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

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.
Comment: 28 pages, 8 figures, 3 tables