|MadSci Network: Science History|
Sorry I've taken so long to give you an answer; sometimes it takes more than a week for us to get you an answer. You asked how we can approximate how many people were on the Earth in "ancient times" (before there were censuses). What you are asking about is historical demography, the study of the history of populations.
I can think of three general ways to estimate the size of historical populations; these are, study of historical records, archaeological study of artifacts, and use of population genetics. I'll describe each of these a little, but I won't go too deep into any one of them. If you have more questions, you can always ask for followups.
First, there are some historical census figures that we can review from large empires that endured for 1000s of years (like the Roman and Chinese empires). These historical empires had to carry out censuses from time to time in order to determine how to tax the people living in them. The problem with these census figures is that they may not be very accurate, but they at least give us some ideas of the scope of the populations that were living under the rule of these empires. The Chinese civilization has thrived for more than 4,000 years, so any surviving census records give us an idea of how the population living in China has grown over time.
If you google "roman empire" census or china dynasty census, you will find plenty of pages that discuss the various merits and utility of relying on these ancient census data.
Second, we can use archaeology to estimate the number of people that could have lived in a given area, based on the artifacts that they left behind (e.g., the number and type of dwellings, or the type of hunting, food storage, food preparation, and agricultural tools that they left behind), the waste-products (trash) that they left behind, and based on the type of resources that were available in that area.
For example, agriculturally-based societies (growing food crops and raising domesticated animals) can generally support larger populations than so-called "hunter-gatherer" societies (that practice only limited domestication, and that migrate), in smaller regions. So, if we see signs of agriculture, domestication, and permanent dwellings, we can conclude that a larger population lived in that area than in an area where we only see signs of temporary dwellings, and seasonal hunting activity.
We also know that some climates and environments are much more able to support large populations than others; this is why many large civilizations develop near sources of fresh water, and why they may collapse when that source of fresh water vanishes or is overused. So, we can evaluate the environment to give us estimates of the capacity for people living under various lifestyles.
For a more concrete example, here is a page that discusses population estiamtes at the Yellow-Jacket Pueblo, and archaeological site in Colorado.
Third, we can use the mathematical tools of population genetics and bioinformatics. For example, we can look at the genes of a modern population, and determine the genetic diversity of that population. The amount of modern genetic diversity in a population can tells us about the size of that population in past generations, using what is called the "coalescent model." The basic idea behind this model is that when there are a lot of people in a population, there will be a greater chance for new polymorphisms (variations in genes) to develop than in small populations. When we measure the number of polymorphisms in a modern population, we can use that measure to estimate how many people there had to have been in the past in order to result in what we see today.
This can be done for any organism, not just for people, and in fact it is being done for everything from cacti to whales. For examples of this sort of work, I went to PubMed and looked for papers with the keywords historical population size estimates. I found this paper:
Roman J, Palumbi SR. Whales before whaling in the North Atlantic. Science. 2003 Jul 25;301(5632):508-10.Here's the abstract from this paper (in blue):
"It is well known that hunting dramatically reduced all baleen whale populations, yet reliable
estimates of former whale abundances are elusive. Based on coalescent models for mitochondrial
DNA sequence variation, the genetic diversity of North Atlantic whales suggests population sizes
of approximately 240,000 humpback, 360,000 fin, and 265,000 minke whales. Estimates for fin
and humpback whales are far greater than those previously calculated for prewhaling
populations and 6 to 20 times higher than present-day population estimates. Such discrepancies
suggest the need for a quantitative reevaluation of historical whale populations and a
fundamental revision in our conception of the natural state of the oceans."
So here, by looking at modern whale populations, we can estimate the size of whale populations before modern whaling industries began.
So, I think that you can see that we have a large number of tools that can be used to estimate the size of historical populations. A researcher who was really earnest about historical demographics would try to use as many of these methods as possible, and since most of us are experts in only one field of study, this means that we usually have to work with a number of other scientists.
If you are really dedicated to learning about this, the best place to start would be PopIndex. This database is maintained at Princeton Univerisity, and puts most of the tools and literature about population research at your fingertips. In particular, take a look at this page on Historical Demography from the PopIndex
A good individual reference to start from might be : Durand, J.D. 1977. Historical estimates of world population: An evaluation. Population and Development Review 3(3):253-296.
Keep asking questions!
Try the links in the MadSci Library for more information on Science History.