[math]~10^{11}[/math], or 100 billion, is a number that floats around. It's usually uncited Carl Haub, or sometimes Tom Ramsey.
Yet Haub's number (108 billion) is an estimate of the number of humans in the last 52,000 years, and Ramsey's (96 billion) is an estimate of the number of humans in the last 1,000,000 years. How can this be? And why do both estimates start with a population of 2, when that's not how populations work? Human population has never been 2.* To be fair, it made their math easier, and their philosophy too, on a half-serious experimental problem, but they took a pass on modeling any pre-Neolithic populations, on the grounds that it wouldn't make much of a difference anyway.
Even if they hadn't taken this pass, their numbers would be different. Both used benchmark years (e.g. 1750 had 795 million people, 1800 had 969 million people) and interpolate the growth in between by using the population growth equation [math]N(t)=N_0e^r^t[/math]. However, Haub's choice was to multiply the birth rate for each year times the population for each year and Ramsey's was to use calculus to get the total number of person-years lived and divide by life expectancy.
Haub's number is much higher, even for just the last 2000 years (62 billion to Ramsey's 48 billion, both updated to 2014), because it assumes a much greater number of infant deaths, especially in the early years. But this doesn't explain the long tail of the growth curve, not even visible on the chart below.
![]()
Wikimedia: El T (Public domain)
It's not that there was no one around in the Paleolithic... the demographers have just taken a pass on an essential definition. What do we mean by human?
Let's follow Ramsey's method back to a few possibilities, all of them arbitrary of course. If we update to 2013, using a life expectancy of 60, Ramsey's method gives 97.5 billion, but 19.6 billion of these are in the -1,000,000 to -9,000 period. Let's work with 97.5 billion - 19.6 billion = 77.9 billion since 9000 BCE, when agriculture was really starting to lift populations in small regions of the world.
If we start with human effective population size and accept a very high estimate of the Toba bottleneck [Ambrose-PDF], i.e. "10,000 reproductive females (Takahata et al., 1995; Klein et al., 1993;
Erlich et al., 1996; Sherry et al., 1997)." the total population in -71,000 could have been something like 30,000. According to Ramsey, "the total person-years from A to B is [P(B)-P(A)](B-A)/{Ln[P(B)
So ((7,500,000-30,000)(-9000
Without doing Haub's interpolations, but instead allowing for what his birth rate method does: push the life expectancy down to ~16, we can add to Haub's 107 billion since 8,000 BCE. and 5.2 billion from then back to Toba. That gives 112 billion and counting.
Yes, not too much of a difference from the handwave, but you can take this calculation back to human-chimpanzee divergence if you're willing to keep guessing on population sizes. Do we reach a trillion hominoids?
The significance is that both numbers are enormous. They are enormous largely because most of the people who have ever lived never became adults. Haub answered the question to address the common saying (incorrect) that more people are alive today than have ever lived (we are at about 7% given his assumptions), but if we're just counting adults over 15, there are 4.4 billion alive today, which might be a fifth of the adults who've lived in the last 2,000 years. This is not unexpected, as so many adults being alive is what has fueled our exponential growth!
* The Young Earth Creationist number could still be about 100 billion, given this belief in an antediluvian population of 9 billion, with no pre-Noah checks on exponential growth.
Yet Haub's number (108 billion) is an estimate of the number of humans in the last 52,000 years, and Ramsey's (96 billion) is an estimate of the number of humans in the last 1,000,000 years. How can this be? And why do both estimates start with a population of 2, when that's not how populations work? Human population has never been 2.* To be fair, it made their math easier, and their philosophy too, on a half-serious experimental problem, but they took a pass on modeling any pre-Neolithic populations, on the grounds that it wouldn't make much of a difference anyway.
Even if they hadn't taken this pass, their numbers would be different. Both used benchmark years (e.g. 1750 had 795 million people, 1800 had 969 million people) and interpolate the growth in between by using the population growth equation [math]N(t)=N_0e^r^t[/math]. However, Haub's choice was to multiply the birth rate for each year times the population for each year and Ramsey's was to use calculus to get the total number of person-years lived and divide by life expectancy.
Haub's number is much higher, even for just the last 2000 years (62 billion to Ramsey's 48 billion, both updated to 2014), because it assumes a much greater number of infant deaths, especially in the early years. But this doesn't explain the long tail of the growth curve, not even visible on the chart below.
It's not that there was no one around in the Paleolithic... the demographers have just taken a pass on an essential definition. What do we mean by human?
Let's follow Ramsey's method back to a few possibilities, all of them arbitrary of course. If we update to 2013, using a life expectancy of 60, Ramsey's method gives 97.5 billion, but 19.6 billion of these are in the -1,000,000 to -9,000 period. Let's work with 97.5 billion - 19.6 billion = 77.9 billion since 9000 BCE, when agriculture was really starting to lift populations in small regions of the world.
If we start with human effective population size and accept a very high estimate of the Toba bottleneck [Ambrose-PDF], i.e. "10,000 reproductive females (Takahata et al., 1995; Klein et al., 1993;
Erlich et al., 1996; Sherry et al., 1997)." the total population in -71,000 could have been something like 30,000. According to Ramsey, "the total person-years from A to B is [P(B)-P(A)](B-A)/{Ln[P(B)
So ((7,500,000-30,000)(-9000
Without doing Haub's interpolations, but instead allowing for what his birth rate method does: push the life expectancy down to ~16, we can add to Haub's 107 billion since 8,000 BCE. and 5.2 billion from then back to Toba. That gives 112 billion and counting.
Yes, not too much of a difference from the handwave, but you can take this calculation back to human-chimpanzee divergence if you're willing to keep guessing on population sizes. Do we reach a trillion hominoids?
The significance is that both numbers are enormous. They are enormous largely because most of the people who have ever lived never became adults. Haub answered the question to address the common saying (incorrect) that more people are alive today than have ever lived (we are at about 7% given his assumptions), but if we're just counting adults over 15, there are 4.4 billion alive today, which might be a fifth of the adults who've lived in the last 2,000 years. This is not unexpected, as so many adults being alive is what has fueled our exponential growth!
* The Young Earth Creationist number could still be about 100 billion, given this belief in an antediluvian population of 9 billion, with no pre-Noah checks on exponential growth.
