Anyone ever trace the population growth of bacteria in a certain amount of medium will see it.After a phase of exponential growth, the population slows itself down and eventually collapse when most cells die from lack of nutrient and buildup of waste.
Unfortunately this is true for most life forms on earth. Every individual maximize its own probability of leaving more offspring at the expense of other individuals of the same species (more precisely, it is the genes that together build the body that do this kind of business).
So far I only heard one species (relax, I am not talking about human) which seems to resist this potentially self-destructive trend of living, for unknown reason(s) this species seems to mentain a very low rate of growth even when there is plenty of resource and no appearent pressure from predation and disease.