Big populations don't go extinct. Small populations do. It's not a surprising finding but it is a significant one.
But why do small populations go extinct?
While the answer is simple to outline the scientific details are complicated. For now, lets stick to the outline version. “Small populations go extinct because (1) all populations fluctuate in size from time to time, under the influence of two kinds of factors, which ecologists refer to as deterministic and stochastic; and (2) small populations, unlike big ones, stand a good chance of fluctuation to zero, since zero is not far away.”
Deterministic factors are those involving straightforward cause-and-effect relations that to some extent can be predicted and controlled: hunting, trapping, destroying habitat, introducing new animals that compete with or prey on existing ones, etc.
Stochastic factors “operate in a realm beyond human prediction and control, either because they are truly random or because they are linked to geophysical or biological causes so obscurely complex that they seem random.” We're talking things like weather patterns, epidemic disease, infestation of parasites, forest fires, etc. Each might cause a downward fluctuation in the population of some species.
In Song of the Dodo, David Quammen gives the following illuminating example.
Think of two species that live on the same tiny island. One is a mouse. Total population, ten thousand. The other is an owl. Total population, eighty. The owl is a fierce and proficient mouse eater. The mouse is timorous, fragile, easily victimized. But the mouse population as a collective entity enjoys the security of numbers.
Say that a three-year drought hits the island of owls and mice, followed by a lightning-set fire, accidental events that are hurtful to both species. The mouse population drops to five thousand, the owl population to forty. At the height of the next breeding season a typhoon strikes, raking the treetops and killing and entire generation of unfledged owls. Then a year passes peacefully, during which the owl and the mouse populations both remain steady, with attrition from old age and individual mishaps roughly offset by new births. Next, the mouse suffers an epidemic disease, cutting its population to a thousand, fewer than at any other time within decades. This extreme slump even affects the owl, which begins starving for lack of prey.
Weakened by hunger, the owl suffers its own epidemic, from a murderous virus. Only fourteen birds survive. Just six of those fourteen owls are female, and three of the six are too old to breed. Then a young female owl chokes to death on a mouse. That leaves two fertile females. One of them loses her next clutch of eggs to a snake. The other nests successfully and manages to fledge four young, all four of which happen to be male. The owl population is now depressed to a point of acute vulnerability. Two breeding females, a few older females, a dozen males. Collectively they possess insufficient genetic diversity for adjusting to further troubles, and there is a high chance of inbreeding between mothers and sons. The inbreeding, when it occurs, tends to yield some genetic defects. Meanwhile the mouse population is also depressed far below its original number.
Ten years pass, with the owl population becoming progressively less healthy because of inbreeding. A few further females are hatched, precious additions to the gender balance, though some of them turn out to be congenitally infertile. During that same stretch of time the mouse population rebounds vigorously. Good weather, plenty of food, no epidemics, genetically it's fine—and so the mouse quickly returns to its former abundance.
Then another wildfire scorches the island, killing four adult owls, and, oh, six thousand mice. The four dead owls were all breeding-age females, crucial to the beleaguered population. The six thousand mice were demographically less crucial. Among the owls there now remains only one female who is young and fertile. She develops ovarian cancer, a problem to which she is susceptible because of the history of inbreeding among her ancestors. She dies without issue. Very bad news for the owl species. Let's give the mouse another plague of woe, just to be fair: a respiratory infection, contagious and lethal, causes eight hundred fatalities. None of this is implausible. These things happen. The owl population—reduced to a dozen mopey males, several dowagers, no fertile females—is doomed to extinction. When the males and the dowagers die off, one by one, leaving not offspring, that's that. The mouse population fluctuates upward in response to the extinction of the owls, a rude signal that life is easier in the absence of predation. Twelve thousand mice. Fifteen thousand. Twenty thousand. But while its numbers are so high it will probably overexploit its own resources and eventually decline again as a consequence of famine. Then rise again. Then decline again. Then …
The mouse population is a yo-yo on a long string. Despite all the accidental disasters, despite all the ups and downs, the mouse doesn't go extinct because the mouse is not rare. The owl goes extinct. Why? Because life is a gauntlet of uncertainties and the owl's population size, in the best of times, was too small to buffer it against the worst of times.
Still curious? Read The Song of the Dodo.