Your phrasing implies the SAME PEOPLE are in the top 1% each year, which is not the case. And implies that what happens to a cohort also happens to everyone WITHIN that cohort, which is also not the case.
Lastly, we don't have income numbers for "people", we have it for "households". (The "top 1%" contains significantly more than 1% of the people.)
Or it contains less than 1% of people if the average household size for the top 1% is smaller than the average household size for the lower 99% (which it most likely is; wealthier people have fewer children on average).
I don't believe that's the case. At least not if we're using income as a proxy for wealth. Arranged by income, wealthier households in general tend to be larger households.
It's well established that the "top 20%" by income contains more than 20% of the earners - lots of dual-income couples - and also contains more than 20% of the people; the "bottom 20%" contains less than 20% of the earners and people. Seems to be true for 1% as well. If you want to check, there's a nice table of household size by income here:
http://en.wikipedia.org/wiki/Household_income_in_the_United_...
Of course, my point still stands: just because it's 1% of households does not necessarily mean that it's >1% of people (it may very well be, though).
Globally, I've seen references for years about high birth rates in poor countries, with (anecdotal?) indications that having multiple children was a requirement if you were going to have someone to take care of you in your old age. I suspect that also ties in heavily with youth mortality rates - you may have multiple children in hopes that some of them will actually make it through.