In many theories on the social and cultural evolution of human societies, the number and density of people living together in a given time and region is a crucial factor. Because direct data on past demographic developments are lacking, and reliability and validity of demographic proxies require careful evaluation, the topic has been approached from several different directions. This paper provides an introduction to a geostatistical approach for estimating prehistoric population size and density, the so-called Cologne Protocol and discusses underlying theoretical assumptions and upscaling transfer-functions between different spatial scale levels. We describe and compare the specifics for farming and for foraging societies and, using examples, discuss a diachronic series of estimates, covering the population dynamics of roughly 40 kyr of European prehistory. Ethnohistoric accounts, results from other approaches—including absolute (ethno-environmental models) and relative estimates (site-numbers, dates as data, etc.) allow a first positioning of the estimates within this field of research. Future enhancements, applications and testing of the Cologne Protocol are outlined and positioned within the general theoretical and methodological avenues of palaeodemographic research. In addition, we provide manuals for modelling Core Areas in M ap I nfo , A rc GIS, QGIS/S aga and R. This article is part of the theme issue ‘Cross-disciplinary approaches to prehistoric demography’.

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