Population of Rome, Continued

Another question often pondered when people discuss the population of ancient cities is: what was the average life expectancy? The formula for computing the average expectation of life is pretty simple:

AverageExpectationOfLife = SumOfTotalYearsLived / TotalIndividualsRecorded

The above formula is basic enough, but Tim G. Parkin, author of Demography and Roman Society, points out the rub:

The simple equation...may often produce what appears to be a realistic figure for average life expectancy, but when ages at death are sorted into age groups (say, 0-1 years, 1-9, 10-19, etc.), serious problems become evident. That infant mortality (i.e., deaths in the first year of life) is grossly underrepresented in the tombstone records has long been recognized; clearly infant deaths, even when burial took place, went largely unrecorded, or at least any such records have not survived in large numbers.

...in other words, infant mortality skews the number so heavily that one thinks of the average lifespan as being low, but people surviving past childhood have a good shot at living much more reasonable (by modern standards, anyway) lifespans. This book also contained some eye opening information on Roman demographics, and it seems the same uncertainty surrounding the estimation of water abounds.

Another interesting point discussed in the book is the ratio between sexes; Beloch and previous authors (Carcopino's Daily Life in Ancient Rome: The People and the City at the Height of the Empire., for example) assumed an equal sex ratio. The evidence put forth by Parkin suggests otherwise, although he makes it quite clear that even his evidence may be off:

Another very striking feature when considering the thousands of epitaphs collected is the preponderance of males over females. If we assume for the moment that in reality the sex ratio over all age groups was approximately equal, this means that in our sample three males were commemorated for every two females...It is true that there is some other evidence...that suggests that males really did outnumber females in certain periods of antiquity.

Another question: how many children did Roman families have? And were the Romans generally monogamous, or did males sometime take multiple wives? The latter question was answered with relative ease: the Romans were monogamous, and generally frowned on polygamy. The former is perilous. Given an average life expectancy of 25 years, a gross reproductive rate of over 2.5 is required to require a stationary population. In other words, each woman needs to bear 2.5 daughters, or about five children. More than that would be population growth; less would be decline. That said, Parkin brings up many issues with estimating Roman family size:

• It was known how may children were born (or often only sons), but not how many survived to adulthood.
  
• Large families may be mentioned because they were abnormal, skewing modern perceptions.
• Daughters often remained anonymous or unmentioned.
• Ancient authors rarely show any demographic interest in average family size.

Through Roman Egyption census records, the average size of households was calculated to around six, including parents and slaves.

Based on the information Parkin brings up, it seems like it should be possible to refine Beloch's

The Population Of Rome

Determining the population of Rome is a rather tricky issue. It's been much debated, and the estimates vary substantially depending upon who's numbers you look at. The research also tends to focus on a relatively narrow window of Roman history (46 BC to AD 15), and tends to focus on a subset of the overall population: recipients of the corn dole. Beloch's 1886 paper, Die Bevölkerung der griechisch-römischen Welt, is the starting point of discussion surrounding the corn dole.

The corn dole (sometimes referred to as the grain dole) was a handout by the Roman government to citizens of Rome. The number of people who received the dole varied, but research shows it varying between 150,000 to 300,000+. The dole started in 123 BC by Gaius Gracchus, and in 58 BC Publius Clodius Pulcher made it completely free. Beloch used the number of qualified male citizens who received the dole as a starting point for estimating the population of Rome. Based on this, he then estimated the number of dependent women, children, and slaves. He also estimated the number of foreigners in the city as well. This resulted in a figure of ~800,000 people inhabiting Rome.

As a verification of the above estimate, Beloch estimated the grain consumption of his computed population and compared that with estimates of the total amount of grain flowing into Rome each year. Here is a table from Gerda De Kleijn's book, The Water Supply Of Ancient Rome - City Area, Water, and Population, which shows the years of the dole and number of recipients:

TODO scan table

There are several issues with this, and especially so when attempting to reconcile the figures with Rome's water supply. For starters, the narrow window of data points is particularly troubling: Beloch's data spans 60 years, but aqueduct information spans in excess of five hundred. Superimposed on our previous graphic of Rome's water supply, it's easy to get a sense of just how small the window really is:

TODO UPDATED GRAPHIC




Another question often pondered when people discuss the population of ancient cities is what the average expectation of life was. The formula for computing the average expectation of life is pretty simple:

AverageExpectationOfLife = SumOfTotalYearsLived / TotalIndividualsRecorded

Here is a graph showing how much the water capacity in Rome increased over time. The y-axis is in quinariae, and the x-axis is time:



...the above numbers were computed using Blackman and Hodge's figures. Notice that this graph is similar to the one I previous posted that tabulated totals in Excel. The big difference with this graph is the x-axis is appropriately scaled with respect to the aqueduct's construction date.

In the perfect world, I'd have enough data to correctly taper each of the horizontal lines, clip out sections where the aqueduct was incapacitated or otherwise non-functional, etc. But it isn't a perfect world, so I have to settle for the above. (which for all intents and purposes isn't that bad)

I recently reviewed another paper by H. Chanson, Hydraulics of Roman Aqueducts:
Steep Chutes, Cascades, and Dropshafts, which had a totally different approach to estimating water capacity. Chanson actually evaluated archaeological evidence to determine the hydraulic flow in ancient Roman aqueducts. His findings are quite interesting: "maximum" flow for the nine major aqueducts was 1,013,960 cubic meters per day. Adding in the Traiana and Alexandrina (I guess there's enough evidence to find their hydraulic potential), Rome was supplied with 1,148,960 cubic meters, per day. The graph for the data tabulated in Chanson's paper looks like so (in this graph, the y-axis is cubic meters per day):



Chanson's data also makes me think that Grimal's data is probably based on hydraulic potential rather than Frontinus' records. And this is probably fine. One interesting thing about these graphs is regardless of the magnitude of the units, they look pretty similar. As in, the overall progression of water flow into Rome is pretty obvious; the overall magnitude seems to be of contention, but not the fact that it A) increased, and B) increased by some proportional amount.

One important thing to note with Chanson's data is that this is the maximum capacity, so it gives us a well-defined upper bound for the aqueduct's delivery potential. However, I doubt the aqueducts were ever running at capacity, and it's probably safe to say that it was common for them to run at half-capacity (or less) during dry months (being spring fed means the water source wasn't constant). So the estimates around ~600,000 cubic meters per day still seem more reasonable to me.

I've also recently been reviewing sources on population; I'll be posting more about that very soon.