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“…can general magnitudes of fertility, mortality and growth be derived from a single recorded age distribution alone?

Calibrating Paleodemography: fertility effects are so strong (and mortality so weak) that stable population analysis gives better results than quasi-stable or dynamic methods * * * Robert McCaa Minnesota Population Center .

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“…can general magnitudes of fertility, mortality and growth be derived from a single recorded age distribution alone?

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  1. Calibrating Paleodemography:fertility effects are so strong (and mortality so weak) that stable population analysis gives better results than quasi-stable or dynamic methods* * *Robert McCaaMinnesota Population Center www.hist.umn.edu/~rmccaa

  2. Popoff and Judson, “Some Methods of Estimation for Statistically Underdeveloped Areas”, in The Methods and Materials of Demography(Elsevier: 2004, 624): “…can general magnitudes of fertility, mortality and growth be derived from a single recorded age distribution alone? “The answer is essentially negative. … “Because past fertility is the dominant factor determining the shape of the age distribution, … a rough estimate of the level of the birthrate may be obtained by the examination of a single age structure.” www.hist.umn.edu/~rmccaa

  3. What’s new??? --that is not already in “Paleodemography of the Americas” (Backbone of History, Cambridge, 2002)? • Quasi-stable and dynamic models (simulated annealing optimization in Bonneuil, forthcoming) • Graphical analysis using “faux” hazard rates, h(t), for both paleo and model populations • Calibration of h(t) and age ratios • When modeling plague epidemics, it is the fertility that has the biggest impact on age structure (birth busts and booms following). www.hist.umn.edu/~rmccaa

  4. Why not quasi-stable or dynamic models? • Quasi-stable (usually means varying mortality): it’s the fertility, stupid! The mortality signal is imperceptible except in extreme conditions. • Dynamic models: Bonneuil’s simulated annealing optimization leads to the “closest path to a stable population”. The best! … but: • Results are heavily dependent on number of age groups • Results range over the entire demographic experience • How would results vary if deposition period was in centuries, rather than years?? Number of skeletons in dozens instead of hundreds?? www.hist.umn.edu/~rmccaa

  5. Why not quasi-stable or dynamic models? (cont’d) Dynamic models (Bonneuil, table 4), fertility: Age groups Coale’s index if(with 95% confidence interval) 3 0.44 [0.19, 0.52] 4 0.43 [0.19, 0.49] 5 0.51 [0.19, 0.52] 6 0.47 [0.17, 0.49] 7 0.39 [0.16, 0.42] • 0.39 [0.19, 0.42] • 0.34 [0.19, 0.42] Range over much of human experience (if = .16-.52) www.hist.umn.edu/~rmccaa

  6. 2. Graphical analysis using “faux” hazard ratesDemographers know:fertility has the biggest impact on population age structure (and on the age distribution of deaths).Next figure shows fertility effects: • Fertility varies from GRR = 2 to 6 (TFR=4-12!) • Mortality is held constant (e0=20 years) • Spread for adults is proportionally large. www.hist.umn.edu/~rmccaa

  7. 2a. Fertility has big effects on age structure of deaths e0 = 20, GRR = 2, 3, 4, 5, 6 www.hist.umn.edu/~rmccaa

  8. 2b. Fertility offers a target for curve-fitting e0 = 50, GRR = 2, 3, 4, 5, 6 www.hist.umn.edu/~rmccaa

  9. 2c. Mortality offers no target at alle0 = 20, 30, 40, 50, GRR = 3 www.hist.umn.edu/~rmccaa

  10. 2d. Mortality effects on age structure are imperceptiblee0 = 20, 30, 40, 50, GRR = 4 www.hist.umn.edu/~rmccaa

  11. 3a. Hazard rates h(t) e0 = 20; GRR = 2.5, 2.9, 3.3, 3.7 www.hist.umn.edu/~rmccaa

  12. 3b. Hazard rates h(t) e0 = 20 & 40; GRR = 2.5, 2.9, 3.3, 3.7 www.hist.umn.edu/~rmccaa

  13. 3c. Fitting Belleville h(t) e0 = 20 & 40; GRR = 2.5, 2.9, 3.3, 3.7 www.hist.umn.edu/~rmccaa

  14. 4. When modeling plague or other catastrophes, remember lagged effects and that fertility… • …has the biggest impact on age structure (birth busts and booms, followed by echoes). • Consider the 1630 plague of Parma (see Manfredi, Iasio & Lucchetti, IJA, 2002) • Death rates • increased 500% in 1630 • 1/2 of normal in 1631 • 1/5 of normal in 1632 • Normal in 1633; 1/2 of normal in 1634, etc. • Birth rates: • Contracted in year 0 by 1/4 • Returned to normal in year 1 • Almost tripled pre-plague frequencies in year 2 • Doubled+ pre-plague in year 3 • Doubled in year 4 • Increased 50% over normal in year 5 • Year 6 & 7 below normal; year 8 normal; 9 = double, year 10 = normal, etc. • Smaller the population the greater the variance and the greater the effects www.hist.umn.edu/~rmccaa

  15. Conclusions • Regardless of method, it is fertility that is being measured—mortality rarely leaves a trace • Therefore, quasi-stable and dynamic models that hold fertility constant and allow only mortality to vary, may be mis-directed. • Point estimates can be deceiving; graphs may provide insight on how tenuous the findings are. • Complex models should be tested against historical datasets, using a double-blind www.hist.umn.edu/~rmccaa

  16. Thank you. * * * *rmccaa@umn.edu www.hist.umn.edu/~rmccaa

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