The gharial (Gavialis gangeticus) is IUCN Critically Endangered — real river sanctuaries in India and Nepal collect wild eggs, incubate them and release ("head-start") hatchlings to boost recruitment. This companion turns that conservation programme into the population model conservation biologists actually use: logistic growth combined with an Allee effect (small populations struggle to find mates, so per-capita growth falls, not just total growth), human-driven mortality, and a direct restocking term:
dN/dt = r·N·(1−N/K)·(N/(N+A)) − m·N + R
r = nest-survival-driven intrinsic growth rate
K = habitat carrying capacity (river-stretch quality)
A = Allee threshold (~40 gharials — below this, mate-finding fails)
m = poaching / net-bycatch mortality
R = sanctuary head-start hatchlings released per year
The equation is integrated with 4th-order Runge–Kutta at a fixed sub-step for stability. Watch what happens at the extremes: raise poaching without raising head-start releases and the Allee term drags a small population toward extinction even though K is large; raise releases enough and a population below the Allee threshold can be pulled back into self-sustaining growth — exactly the argument for active head-starting programmes rather than habitat protection alone.