Re: What is the estimated total number of humans that have ever lived?

It is difficult to anchor this sort of problem to any of the traditional 
branches of science. It is the sort of problem that is often tackled by 
geographers, or applied mathematicians, or epidemiologists, or 
statisticians. The fact that your question has been left unanswered for so 
long suggests that it is not a routine and accepted part of any particular 
discipline.

I will have a try at working through such an estimate, explaining the steps 
as I go. I am not an expert on human history and prehistory, or human 
biology and evolution, or matters of that sort at all. I am a chemist, with 
some expertise in mathematical modelling. The figures that I will use are 
"Off the top of my head" -- with a little research into historical census 
figures and other estimates of world population, you may be able to do much 
better.

The first difficulty we run into is that there is no completely clear 
consensus on when we start counting "humans". One view, which I do not take 
seriously, is that we start the count with 2 humans, 6000 years ago, or 
with 8 humans 5000 years ago. Nice firm starting points like those would 
make the count much easier! But the orthodox scientific view is much less 
definite. Do we start counting human with "Homo...", thereby including Homo 
erectus and Homo habilis, or do we wait until we have Homo sapiens? Even if 
we fix a position on this issue, we are left with considerable uncertainty 
as to the actual dates when each of these species emerged, and on the size 
of the early populations. It is difficult to see how we are ever going to 
find evidence from the fossil record that would give us a good fix on early 
population sizes, or complete certainty about dates. However, because 
populations were certainly much smaller in those early days, these 
uncertainties might not have much effect on our final answer.

So to make an estimate, we will divide human history into 3 periods. 

The first period extends from the beginnings of humanity to the close of 
the last ice age about 7000 years ago. For this period there is only a very 
limited fossil and archaeological record of humanity.

The second period extends from about 7000 years ago to about 200 years ago. 
There is a rich archaeological record for the whole period, and a detailed 
historical record for the latter part of it.

The third and final period covers the last 200 years, for which detailed 
census records can give us a very reliable population count for most 
countries.

The main thing that we know about the early human communities is that they 
must have been hunter-gatherers, and somewhat nomadic. So we make estimates 
about such things as how large a population could be supported in certain 
areas, life expectancies, incidence of mortality among newborns, by 
comparison with modern hunter-gatherer communities. It still leaves 
considerable uncertainties. But we can put some sort of limits on the 
population. I think it would be fair to say that humanity began sometime 
between about 100 000 and 1 000 000 years ago, with a more or less stable 
population somewhere between 50 000 and 1 000 000, and that life expectancy 
at birth was probably in the range 15 to 40 years. That gives a lowest 
possible estimate of 

50 000 people x 100 000 years / 40 years per person = 125 million people

and an highest possible estimate of 

1 000 000 people x 1 000 000 years / 15 years per person = 83 billion 
people.

For period 2, we could enquire into a lot of historical detail. But a 
simple model where we suppose that the population grew from about 1 million 
at the beginning of the 6800 year period to 200 million at the end of it. 
The best growth model for this period is probably a simple exponential 
growth.

pop = 1 000 000 x exp( log(200) x t/6800)

If you integrate this over the period, you get 

pop years = 6800/log(200) x (200 000 000 - 1 000 000) = 255 000 000 000 
person years

dividing through by an average life expectancy at birth of 50 years gives

5.1 billion people.

Finally, to look at the third period, a calculation can be made based on 
census figures. I do not know what the current world population is, so I am 
going to assume that it was about 4 billion in 1970, roughly the average 
birthdate of the present population, and that this figure was achieved by a 
steady doubling each 40 years since 1800

pop years = 170/log(20) x ( 4 000 000 000 - 200 000 000) = 215 000 000 000

dividing through by 50 years once more gives

4.3 billion people

To this figure must be added the 6 billion(?) alive today.

The overall result of my (very crude) estimate is

Period 1: between 120 million people and 80 billion people!!
Period 2: around 5 billion people
Period 3: around 10 billion people

And you can see that we sill get nowhere without making some more precise 
guesses and assumptions about period 1. My instinct is that the high figure 
is unrealistic, and that the upper limit is more like 5 billion -- that 
would provide an estimate for the number of people who have ever lived 
between 15 and 20 billion.

I do not think that the detail of the estimate I have just gone through is 
worth very much. But it should give you some insight into the sorts of 
processes you have to go through in doing such estimation, and someone with 
more expertise in human history and a little research effort may be able to 
do much better.