The theoretical literature on human population dispersal processes at the large time and space scale is reviewed, including references to and discussions of relevant empirical data. The basic Fisher-KPP reaction-diffusion system is summarized for the single population situation, and developments relating to the Allee effect, density-dependent dispersal, time delay, advection, spatial and temporal heterogeneity, and anomalous and stratified diffusion are reviewed. Two- and three-population competitive reaction-diffusion systems of Lotka-Volterra type are also reviewed, as are dynamic approaches to carrying capacity that incorporate predator-prey instabilities, ecosystem engineering, and gene-culture coevolution.

Inferring the past demography of human populations has been classically approached through data from the archaeological record but more recently by the use of genetic data from contemporary samples. Building realistic demographic models at the continental scale is a necessary step toward the improvement of current genomic methods aimed at finding genes under selection. In light of recent advances in Bayesian statistical inference, we discuss here the importance of considering spatially explicit approaches for modeling population expansion and dispersal. Neutral processes, such as the surfing phenomenon, that occur at the front of a range expansion may indeed mimic selection, and they may have played a significant role in spreading particular alleles over large geographic areas. Finally, we discuss a few important issues that require further investigation, notably the use of archaeological data to inform population genetic models, the simulation of range contraction and reexpansion, and the importance of long-distance dispersal.

The extent to which colonizing farmer populations have overwhelmed or “replaced” indigenous forager populations, as opposed to having intermarried with them, has been widely debated. Indigenous-colonist “admixture” is often represented in genetic models as a single parameter that, although parsimonious and simple, is incongruous with the sex-specific nature of mtDNA and Y-chromosome data. To help interpret genetic patterns, we can construct useful null hypotheses about the generalized migration history of females (mtDNA) as opposed to males (Y chromosome), which differ significantly in almost every ethnographically known society. We seek to integrate ethnographic knowledge into models that incorporate new social parameters for predicting geographic patterns in mtDNA and Y-chromosome distributions. We provide an example of a model simulation for the spread of agriculture in which this individual-scale evidence is used to refine the parameters.

Attempts to describe language competition and extinction in a mathematical way have enjoyed increased popularity recently. In this paper I review recent modeling approaches and, based on these findings, propose a model of reaction-diffusion type. I analyze the dynamics of interactions of a population with two monolingual groups and a group that is bilingual in these two languages. The results show that demographic factors, such as population growth or population dispersal, play an important role in the competition dynamic. Furthermore, I consider the impact of two strategies for language maintenance: adjusting the status of the endangered language and adjusting the availability of monolingual and bilingual educational resources.

Demography plays a large role in cultural evolution through its effects on the effective rate of innovation. If we assume that useful inventions are rare, then small isolated societies will have low rates of invention. In small populations, complex technology will tend to be lost as a result of random loss or incomplete transmission (the Tasmanian effect). Large populations have more inventors and are more resistant to loss by chance. If human populations can grow freely, then a population-technology-population positive feedback should occur such that human societies reach a stable growth path on which the rate of growth of technology is limited by the rate of invention. This scenario fits the Holocene to a first approximation, but the late Pleistocene is a great puzzle. Large-brained hominins existed in Africa and west Eurasia for perhaps 150,000 years with, at best, slow rates of technical innovation. The most sophisticated societies of the last glacial period appear after 50,000 years ago and were apparently restricted to west and north-central Eurasia and North Africa. These patterns have no simple, commonly accepted explanation. We argue that increased high-frequency climate change around 70,000–50,000 years ago may have tipped the balance between humans and their competitor-predators, such as lions and wolves, in favor of humans. At the same time, technically sophisticated hunters would tend to overharvest their prey. Perhaps the ephemeral appearance of complex tools and symbolic artifacts in Africa after 100,000 years ago resulted from hunting inventions that allowed human populations to expand temporarily before prey overexploitation led to human population and technology collapse. Sustained human populations of moderate size using distinctively advanced Upper Paleolithic artifacts may have existed in west Eurasia because cold, continental northeastern Eurasia–Beringia acted as a protected reserve for prey populations.

Studies that have modeled interactions between language evolution and demographic processes are reviewed. The models are classified in terms of three different approaches: analytical modeling, agent-based analytical modeling, and agent-based cognitive modeling. I show that these approaches differ in the complexity of interactions that they can handle and that the agent-based cognitive models allow for the most detailed and realistic simulations. Thus readers are provided with a guideline for selecting which approach to use for a given problem. The analytical models are useful for studying interactions between demography and language evolution in terms of high-level processes; the agent-based analytical models are good for studying such interactions in terms of social dynamics without bothering too much about the cognitive mechanisms of language processing; and the agent-based cognitive models are best suited for the study of the interactions between the complex sociocognitive mechanisms underlying language evolution.

Previous empirical studies of population size and language change have produced equivocal results. We therefore address the question with a new set of lexical data from nearly one-half of the world’s languages. We first show that relative population sizes of modern languages can be extrapolated to ancestral languages, albeit with diminishing accuracy, up to several thousand years into the past. We then test for an effect of population against the null hypothesis that the ultrametric inequality is satisfied by lexical distances among triples of related languages. The test shows mainly negligible effects of population, the exception being an apparently faster rate of change in the larger of two closely related variants. A possible explanation for the exception may be the influence on emerging standard (or cross-regional) variants from speakers who shift from different dialects to the standard. Our results strongly indicate that the sizes of speaker populations do not in and of themselves determine rates of language change. Comparison of this empirical finding with previously published computer simulations suggests that the most plausible model for language change is one in which changes propagate on a local level in a type of network in which the individuals have different degrees of connectivity.

