A new method for estimating growth and fertility rates using age-at-death ratios in small skeletal samples: The effect of mortality and stochastic variation

The common procedure for reconstructing growth and fertility rates from skeletal samples involves regressing a growth or fertility rate on the age-at-death ratio, an indicator that captures the proportion of children and juveniles in a skeletal sample. Current methods derive formulae for predicting growth and fertility rates in skeletal samples from modern reference populations with many deaths, although recent levels of mortality are not good proxies for prehistoric populations, and stochastic error may considerably affect the age distributions of deaths in small skeletal samples. This study addresses these issues and proposes a novel algorithm allowing a customized prediction formula to be produced for each target skeletal sample, which increases the accuracy of growth and fertility rate estimation. Every prediction equation is derived from a unique reference set of simulated skeletal samples that match the target skeletal sample in size and assumed mortality level of the population that the target skeletal sample represents. The mortality regimes of reference populations are based on model life tables in which life expectancy can be flexibly set between 18 and 80 years. Regression models provide a reliable prediction; the models explain 83–95% of total variance. Due to stochastic variation, the prediction error is large when the estimate is based on a small number of skeletons but decreases substantially with increasing sample size. The applicability of our approach is demonstrated by a comparison with baseline estimates, defined here as predictions based on the widely used Bocquet-Appel (2002, doi: 10.1086/342429) equation.