How big does a population need to be before demographers can ignore individual-level randomness in demographic events?

TL;DR

This study uses microsimulation to determine at what population size individual-level randomness significantly impacts demographic indicators, finding that small populations around 100 are heavily affected, while larger ones of 10,000 are not.

Contribution

It provides empirical thresholds for population sizes where individual randomness can be ignored in demographic analysis, especially relevant for historical population studies.

Findings

Randomness significantly affects populations of about 100.

Effects diminish with increasing population size, negligible at 10,000.

Implications for demographic analysis depend on population size.

Abstract

When studying a national-level population, demographers can safely ignore the effect of individual-level randomness on age-sex structure. When studying a single community, or group of communities, however, the potential importance of individual-level randomness is less clear. We seek to measure the effect of individual-level randomness in births and deaths on standard summary indicators of age-sex structure, for populations of different sizes, focusing on on demographic conditions typical of historical populations. We conduct a microsimulation experiment where we simulate events and age-sex structure under a range of settings for demographic rates and population size. The experiment results suggest that individual-level randomness strongly affects age-sex structure for populations of about 100, but has a much smaller effect on populations of 1,000, and a negligible effect on populations of 10,000. Our conclusion is that analyses of age-sex structure in historical populations with sizes on the order 100 must account for individual-level randomness in demographic events. Analyses of populations with sizes on the order of 1,000 may need to make some allowance for individual-level variation, but other issues, such as measurement error, probably deserve more attention. Analyses of populations of 10,000 can safely ignore individual-level variation.