Toward a theory of punctuated subsistence change

Significance

The questions of how, when, and why humans transitioned from hunting and gathering to food production are important to understand the evolution and sustainability of agricultural economies. We explore cross-cultural data on human subsistence with multivariate techniques and interpret the results from the perspective of human societies as complex adaptive systems. We gain insight into several controlling variables that may inordinately influence the possibilities for subsistence change and into why the forager–farmer transition occurred quickly in some cases and more gradually in others.

Abstract

Discourse on the origins and spread of domesticated species focuses on universal causal explanations or unique regional or temporal trajectories. Despite new data as to the context and physical processes of early domestication, researchers still do not understand the types of system-level reorganizations required to transition from foraging to farming. Drawing upon dynamical systems theory and the concepts of attractors and repellors, we develop an understanding of subsistence transition and a description of variation in, and emergence of, human subsistence systems. The overlooked role of attractors and repellors in these systems helps explain why the origins of agriculture occurred quickly in some times and places, but slowly in others. A deeper understanding of the interactions of a limited set of variables that control the size of attractors (a proxy for resilience), such as population size, number of dry months, net primary productivity, and settlement fixity, provides new insights into the origin and spread of domesticated species in human economies.

Recent work highlights that the transition from foraging to farming was nonlinear and heterogeneous (e.g., refs. 1–7). That is, rather than an inevitability, early shifts to food production were only one of many possible outcomes that could have been reached for a given set of dynamically interacting social and ecological variables. Although the forager–farmer transition is one of the most fundamental changes in human evolution, our understanding of the forager–farmer transition is theoretically fractious (1, 3–6, 8–36), with scholarly discourse dominated by the assumption that the forager adoption of domesticates was driven either by subsistence necessity or because domesticates provided a desirable opportunity or assurance. Given our adaptive flexibility, however, it is clear that both options are possible, depending on the situation. The challenge is distinguishing the contextual settings in which adoptions were linked to necessity versus opportunity. Simply put, there is currently no sufficient theory to explain the nonlinear and contingent worldwide transitions from foraging to farming.

In this paper, we use concepts from Dynamical Systems Theory (SI Text S1) to model subsistence variation among contemporary ethnographic groups from an evolutionary perspective. We focus on a critical question: How can researchers use the concepts of attractors and repellors—so integral to understanding many nonlinear dynamical systems—to describe variation in the subsistence strategies of human societies? This framing provides general insights into why transitions from foraging to farming, at a global scale, exhibit nonlinearity and heterogeneity, and why the shift was sometimes gradual, and other times punctuated. Drawing upon comparative ethnographic case studies, we formalize the use of cross-cultural data in a theory-backed methodology to ascertain how the attractor/repellor concept can be use to describe subsistence variation in human societies. Our analysis elucidates broad, multidimensional trends across the breadth of human subsistence practices and is a step toward developing a theory of nonlinear subsistence change in human societies.

SI Text S1: Dynamical Systems Theory, Complex Adaptive Systems, Social-Ecological Systems, and Resilience Theory

Dynamical systems theory (DST) (often also referred to as “complex systems theory” or “complexity theory”) is a body of theory that has evolved out of the work of researchers across a variety of disciplines (but particularly physicists, ecologists, and computer scientists) who, in the latter half of the 20th century, began to rethink previously accepted notions about the linear nature of natural phenomena (75). They challenged the idea that the outcome of a series of stimulus events on natural systems could be accurately predicted, if only the “correct” equation could be found. In other words, researchers began to question the validity of the quest for unified causal explanations. A reexamination of the linkages between stimuli and results, largely informed by the advent of computer-based simulation modeling, led to the idea of feedback loops and uncertainty; “predictability” was replaced by “emergent properties” as the epitomizing factor of natural systems (76).

Complex adaptive systems (CAS) are a special subset of dynamical systems. The CAS concept is, in essence, a framework for investigating how the independent decisions and actions of individual components of a system (i) self organize, (ii) are dynamic and change over time, (iii) interact to derive novel, unpredictable, emergent properties of the system, and (iv) may adapt to work in the interest of the system as a whole (37, 38). The focus of CAS research has been to use alternative methods of analysis—particularly simulation with agent-based models—to understand these properties in a variety of complex systems, including human social systems, in a way that reductionism cannot achieve.

The types of CAS that are of most interest to archaeologists are “socio-ecological systems” (SES) (also referred to as “coupled human and natural systems” or “socio-natural systems”). SES are defined by Glaser et al. (ref. 77, p. 4) as “complex, adaptive system[s] consisting of a bio-physical unit and its associated social actors and institutions. The spatial or functional boundaries of the system delimit a particular ecosystem and its problem context.” Importantly, this defines SES as “real,” tangible things that exist in the physical world with distinct boundaries in time and space, and so can be observed and studied empirically. Thus, SES can be studied as regionally distinct analytical units (78). This property is particularly helpful for archaeologists, who are accustomed to conducting research at regional scales.

