http://www.ex-astris-scientia.org/incon ... federation
And it mentions:
The question is, how many humans could there, conceivably, be? When I did calculations for my setting, I used following calculator:Still, with "only" several billion humans (Earth plus colonies) among a trillion, it remains a problem why humans are that dominant in the Federation. Maybe it is just that humans like to travel and to explore that they are seen everywhere.
Now, lifespans etc. were different, since I made up a new species (space vampires, essentially), but point is that population ended with 100 billion within 247 years, and 200 billion in 300 years. I used starting point 6 billion, which Earth had in 1999. Between 1999 and 2349 is 350 years. So assuming 2.5 fertility rate, 30 years first birth, and 120 years human age, there should be some 63 billion humans in the Federation, out of cca 1 trillion - so 6,3%. Fertility rate of 3,0 and 25 years first birth age would push this up to 571 billion, which is a lot. 30 years first birth age would give some 313 billion. All and all, it is not impossible - if still rather unlikely - for humans to be dominant species in Federation. Or else 900 billion casualties referred to in DS9 is a small percentage of populace - assuming 150 species with similar populace, total populace of Federation could be anywhere between 9,45 and 85,65 trillion. Of course, 900 billion math is obvious: 150 member worlds * 6 billion = 900 billion, so think tank was seemingly implying that it would take complete extermination of each species homeworld - but little else - for Federation as a whole to surrender; but this tells little about total population of UFP. Now in World War II Soviet Union - while victorious - took 14,2% casualties. This would seem to suggest maybe 6,34 trillion people in Federation. Using Japan for an upper limit - seeing how it surrendered after "only" two major cities were nuked - it suffered 1,8% of casualties. This in turn would suggest an upper limit of 50 trillion people in Federation.
All and all, numbers are all over the place.
But then again, if we assume that humanity kept following current "progressive" policies, it ought to have gone extinct by 24th century, so YMMV.