Radiocarbon summed probability distribution (SPD) methods promise to illuminate the role of demography in shaping prehistoric social processes, but theories linking population indices to social organization are still uncommon. Here, we develop Power Theory, a formal model of political centralization that casts population density and size as key variables modulating the interactive capacity of political agents to construct power over others. To evaluate this argument, we generated an SPD from 755 radiocarbon dates for 10 000-1000 BP from Central, North Central and North Coast Peru, a period when Peruvian political form developed from 'quasi-egalitarianism' to state levels of political centralization. These data are congruent with theoretical expectations of the model but also point to an artefactual distortion previously unremarked in SPD research. This article is part of the theme issue 'Cross-disciplinary approaches to prehistoric demography'.Hunter-gatherer population growth rate estimates extracted from archaeological proxies and ethnographic data show remarkable differences, as archaeological estimates are orders of magnitude smaller than ethnographic and historical estimates. This could imply that prehistoric hunter-gatherers were demographically different from recent hunter-gatherers. However, we show that the resolution of archaeological human population proxies is not sufficiently high to detect actual population dynamics and growth rates that can be observed in the historical and ethnographic data. We argue that archaeological and ethnographic population growth rates measure different things; therefore, they are not directly comparable. While ethnographic growth rate estimates of hunter-gatherer populations are directly linked to underlying demographic parameters, archaeological estimates track changes in the long-term mean population size, which reflects changes in the environmental productivity that provide the ultimate constraint for forager population growth. We further argue that because of this constraining effect, hunter-gatherer populations cannot exhibit long-term growth independently of increasing environmental productivity. This article is part of the theme issue 'Cross-disciplinary approaches to prehistoric demography'.Demographic processes directly affect patterns of genetic variation within contemporary populations as well as future generations, allowing for demographic inference from patterns of both present-day and past genetic variation. Advances in laboratory procedures, sequencing and genotyping technologies in the past decades have resulted in massive increases in high-quality genome-wide genetic data from present-day populations and allowed retrieval of genetic data from archaeological material, also known as ancient DNA.  https://www.selleckchem.com/products/Docetaxel(Taxotere).html  This has resulted in an explosion of work exploring past changes in population size, structure, continuity and movement. However, as genetic processes are highly stochastic, patterns of genetic variation only indirectly reflect demographic histories. As a result, past demographic processes need to be reconstructed using an inferential approach. This usually involves comparing observed patterns of variation with model expectations from theoretical population genetics. A large number of approaches have been developed based on different population genetic models that each come with assumptions about the data and underlying demography. In this article I review some of the key models and assumptions underlying the most commonly used approaches for past demographic inference and their consequences for our ability to link the inferred demographic processes to the archaeological and climate records. This article is part of the theme issue 'Cross-disciplinary approaches to prehistoric demography'.The study of past population dynamics is imperative to our understanding of demographic processes in the context of biology, evolution, environment and sociocultural factors. Retrospective consideration of a population's capacity to resist and adapt to change aims to contribute insights into our past, a point of comparison to the present and predictions for the future. If these aims are to be achieved, the accuracy and precision of palaeodemographic methods are of paramount importance. This article considers the emergence of skeletally based palaeodemographic methods, specifically life tables and demographic proxies, and early controversies and issues. It details the process of methodological development and refinement, and success in addressing many of the historical limitations. The contribution and potential of skeletally based methods are discussed and comparisons and contrasts made with alternative palaeodemographic approaches, and avenues for future research are proposed. Ultimately, it is concluded that skeletal analysis provides unique opportunities to investigate population dynamics with spatial specificity, examine individuals and groups within a population, and integrate demographic and pathological information to evaluate population health in the past. This article is part of the theme issue 'Cross-disciplinary approaches to prehistoric demography'.The northern American Southwest provides one of the most well-documented cases of human population growth and decline in the world. The geographic extent of this decline in North America is unknown owing to the lack of high-resolution palaeodemographic data from regions across and beyond the greater Southwest, where archaeological radiocarbon data are often the only available proxy for investigating these palaeodemographic processes. Radiocarbon time series across and beyond the greater Southwest suggest widespread population collapses from AD 1300 to 1600. However, radiocarbon data have potential biases caused by variable radiocarbon sample preservation, sample collection and the nonlinearity of the radiocarbon calibration curve. In order to be confident in the wider trends seen in radiocarbon time series across and beyond the greater Southwest, here we focus on regions that have multiple palaeodemographic proxies and compare those proxies to radiocarbon time series. We develop a new method for time series analysis and comparison between dendrochronological data and radiocarbon data.