Invasive Species Impact Calculator

This calculator combines two classic ecological models to project both how fast an invasive population grows and how far it physically spreads. Population growth follows the standard exponential model, N(t) = N₀ × e^(rt), driven by your intrinsic growth rate r — invasive species often post unusually high r values (0.3-2.0+) precisely because they've escaped the predators, parasites, and competitors that keep native populations in check. Spatial spread is modeled as radial expansion from an assumed initial circular patch: starting radius is back-calculated from your initial population at an assumed founding density of 10 individuals/km², and that radius grows linearly at your specified spread rate (km/year) — a reasonably standard simplification in invasion ecology for species that expand via a wave-like advancing front. The two models are then coupled through a carrying capacity: population at any year is capped at whatever the currently occupied area could support at 1,000 individuals/km², and occupied area itself can't exceed your total habitat area.

This means population growth can hit a ceiling and plateau once either density or available space becomes limiting, even while r stays fixed — the model doesn't let the population run away to infinity. From this it derives time to full invasion (algebraically solving for when the expanding circle covers the entire habitat area) and population doubling time (ln(2)/r, straight from exponential growth theory). Because both the founding density and carrying-capacity density are fixed assumptions rather than measured inputs, and the model assumes uniform circular spread with no barriers, corridors, or Allee effects, treat the projections as order-of-magnitude planning tools for prioritizing control effort and timelines — not as precise forecasts for a specific real-world invasion, which will follow the actual terrain, dispersal vectors, and control interventions rather than a smooth expanding circle.