Archaeological demography investigates the structure and dynamics of past human populations using evidence from traces of human activities and remnants of material culture in the archaeological record. Research in this field is interdisciplinary, incorporating findings from anthropology, paleogenetics, and human ecology but with a remit that extends beyond the primarily biological focus of paleodemography. Important questions addressed by archaeological demography include the establishment of methods for inferring past population structure, the timing of the emergence of modern human demographic systems, the relative importance of attritional and catastrophic patterns of mortality, and the search for adaptive explanations for demographic transitions, colonization events, and population extinctions. Archaeological evidence, including the extent of settlements and site catchment areas as well as measures of the exploitation, consumption, and discard of materials and artifacts, have traditionally been used as proxies for estimating past population size and density. In recent years this evidence has been supplemented by increasingly large data sets compiled from radiocarbon dating programs. These data sets have been used to investigate demographic waves of advance during continental-scale periods of colonization and cultural change and to detect episodes of population decline, extinction, and hiatuses in settlement history. By considering studies of human genetic diversity that indicate temporary but drastic reductions in effective population size, I hypothesize that catastrophic mortality may have had an important role in long-term population processes and may have limited long-term rates of growth, particularly in prehistoric populations.

Using a database of 499 archaeological assemblages from 332 sites in Europe, we statistically test a model of the economic reactivity of the hunter-gatherer production system to climatic variations. This model predicts an increase in the diversity of lithic tools during harsh cold periods, in order to maintain carrying capacity, and a reduction during favorable climatic periods. Diversity was measured from the variations in flint tool distributions in traditional Bordes typological categories, using Shannon’s derived diversity index (D). Reactivity was measured in 190 archaeological assemblages from 103 sites of the Middle Paleolithic in Europe (mainly France). The Neanderthals show technological inertia in the development and use of lithic tools for 200,000 years, despite the four cool to cold macroclimatic periods they experienced.

Although difficult to estimate for prehistoric hunter-gatherer populations, demographic variables—population size, density, and the connectedness of demes—are critical for a better understanding of the processes of material culture change, especially in deep prehistory. Demography is the middle-range link between climatic changes and both biological and cultural evolutionary trajectories of human populations. Much of human material culture functions as a buffer against climatic changes, and the study of prehistoric population dynamics, estimated through changing frequencies of calibrated radiocarbon dates, therefore affords insights into how effectively such buffers operated and when they failed. In reviewing a number of case studies (Mesolithic Ireland, the origin of the Bromme culture, and the earliest late glacial human recolonization of southern Scandinavia), I suggest that a greater awareness of demographic processes, and in particular of demographic declines, provides many fresh insights into what structured the archaeological record. I argue that we cannot sideline climatic and environmental factors or extreme geophysical events in our reconstructions of prehistoric culture change. The implications of accepting demographic variability as a departure point for evaluating the archaeological record are discussed.

In this paper I propose that evolutionary demography and associated theory from human behavioral ecology provide a strong basis for explaining the available evidence for the patterns observed in the first agricultural settlement of Europe in the 7th–5th millennium cal. BC, linking together a variety of what have previously been disconnected observations and casting doubt on some long-standing existing models. An outline of relevant aspects of life history theory, which provides the foundation for understanding demography, is followed by a review of large-scale demographic patterns in the early Neolithic, which point to rapid population increase and a process of demic diffusion. More localized socioeconomic and demographic patterns suggesting rapid expansion to local carrying capacities and an associated growth of inequality in the earliest farming communities of central Europe (the Linear Pottery Culture, or LBK) are then outlined and shown to correspond to predictions of spatial population ecology and reproductive skew theory. Existing models of why it took so long for farming to spread to northern and northwest Europe, which explain the spread in terms of the gradual disruption of hunter-gatherer ways of life, are then questioned in light of evidence for population collapse at the end of the LBK. Finally, some broader implications of the study are presented, including the suggestion that the pattern of an initial agricultural boom followed by a bust may be relevant in other parts of the world.

We describe a combination of methods applied to obtain reliable estimations of population density using archaeological data. The combination is based on a hierarchical model of scale levels. The necessary data and methods used to obtain the results are chosen so as to define transfer functions from one scale level to another. We apply our method to data sets from western Germany that cover early Neolithic, Iron Age, Roman, and Merovingian times as well as historical data from AD 1800. Error margins and natural and historical variability are discussed. Our results for nonstate societies are always lower than conventional estimations compiled from the literature, and we discuss the reasons for this finding. At the end, we compare the calculated local and global population densities with other estimations from different parts of the world.

In the field of archaeology, demography has sometimes seemed something of a phantom science. Many explanatory models in archaeology have taken population density as a central theme. But the quantitative precision and broad sweep of the resulting formulations, scientific enough in their intentions, have often been undermined by the difficulties in the practice of estimating population densities for the prehistoric or early historic past. Indeed, even for the Classical world, where historical and literary texts as well as inscriptions are available to supplement the settlement remains still visible on the ground, the estimation of population has been a field of controversy for more than a century (Beloch 1886). Problems of estimation have undermined those quantitative intentions of the would-be scientist. Yet despite these practical problems, the attractions of the explanations already proposed have been considerable. [...]