I don't know of any correlation between urban environment and serial killers. I think a much more significant trend has been the increase in mobility in American society. while I do not believe that this necessarily has increased the number of serial killers, it has probably allowed the organized (more sociopathic versus psychopathic) serial killers to operate longer before capture. As for the connection between hunting and decreased level of serial killing, I also know of no connection.
Correlations I do know of in serial killers: As children, they tend to do two or more of the following; set fires, torture animals, continue to wet beds late in childhood. The first two are thought to relate to a fascination with power, destruction, and a disregard for others. That reminds me of another large factor in the make-up of a serial killer, depersonalization of the victim. There is a slighter correlation between serial killers and abuse in the home (i.e., several serial killers come from backgrounds of neglect and/or violence, but only very, very few people raised in neglect and/or violence ever become serial killers). Serial killers tend to be fantasy driven, starting out with a violent fantasy through which they feel powerful, over time the fantasy builds, becoming more elaborate. The serial killer will reach a point where imagining is no longer enough, so they begin to act out their fantasy, often starting with simulated activity, then moving on to animals. If not stopped, they continue to increase the level of violence and the type of target evolves. This is both because the serial killer gains in sophistication through practice and finds that he needs greater levels of violence and/or more difficult targets to gain the same thrill. Oftentimes they will make the switch from animals to humans, starting with assaults, then serial rapes, then finally murder. Also, they may start with children and work up to adults.
Interestingly, recent studies have suggested that violent crime is not related to urban vs rural differences, socioeconomic status, or ethnic background, but rather the values and sense of family within neighborhoods. In those neighborhoods where people know each other, where it is considered the responsibility of all adults to look out for the neighborhood kids, these were the ones with the lowest violent crime rates. The main study showing this was one done of the area in and around Chicago.
Also, I would suggest that it is not the frequency or severity of punishment which most strongly effects crime rates, but rather the certainty and consistency of punishment. Few people commit crimes with the expectation of being punished (with the exception of those who do it as some sort of protest or statement).