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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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Hist umn 2f 7ermccaa

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


Hist umn 2f 7ermccaa

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.”

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Hist umn 2f 7ermccaa

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).

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Why not quasi stable or dynamic models

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??

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Why not quasi stable or dynamic models cont d

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)

30.44 [0.19, 0.52]

40.43 [0.19, 0.49]

50.51 [0.19, 0.52]

60.47 [0.17, 0.49]

70.39 [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)

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Hist umn 2f 7ermccaa

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.

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2a fertility has big effects on age structure of deaths e 0 20 grr 2 3 4 5 6

2a. Fertility has big effects on age structure of deaths e0 = 20, GRR = 2, 3, 4, 5, 6

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2b fertility offers a target for curve fitting e 0 50 grr 2 3 4 5 6

2b. Fertility offers a target for curve-fitting e0 = 50, GRR = 2, 3, 4, 5, 6

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2c mortality offers no target at all e 0 20 30 40 50 grr 3

2c. Mortality offers no target at alle0 = 20, 30, 40, 50, GRR = 3

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2d mortality effects on age structure are imperceptible e 0 20 30 40 50 grr 4

2d. Mortality effects on age structure are imperceptiblee0 = 20, 30, 40, 50, GRR = 4

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3a hazard rates h t e 0 20 grr 2 5 2 9 3 3 3 7

3a. Hazard rates h(t) e0 = 20; GRR = 2.5, 2.9, 3.3, 3.7

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3b hazard rates h t e 0 20 40 grr 2 5 2 9 3 3 3 7

3b. Hazard rates h(t) e0 = 20 & 40; GRR = 2.5, 2.9, 3.3, 3.7

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3c fitting belleville h t e 0 20 40 grr 2 5 2 9 3 3 3 7

3c. Fitting Belleville h(t) e0 = 20 & 40; GRR = 2.5, 2.9, 3.3, 3.7

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4 when modeling plague or other catastrophes remember lagged effects and that fertility

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

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Conclusions

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

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Thank you rmccaa@umn edu

Thank you. * * * *rmccaa@umn.edu

www.hist.umn.edu/~rmccaa


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