Index

Handout for the Department Meeting 19990419

Paine, Richard R. and Henry C. Harpending (1998) Effect of sample bias on paleodemographic fertility estimates. Am. J. Phys. Anthropol., 105: 231-240.

Possible problems in demographic reconstruction from skeletal remains -> 4 causes of bias

1. culture-based biases in mortuary behavior or in other behavioral factors such as warfare
   
   • The hill-grave cemetery of the Hallstatt (early Iron Age) period in central Europe mostly consists of adult males of higher socioeconomic status, around the prince's burial hill.
   • Norris Farms #36 in the Illinois Valley had greater numbers of young adult deaths than expected, which were caused by chronic warfare.
2. taphonomic processes
   
   • Subadult's bones are smaller, lighter, and less calicified than adult's, so less likely remain as fossils.
   • Walter et al. (1988): Mission La Purisima, California: burial record contained 32% as 18 years old or younger, but skeletal collection only contained 6% 18 years or younger.
3. archaeological recovery
   
   • Adult's bones are usually moved from primary (casual) burial to second (residential) grave, but subadult's are sometimes degraded before redeposition. That's partly why bones from archaeological sites are mostly adults.
4. age estimation methods (to cause underestimation of older adults)
   
   • Standard method of age estimation uses 1) pubic symphysis, 2) auricular surface, 3) cranial suture closure. It causes discrepancy of estimated ages from those of the model life table, extremely in age over 45 (eg. Table 1). There also is the "reference population influence".

Object:

to what extent the biases mentioned above contribute to distorting fertility estimates?

Methodological basis:

Required condition of skeletal series: 1) actual demographic rates, 2) patter and extent of biases are known. Such samples are not available. -> computer simulated skeletal series.

Simulation:

Brass's logit system⁽¹⁾ -> spline interpolation -> the risk of a person age x dying before age x+1 as dx = (l_x -l_x+1)/(l_x) -> expected number of death by age in stable population as e^-rx(l_x - l_x+1) -> constructing cumulative risk of death by age -> generating random number in [0,1] for each individual to determine one's death age. -> 180 simulated skeletal samples of sizes 50, 100, 250 (the results were only given for the cases of 250).

Base condition:

the same life expectancy, expanding (r=0.01, CBR=31), stationary (r=0, CBR=23), rapidly declining (r=-.01, CBR=16). 60 simulations.

Bias inclusion:

1) age-at-death estimation as methodological bias; in 60 simulations, age at death of all individuals over 40 were altered as Table 1. -> Fig.2

2) infant underenumeration as archaeological bias; in 60 simulations, 50% of all children 4 years of age or younger were removed (there is no reliable basis about the value 50%)-> variation in total population -> Fig.3

Results and Discussion:

1) overestimation of fertility and birth rates due to age estimation bias increases with true CBR increasing; if the best-fitting model to the Sunwatch Village had CBR of 56 (Fig. 1), the actual CBR might be 40-45 ( 20%).

2) 50% infant underenumeration depresses both fertility and CBR by 20-25%. To utilize this result, adequate estimation about loss of infant underrecovery is necessary.

3) "Unbiased" estimates based on best-fit West model raised 4.72% lower CBR than true value, which reflects small-scale difference of mortality shape between two models.

4) Methodological bias may be controllable, but infant underenumeration is more serious problem because there is quite a few studies to quantify that, and one possible approach is integrated archaeological strategy, including estimation of population growth, population density, cultural settings, warfare, and epidemic diseases.

1. Y(a)=+Y_s(a), q(a)=exp(2Y(a))/(1+exp(2Y(a)), where Y_s(a) is the logit of age-specific mortality.