As the environment or population size changes, the single-species state may cease to be stable, so that small, random disturbances can cause big changes. Like a stick being bent by stronger and stronger forces, something suddenly gives and the stick snaps in two. Why? Because the two-part state is stable, whereas one overstressed stick is not.
A population of organisms is stable if small changes in form or behaviour tend to be damped out; if is unstable is they grow explosively. Theory shows that gradual changes in environment or population pressure can suddenly trigger a change from a stable state to an unstable one.Sudden climate changes are well documented in Earth's geological history. The causes of these sudden climate changes are not well understood, but you have to think that what we have done to the atmosphere is surely tempting fate.