I play vanilla df and I've always gotten around 70 migrants with in the first year and a half. Is migrant immigration procedural. I've only played 3 fortresses so far. (because I wait till all the dwarves are dead) Using default settings at 250 years.
Someone, somewhere, will have better detail than me (try the Wiki?), but they are both dynamic in numbers (a greater amount of wealth produced draws more individuals to your fort, quicker, at least until your population cap is unmet or its the 'unstoppable' first few immigrations) and in membership (which individuals turn up with which specialisms, albeit with a bias towards filling 'unfilled' specialisations, hence cries of "Oh no, not another cheesemaker!", or similar, by those who have no interest in a given worker-type and either train up as another job or put straight into the military).
Or so I still think it is, as it may have changed, in one or other major changes to the game engine. But these were definitely tangible 'facts' for me a few major updates ago, and identified by dealing with 'reruns', either from deliberate save-scumming to the.season's end prior to a migrant wave and then an undesirable event that encouraged use of the seasonal save (if I was fixated on something absolutely needing rewinding) or else an unfortunate game-crash and restart to a similar result. Taking the opportunity to ramp up craft-goods production, prior to traders, seemed to trend an increasing number of new arrivals, whilst even with no obvious change to fortress progress/value, one fork of time might have brought a professional armourer, but a subsequent fork just resulted in including him out (and all others one could recall).
Some of the wave-information may be set some time prior to the arrival, some might be.finalised just before the walk onto the map. Again, someone will doubtless have information about current behaviour, which I haven't poked and prodded for a while.