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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Calibrating Paleodemographyfertility 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
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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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Whats new??? --that is not already in
Paleodemography of the Americas (Backbone of
History, Cambridge, 2002)?

1. Quasi-stable and dynamic models (simulated
   annealing optimization in Bonneuil, forthcoming)
2. Graphical analysis using faux hazard rates,
   h(t), for both paleo and model populations
3. Calibration of h(t) and age ratios
4. 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?

• Quasi-stable (usually means varying mortality)
  its the fertility, stupid! The mortality signal
  is imperceptible except in extreme conditions.
• Dynamic models Bonneuils 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? (contd)

• Dynamic models (Bonneuil, table 4), fertility
• Age groups Coales 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)

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2. Graphical analysis using faux hazard
ratesDemographers knowfertility 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 (TFR4-12!)
• Mortality is held constant (e020 years)
• Spread for adults is proportionally large.

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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
e0 50, GRR 2, 3, 4, 5, 6
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2c. Mortality offers no target at alle0 20,
30, 40, 50, GRR 3
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2d. Mortality effects on age structure are
imperceptiblee0 20, 30, 40, 50, GRR 4
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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) e0 20 40 GRR 2.5,
2.9, 3.3, 3.7
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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

• 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

• Regardless of method, it is fertility that is
  being measuredmortality 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_at_umn.edu