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When ethologist John Calhoun had lot of rats placed into a small space and allowed them to grow freely, the results were chaotic--cannibalism and dead infants (just to name a few). Thus, overcrowding does not seem like it leads up to anything psychologically good in social behavior. Would people follow in a similar path of disorder? According to life history theory--no.
The influence of density on our psychological mind doesn't deteriorate with crowding; it simply changes. The life history theory is a theory about how animals and people allocate their time and energy on things like growing, mating and parenting. This is largely shaped by the environment that they live in. In a large and lowly populated area, organisms adopt a "fast" life history strategy where they can reproduce more and invest less time with each offspring due to the rich environment. In other words, it's quantity over quality. However, when density kicks up, a "slow" life history strategy is preferred. Here, organisms prioritize quality over quantity. Due to the competitive environment, fewer off-springs are produced and more time and energy is invested in bringing them up to survive.
So, does living in cities induce people to adopt a slow life history strategy? It would certainly make sense given the space constraint and the competition. Research does indicate that yes, it seems that people who stay in high density areas do marry later and have fewer children but were more invested in their education and their children's education. In short-term situations results indicated the same thing. This implies that people do tend to shift towards a slower life history when thinking about increasing population densitites. Yet it is important to note that it does not always lead to a shift in life history. Individual differences also needs to be considered.
Source material from Scientific American