Advances in Complex Systems

We consider the dynamics of cultural evolution in spatially-structured populations. Most spatially explicit modeling approaches can be broadly divided into two classes: micro- and macro-level models. Macro-level models study cultural evolution at the population level and describe the average behavior of the considered system. Conversely, micro-level models focus on the constituent units of the system, and study the evolutionary dynamics that emerge out of the interaction between these units. In this paper, we give an overview of the general properties of micro- and macro-level models using the examples of agent-based simulations and of continuum models based in diffusion theory; we highlight how both frameworks account for spatially-dependent processes. We argue that both micro- and macro-level models are well-suited to describe the process of cultural evolution in spatial settings and stress that micro- and macro-level models should not be considered as competing alternatives, but rather as complementary tools that can provide different insights into cultural evolutionary dynamics. Although adding spatial components to any model increases its complexity, we argue (based on the findings presented by contributors to this Special Issue of Advances in Complex Systems), that the incorporation of space into the evolutionary framework is a necessary step towards a more complete understanding of the process of cultural evolution.

This article focusses on the importance of space in mathematical models of cultural evolution, cooperation, niche construction and social learning. We discuss the benefits of including spacial effects in these evolutionary models and illustrate how the inclusion of space has changed accepted and long-standing results. We also briefly discuss the spatial dynamics of these systems and suggest future directions for research investigating spatial evolution.

Population geneticists have shown that the effects of local extinction and recolonization on selectively neutral genetic diversity are sensitive to the number of individuals that migrate between groups. Here, we employ a spatially explicit metapopulation model to investigate the extent to which the effects of local extinction on selectively neutral cultural diversity and change are sensitive to intergroup cultural transmission — the rate at which cultural variants are transmitted between groups. Our results show that the level of intergroup cultural transmission as well as the topology of the social network that mediates cultural transmission between groups influence the way in which local extinctions affect total diversity, group differentiation, and the rate at which copy errors accumulate in structured populations. The results are discussed in the context of the archaeological record of Middle and Upper Paleolithic societies.

The complex interactions between social learning and biological change are key to understanding the human species and its origins. Yet paleoanthropological models often focus only on the evolution of the human genome and physical characters, while behavior is treated as an epiphenomenon of biological evolution. We present the results of a series of experiments that use computational models, parametrized with new archaeological data, to simulate the complex dynamics of human biocultural evolution in the changing environment of OIS (Oxygen Isotope Stage) 3 of western Eurasia (~58000–27000 ka). These experiments allow us to compare alternative trajectories of human evolution, resulting from differing combinations of socioecological behaviors and biological conditions, against the paleoanthropological record.

In a recent work on the wave of advance of a beneficial technology and associated hitchhiking of cultural and biological traits, we simulated the advance of neolithic agriculture into Europe. That model embraced geographical variation of land fertility and human mobility, conversion of indigenous mesolithic hunter-gatherers to agriculture, and competition between invading farmers and indigenous converts. A key result is a sharp cultural boundary across which the agriculturalists' heritage changes from that of the invading population to that of the converts. Here we present an analytical study of the cultural boundary for some simple cases. We show that the width of the boundary is determined by human mobility and the strength of competition. Simulations for the full model give essentially the same result. The finite width facilitates irreversible gene flow between the populations, so over time genetic differences appear as gradients while e.g. linguistic barriers may remain sharp. We also examine the various assumptions of the model relating to purposeful versus. random movement of peoples and the competition between cultures, demonstrating its richness and flexibility.

We introduce a modeling framework that can be applied to cases of multiple converging fronts during episodes of population expansion and innovation diffusion, referring to two prehistoric case studies known archaeologically (the spread of pottery-making in Europe, and the spread of farming in southern Africa). We model front propagation using Fast Marching methods, drawing on the analogy with crystallization processes to build compoundly-weighted Voronoi diagrams of a spatially partitioned surface in which the zones of influence of each competing spreading process are determined by their respective front initiation times and propagation rates. We analyze the phase space for the general two-source case, and illustrate the potential of this approach by modeling the evolving interface for the archaeological case studies.

Humans divide themselves up into groups based on a shared cultural identity and common descent. Culturally inherited differences in dress, language, and institutions are often used as symbolic markers of the boundaries of these ethnic groups. Relatively little is known about the function of such ethnic groups, and why ethnic diversity is high in some regions yet lower in others. In this paper, we demonstrate how investigating the spatial distribution of ethnolinguistic groups can reveal the factors that affect the origin and maintenance of human ethnic group diversity. Here we describe the use of a Geographic Information System to construct a large database that integrates information about languages with a number of environmental, ecological, and ethnographic variables. Using these data on the spatial distribution of ethnolinguistic groups, we employ a hierarchical linear modeling approach to test a variety of hypotheses concerning the function of such groups. Despite revealing intriguing spatial patterns such as the latitudinal gradient in ethnolinguistic diversity, previous analyses suggested that the direct effects of environmental variables on the distribution of ethnolinguistic groups were in fact quite small. Here we show that the strength of the relationship between ethnolinguistic area and environmental variables is stronger in societies whose primary mode of subsistence is foraging. We then go on to demonstrate this same finding using the estimated native distributions of ethnolinguistic group in the Americas and Australia. In particular, Net Primary Productivity is shown to be a good predictor of the area covered by ethnolinguistic groups in foragers but not in agriculturalists. This provides support for the idea that the factors affecting ethnic diversity have changed in a systematic way with changes in subsistence strategies and social organization. We highlight future avenues for spatially explicit investigations of the evolution of ethnic diversity, and suggest that the evolutionary ecological approach adopted here may provide important insights into processes affecting ethnic diversity in the modern world.

