In order to breed, couples need their own house, and villagers can live up to their eighties but women only breed until forty. This results in waves of population growth followed by decline as old codgers continue to occupy their old houses, preventing new families from moving in. Even as they die and young couples take to cranking out the bambinos, it takes another ten years for these to get to about twenty years old (don't ask) and become fully functional underlings. Thus, the waves of dieback can grow quite significant, to a third of your population:
In the early years it can actually cost you the game, if you allow your entire population to advance past breeding age. You can shore up your numbers by admitting nomads to your village. Sure, they're uneducated, unhealthy, unequipped and unwashed, but what could go wrong?
Nomads and traders increase the odds of an epidemic in your village, and this bunch apparently hailed direct from Caffa. I didn't even know about that feature until it happened to me and I looked it up but it fits so damn perfectly, yet another example of Banished's elegance. A triumph soured, my attempt to speed my town's recovery turned into an added five-year slump (visible in the first graph, the small spike in the third trough) and ironically the population cycle was finally dampened by a well-placed double epidemic a generation later.
Like an uppercut from a dragon. Look, ma, no cutscenes!