Notes
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A note on graphs and computations in this paper. Here I follow the conventions of demography, rather than paleodemography, and use the logarithmic scale on the vertical axis to display death frequencies, percentages or mortality quotients. Asch (1976:40) notes that to the human eye the logarithmic scale seems to minimize differences at higher levels of mortality, but I would reply that the normal scale obscures significant variations at the middle ages, particularly those where age determinations are most reliable and the perdurance of specimens is greatest. Current paleodemographic practice of using the normal arithmetic scale lulls the reader into discounting deviations at the youngest and oldest ages, and ignoring significant deviations at intermediate ages. Second, as recommended by Moore et al. more than two decades ago (1975), confidence intervals are reported for estimates of death rates, and, are displayed in the corresponding graphics. Then, to maintain constant vertical axes in all graphics, lower confidence intervals are truncated at .005 (i.e., an annual death rate of 5 per thousand at the specified age interval), whenever necessary. Fourth, as a matter of convenience, and following paleodemographic convention (Johansson and Horowitz, 1986), model life tables are based on female parameters from the Coale and Demeny series region West (1983). The suitability of alternative models is also discussed below. Fifth, I use STATA's "ltable" function (STATA 1995) to fit observed hazard rates for ages 0, 1, 5, 15, 25, 35, 45, 55, 65, and 75--data permitting--against each of 20 model life tables with gross reproductions ratios (GRR) of 2, 3, 4, 5, and 6 female children (or average completed family sizes of four to twelve children) and life expectancies at birth (e0) of 20, 30, 40, and 50 years (Coale and Demeny 1983). This exceedingly broad range of model populations is considered to take into account all likely combinations of fertility and mortality, thereby avoiding the fatal mistake--common for decades in the history of paleodemography--of modelling only stationary populations. Finally, the mean age at maternity is assumed to be 29 years. Hypothesizing a younger mean slightly inflates hazard rates for model populations compared below.
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The unrepentant, mortality-fixated paleodemographer should recall that the minimal effects of mortality preclude blaming death rates for these peculiar age pyramids--whenever populations are stable. The bulging age structure in paleopopulations (and modern ones for that matter. at young adult ages would generate lots of births (and in turn many deaths in infancy and childhood), which then compensates for the apparent bulge.
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