But that won't shape history, unless these people are also having children. If atheism coincides with having <2 children, it will only be a series of disconnected blips in statistics.
The point is that if they influence other people's children into being atheists too, then the atheist section of the population grows.
If your argument is that an entirely atheist population would eventually die out altogether (having no other children to convert) then I misunderstood, but still that an equilibrium will be reached.
Furthermore, it seems plausible that conversion to a group depends positively on the dominance that group (e.g., more opportunities to be converted as you interact with random others in daily life).
So all else being equal (or unknown), then my money's on the group with the highest birth rate.
I was thinking that "children" may be a function of total population. At least below some threshold people may have more kids than they would otherwise out of a sense of "duty", or the desire for continuation of the species (which seems to be inherent -- people sacrificing themselves to save "the world" usually do it to safe humanity).
If, in reality, people are having children out of a sense of duty to save the world from extinction due to underpopulation then I'm wondering why I didn't get the memo.
Though I think I would need a proper simulation now to see if it works out as I imagine it to work out... :)