Is the fraction of people ever born who are currently alive rising or falling?

Background: Some journalists and demographers have asked: How many people have ever been born? What is the fraction F(t) of those ever born up to calendar year t who are alive at t? The conditions under which F(t) rises or falls appear never to have been analyzed. Objective: We determine under what conditions F(t) rises or falls. Methods: We analyze this question in the model-free context of current vital statistics and demographic estimates and in the context of several demographic models. Results: At present F(t) is very probably increasing. Stationary, declining, and exponentially growing population models are incapable of increasing F(t), but a doomsday model and a super-exponential model generate both increasing and decreasing F(t). Conclusions: If the world's human population reaches stationarity or declines, as many people expect within a century, the presently rising fraction of people ever born who are now alive will begin to fall. Comments: It is curious that nearly all empirical estimates of the number of people ever born assume exponential population growth, which cannot explain increasing F(t).