Overshoot and Die-Off

In 1944, 29 reindeer were released on St Matthew Island, an Alaskan island with no predators and thick mats of lichen to eat. By 1963 the herd had exploded to about 6000. Then the lichen, which grows painfully slowly and had taken centuries to build up, ran out. The next winter nearly the whole population died, leaving around 42 reindeer. That is overshoot and die-off: a population blows past carrying capacity (K) instead of settling onto it, because the food supply gets consumed faster than it can regrow.

The S-shaped logistic curve assumes a population slows its growth as soon as resources get scarce. Real populations lag behind that signal. Reindeer keep breeding at high rates for a year or two after food has already started thinning, because body condition and birth rates respond to scarcity with a delay, not instantly. By the time births finally slow, the herd is still eating into a shrinking lichen supply, so the population keeps climbing past K. Once the food base collapses, there is not enough left to support even the original K, so the crash overshoots downward too, often to a small fraction of the peak.

This is why populations rarely glide onto K the way the textbook logistic curve suggests; lag time turns smooth growth into boom and bust. The connection forward matters: if the overshoot was severe enough to destroy the resource itself, such as stripping vegetation past its ability to regenerate, carrying capacity does not just get temporarily exceeded. It gets permanently lowered, so the population that eventually stabilizes settles at a new, smaller K than before.