Lifespan:does this idea make sense? why or why not.?

Recently a friend and i chatted about the different lifespans of different species. We noticed that Animals that produce a lot of young usually have shorter lifespans than animals that don't (a rat vs. elephant). The reason for this being, we agreed on, that in order for the next generation to prosper the older generation has to die off thus reducing competition over resources(food,water,shelter etc.), but if the species does not reproduce often, it would have a longer lifespan so it can have more opportunities to make more Does this Idea make sense? another question we wanted to ask was; Is this why humans nowadays have longer lifespans(modern conveniences and diet aside) because we individually produce less offspring than we did say 1000 years ago(due to birthcontrol, the socially inept, etc) If this is a valid theory, than a whole new set of interesting topics can be asked