, since these dynamics only become visible over decades.
Real-world relevance: this is the core reason regulators worry less about a pollutant's raw concentration in water and more about its persistence (half-life) and its tendency to biomagnify — a compound that is diluted to near-nothing in the environment can still reach dangerous concentrations in the tissue of a top predator, humans included.