A group of people stranded on a deserted island, as a matter of common sense, would not be able to have their population grow indefinitely. Space limitations are an obvious limiting factor, but also these people would require food, shelter and potable water in order to survive. The island, it would seem, would have a carrying capacity; it would have a maximum rate of consumption that it would be able to sustain. New technologies may increase this maximum rate somewhat, but only somewhat. The rate of consumption of the population may increase as a result of the growth of the population or as a result of the increased rapacity of the individuals or both. If the needs of the islands population exceeds the sustainable rate of consumption allowable by the islands available resources the results would be the same as those witnessed in every other region of the world plagued by scarcity: the breakdown of social structures, war, famine, etc. Averting social disintegration and maintaining the habitability of the island would require implementing sustainable modes of resource acquisition and consumption and taking steps to avoid runaway population growth before problems arise. In other words the rate of consumption must be kept below the maximum rate allowable by the islands renewable resources.
Granted planets are not islands, but with regard to the use of resources used to provide food, shelter and potable water, an analogy between an island and Earth seems reasonable and illuminating. If so then it would be imperative for the Earth's population to 1) recognize that a maximum rate of consumption exists and 2) to avoid exceeding it by employing sustainable methods for acquiring needed resources and 3) maintaining the Earths population below a critical limit. This would require long term forethought and a willingness to address problems that are not yet felt; two things the human species does not do well (most likely because solving the reoccurring problems in our evolutionary histories did not require these traits).
In my opinion finding solutions to the sustainability problem will be the most difficult challenge the human species has ever faced, primarily because we and our institutions seem to be so ill equipped for these types of problems. In future posts I would like to explore some of the psychological, social, political, and ideological obstacles to successfully meeting these challenges.