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