Among the most important variable are the average length of a generation, the number of lifetime births per woman, and the likelihood that a infant born will live long enough to reproduce. The extent to which there is sex specific infanticide or pre-reproductive sex biased mortality and polygamy (or serial monogamy) also influences genetic inheritance of uniparental genetic traits such as mitochondrial DNA (mtDNA) and non-recombining Y-DNA (NRY-DNA or commonly, if not perfectly accurately, just Y-DNA), and of X chromosome linked autosomal genetic traits. An understanding of the extent to which woman have children from multiple men, either due to cuckoldry or sequential relationships (e.g. remarriage of widows) also has some impact on the models.
Often fairly simple models that assume a twenty-nine year generation, steady exponential population growth from the estimated population at time X to the estimated population at the time of the DNA samples taken that lead to the average woman having modestly more than two children who survive to reproduce per lifetime are sufficient for these models. But, better models also informed by absolute effective population size are necessary to understand the impact of factors like population bottlenecks and rapid population expansions, and differential expansion rates of population genetic markers of populations that co-existed at the same time.
Dienekes Anthropology Blog notes a recent paper making an imperfect effort to model the expansion of the predominant Y-DNA clades of Western Europe (a subset of Y-DNA R1b) and of Africa, based upon publicly available datasets. The abstract states the main conclusion
The best-fitting models in Africa and Europe are very different. In Africa, the expansion took about 12 thousand years, ending very recently; it started from approximately 40 men and numbers expanded approximately 50-fold. In Europe, the expansion was much more rapid, taking only a few generations and occurring as soon as the major R1b lineage entered Europe; it started from just one to three men, whose numbers expanded more than a thousandfold.I make an effort to translate the conclusions of the paper on the European expansion of the leading subset of R1b into some of these basic demographic parameters with some back of napkin calculations and references to the literature in a series of comments to the post.
Fertility and Mortality in Premodern Japan
My ongoing analysis has also lead me to an open access paper on fertility and mortality in pre-modern Japan based on an analysis done in 1974 of four village family registries going back to the 1720s.
The paper has a wealth of interesting details. For example, the author notes a statistically apparent systemic falsification of birth dates divisible by five or containing the numbers four or nine, because they were disfavored for superstitious reasons. The village family registries also show clear signs of deliberate suppression of data on infant mortality and infanticide making it an unreliable source for that data point, which, fortunately, is one of the easier to obtain prehistoric data points to obtain from other sources.
The paper also contains a discussion of the use of infanticide and abortion in Tokugawa era Japan as a means of birth control on a widespread basis and widespread deferral of marriage and childbearing to after ages twenty to twenty-two (consistently twenty-two or later in all four villages in all four periods, on average), as means by which Japan started to make the demographic transition associated with industrialization and modernity even before the Meiji period (which commenced 1867). Less than 5.2% of births in the entire data set were to teenagers (half the modern U.S. rate for native born women) and only one out of 779 was to a girl under the age of fifteen. Infanticide in that era was returned to as "returning" the infant in the Japanese language at the time, and may have been practiced particularly frequently with inappropriately early out of wedlock births which may have at any rate been rare. Abortion started to be used as a form of birth control in Japan in the late Tokugawa era.
The percentage of children age one not surviving to reproductive age (twenty-two), was never lower than twenty-five percent, and aside from one time period in one village where it was sixty-percent, tended to hover around thirty to forty percent. If one adds a 15% to 20% infant mortality apart from infanticide, which is typical of the premodern era, one find a likelihood of a newborn infant surviving to reproduce of between 48% on the pessimistic end to 64% on the optimistic end, setting aside outlier periods with survival rates as low as about 32%. Considering that Edo period Japan was probably better off than most pre-modern places as evidenced by a below typical premodern total crude death rate at all four villages throughout the data set, one can establish some reasonable assumptions for demographic modeling purposes:
An assumption that half of children born survive to reproduce in normal times, that two-thirds of children born survive to reproduce in the best of times, and that one-third of children born survive to reproduce in harm times.
While these estimates are crude, they do have the virtue of being based on accurate pre-industrial record keeping rather than modern figures (about 90%-95% of children born now survive to reproduce (the low end including a factor for non-reproduction despite living to reproductive age that was rare in premodern times) with a large share of selective effects in modern times due to generation length and lifetime fertility), although they may be optimistic for earlier Mesolithic, Neolithic and Bronze Age populations. Thus, in normal times, replacement rate reproduction is about four children per lifetime, but just three in good times, and six in bad times.
For one village, that was typical, the average age at the birth of a first child was twenty-two and the average age at last birth was thirty-six (implying a generation length of approximately twenty-nine), implying a quite brief fourteen year period of childbearing, on average, for Japanese women of that era. Age at first childbirth appears to be one of the key indicators for premodern lifetime fertility per woman that would have been within the control of pre-moderns other than infanticide rates.
This implies the odds of a parent losing a child sometime in a lifetime would have been about 80% in good times, 98% in normal times, and 99%+ in bad times. Child mortality risk was higheest before age six and particularly high in the first two years, with the risk falling to close to prime of life adult levels after that point. The odds of a child losing at least one parent before having a child of their own ranged from about 20%-30%., although the odds of losing both parents in that time frame averaged about 2%-4%., with later birth order children obviously at greater risk in both cases.
The data set also nicely illustrates the demographic impact of the Temmei Famine of 1787 which hit central Japan particularly hard, and provides an example of the likely impact of similar events of that magnitude in history and prehistory.
It is hard to tell, however, how much of an impact resource scarcity had on factors like age at first marriage, infanticide rates, and pre-reproductive death rates.
A next step will be to locate papers on onset of menses in premodern times relative to modern times, and between forager and farmer populations in pre-modern times. For most of history, this has happened later, setting a floor on the window of lifetime fertility. I am also looking for more historical data on premodern death rates from childbirth.