It's worth noting that in the current version, babies are born and people die of old age *where you're playing* -- so, for instance, babies are born in the fortress you're currently playing, and people who are old enough to die of old age will do so immediately on entering the map of the fortress you're currently playing or, in adventure mode, immediately upon your adventurer entering the map they inhabit.
Of course, that basically means "things are static as long as you stay away from them", and "people die more than they are born". Throw in the fact that only human sites (and uninhabited abandoned player fortresses) exist in adventure mode in the current version and you've got a handful of young dwarves being born as long as the player keeps fortresses running and a lot of humans dying once the player has played long enough that most of the humans are old. It's very weird.
And, of course, positions in civilizations are generally not replaced (except for the caravan members and diplomat who currently are new each year because they're erroneously fired upon leaving the fortress map; but these are currently unimportant except in fortress mode anyway), so the little cycle of life there is doesn't matter much in the long run to the civilizations. Not that the civilizations do anything else in the long run either.
That will be changing in the next release also, with civilizations continuing to grow and wage war at least to some extent and in certain circumstances, historical figures having children outside of where the player is playing, historical figures dying outside of where the player is playing, and new people being appointed to positions so the civilizations can carry on. It's not as complete as it sounds, but what's in there should at least work, enough of the different needed prerequisites are in there for there to be a basic supporting framework for whatever else Toady starts making civilizations do during play that they've done before during worldgen.