We present an agent-based model for voluntaristic processes allowing the emergence of leadership in small-scale societies, parameterized to apply to Pueblo societies of the northern US Southwest between AD 600 and 1300. We embed an evolutionary public-goods game in a spatial simulation of household activities in which agents, representing households, decide where to farm, hunt, and locate their residences. Leaders, through their work in monitoring group members and punishing defectors, can increase the likelihood that group members will cooperate to achieve a favorable outcome in the public-goods game. We show that under certain conditions households prefer to work in a group with a leader who receives a share of the group's productivity, rather than to work in a group with no leader. Simulation produces outcomes that match reasonably well those known for a portion of Southwest Colorado between AD 600 and 900. We suggest that for later periods a model incorporating coercion, or inter-group competition, or both, and one in which tiered hierarchies of leadership can emerge, would increase the goodness-of-fit.

This paper explores the role of mathematical models in archaeology and history. Variants of a particular model — an entropy-maximizing spatial interaction model which also functions as a location model — are presented through two case studies. The first is an example from Archaeology which throws light on settlement sizes in the 9th and 8th century BC Greece; the second is from History and explores the evolution of the United States' urban system from 1790–1870 with particular reference to the impact of railways. The approach is essentially interdisciplinary and uses concepts from Geography, Economics, Physics and Ecology.

In this article, we examine a variety of quantitative models for describing archaeological networks, with particular emphasis on the maritime networks of the Aegean Middle Bronze Age. In particular, we discriminate between those gravitational networks that are most likely (maximum entropy) and most efficient (best cost/benefit outcomes).

Many explanations for the sigmoid or S-shaped curves that characterize the diffusion of innovations through time have been proposed. Recent studies demonstrate that social learning mechanisms, including conformist strategies, and heterogeneous adoption thresholds related to economic inequality and the decreasing cost of goods can generate these S-shaped cumulative frequency curves. The present study of a regional material culture sequence expands our inquiry concerning the underlying social forces that structure diffusion through both space and time. Using historic New England gravestones and their associated documents, this study considers both cultural transmission between stone carvers and consumer choices. Social learning among consumers can generate both wave-like diffusion patterns through space and lead to the persistence of cultural variants in certain locales.

We observe a marked increase in the spatial homogeneity of the popularity of first names across the United States in recent decades. We explain this by calibrating a modified standard model of neutral cultural evolution to the record of first name popularities for the United States as a whole since 1900 and across the individual states over the last 50 years. We obtain estimates of both the temporal and spatial diversity of the speed of cultural evolution during the 20th century and early 21st century. We find that the speed of innovation of popular baby names accelerated substantially since the end of the 20th century. We suggest that the increased inventiveness has driven a drift process that increased the geographic diversity across the United States.

Random copying is a simple model for population dynamics in the absence of selection, and has been applied to both biological and cultural evolution. In this work, we investigate the effect that spatial structure has on the dynamics. We focus in particular on how a measure of the diversity in the population changes over time. We show that even when the vast majority of a population's history may be well-described by a spatially-unstructured model, spatial structure may nevertheless affect the expected level of diversity seen at a local scale. We demonstrate this phenomenon explicitly by examining the random copying process on small-world networks, and use our results to comment on the use of simple random-copying models in an empirical context.

In this paper, we seek to build on existing mathematical studies of cultural change by exploring how the diversity of adaptive cultural traits evolves by innovation and cultural transmission when the payoff from adopting traits is both uncertain and frequency dependent. The model is particularly aimed at understanding the evolution of subsistence trait diversity, since the payoff from exploiting particular resources is often variable and subject to diminishing returns as a result of overexploitation. We find that traits that exploit the same shared resource evolve most quickly when intermediate rates of cultural transmission promote fluctuation in trait diversity. Higher rates of cultural transmission, which promote predominantly low diversity, and lower rates, which promote predominantly high diversity, both retard the adoption of traits offering higher payoff. We also find that the distribution of traits that exploit independent resources can evolve towards the theoretical Ideal Free Distribution so long as the rate of cultural transmission is low. Increasing the rate of cultural transmission reduces trait diversity, so that a more limited number of "niches" are occupied at any given time.

Macro-evolutionary investigations into cross-scale patterns of body size variation have put many of the pieces of the evolutionary body size puzzle in place. To further tackle micro- and meso-scale process-based reasons underlying changes in body size, researchers compare natural populations across different habitat structures, assessing which habitat structures correspond to which changes in body size variation. The complex multi-scale dynamics underlying the effect of the external environment on body size evolution, however, inherently limits empirical interpretations with regard to the differential contribution of particular aspects of habitat architecture on body size variation, leaving open many questions as to the how and why of changes in body size variation across different habitats. We develop an agent-based simulation approach with the principal aim of investigating the differential effects of particular habitat conditions on the evolution of body size and other life history traits. Our approach simulates animals' individual decisions with regard to growth and reproduction, and records their effect on population-level variation across different habitat structures. This approach has the potential to include numerous different habitat conditions and/or growth laws and allows detailed controlled comparisons of the isolated effects of particular habitat conditions and/or perturbations. In the current study, we assess the usefulness of our approach in a pilot exploration of the effects of predation and resource distribution on body size variation in mammals. We find independent effects of predation, resource availability and resource predictability on changes in body size and quantify the relation between body size and population size across different habitat conditions.