Considerable debate exists about whether DST is truly an integrative or unified paradigm (37, 38, 40, 79–81). This confusion is, in large part, a consequence of the widely varying nomenclature used by DST researchers. In addition to complexity theory, CAS, and SES, there is also “resilience theory” (RT) [conceived by C. S. Holling (first described in ref. 41) and popularized by two edited volumes (82, 83)], which is frequently considered as intellectually distinct from DST. The RT approach may not be very well-integrated with the CAS/SES approaches, but there is much methodological and conceptual overlap between them because both derive from similar early DST roots. More importantly to the research presented here, both are useful sources of ideas for a dynamical systems view of change in human systems. In particular we use (i) the interrelated ideas of the adaptive cycle, resilience, and “panarchy” (42, 82–85) and (ii) the parallel ideas of critical transitions, catastrophic regime shifts, “tipping points,” “basins of attractions,” and alternative stable states (39, 76, 86–89). We use these and other concepts in our discussion of change in nonlinear systems in SI Text S2.

Dynamical Systems and Human Ecology

We start from the premise that human societies are complex adaptive systems, with heterogeneous agents at several levels of organization, who interact with each other and the biophysical environment (SI Text S1, SI Text S2, and Figs. S1 and S2). Complex adaptive systems are a special subset of dynamical systems in which the independent decisions and actions of individual components of the system (i) self organize, (ii) change over time, (iii) interact to derive novel emergent properties of the system, and (iv) may adapt to work in the interest of the system as a whole (37, 38). Viewing human societies as complex systems helps generate hypotheses for the way in which human–natural system components should interact and evolve over time (Figs. S3 and S4). Here, we propose that (i) the feedback between humans and their resources may lead to “attractors” and “repellors” that describe the variation in human subsistence systems and that (ii) a small number of “controlling” variables may disproportionately affect change within subsistence systems. If these propositions have merit, then, using a few important variables, we should be able to identify clusters of societies in the ethnographic record that occupy similar, although not isomorphic, attractors. These clusters will be separated by economic voids where subsistence strategies are unlikely to persist due to the presence of repellors.

Fig. S1.

(A) A 2D representation of the adaptive cycle showing how system potential and connectedness change over time. (B) A 3D representation of the adaptive cycle, which adds an axis of resilience. (C) An illustration showing how different adaptive systems exist at different scales. (D) An illustration of the concept of panarchy, showing the positive and negative feedback connections between different scales of adaptive systems. Modified from refs. 101 and 83, with permission from Elsevier and Island Press.

Fig. S2.

The adaptive cycle plotted as a time series graph. The x axis is time, and the y axis is an indicator variable for system potential, connectedness, or resilience. The solid green line shows the expected pattern for system potential, the dashed green line shows the expected pattern for system connectedness over time, and the dashed red line shows the expected pattern for resilience over time.

Fig. S3.

Diagram of potential trajectories of an adaptive system over time. At any time t, a new cycle begins. Arrows indicate steady-state trajectories for continual remember, revolt, or remain, but note that multiple pathways (combinations of remember, revolt, or remain between any time t) could have been taken to achieve any of the potential system states at time t4.

Fig. S4.

Diagram of different types of system state change. The line in A represents linear steady-state change over time. The line in B represents a more complex pattern of change, where change occurs more rapidly under certain ranges of conditions. The line in C represents a system with a “critical transition.” Modified from ref. 92.

In dynamical systems theory, attractors are system states toward which (all else being equal) a complex adaptive system will tend to evolve, and, conversely, repellors are system states that the system will tend to avoid (39, 40). In other words, an attractor is a configuration of system subcomponents that are relatively stable over time whereas a repellor is a configuration that is not. Thus, at any given time, a complex adaptive system is always evolving toward an attractor, but rarely reaches it (i.e., the system is never in “equilibrium”). Importantly, the size of an attractor determines its resilience, which is how much environmental change a system can cope with before feedbacks between variables change (SI Text S2 and Fig. S5) (41). Attractors emerge from these kinds of feedbacks, and our working supposition is that human subsistence attractors emerge from cross-scale feedbacks between human and natural resources in socio-natural systems.

Fig. S5.

A time series of stability landscapes crossing over a critical transition point. Note that initially there is only one attractor (stable state), but, as the system is stressed, another attractor develops. When the system is stressed past the critical threshold (F2), it is pulled to the second attractor, and a new stable state is achieved. The depth of the basin of attraction indicates the amount of system resilience. Modified from ref. 86, with permission from Elsevier.

Complex systems are usually in a dynamic state that is largely dominated by the force of a local attractor, but not solely controlled by it. Because these systems are dynamical, evolving, and open, their attractors and repellors also change in strength and configuration as system subcomponents and emergent, macrolevel conditions change (Fig. S5). This property holds major implications for how complex adaptive systems change over time. An interesting set of possibilities for change occurs when a system is positioned between two or more attractors. Systems operating in such intermediary locations are available to move from the sphere of influence of one attractor to another. These transitions can occur either gradually or as very rapid-phase changes, depending on the resilience of each of the attractors (SI Text S2 and Figs. S3 and S4) (39). These properties also control whether the transition is immediately reversible (i.e., related to choices of opportunity) or represents a true bifurcation (i.e., related to choices of necessity).

In dynamical systems, it is often the case that a few variables control the dynamics of the system, including the emergence of attractors and repellors (42). Controlling variables are those that have a disproportionate impact on the feedback between individuals and their use of resources and thus strongly affect the structure of a system. For example, Holling (43) found that, from host–parasite, to lakes, to the boreal forest, only three to four variables control the structure of dynamical systems models of ecosystems. Similar observations have been made of dynamical systems models that describe socio-natural systems (e.g., refs. 44–49). In one of these examples, Freeman and Anderies (50) argue that the ratio of population to resources controls a regime change from a mobile foraging to an intensive, property-based foraging attractor. The meta-insight that we pull from these models is that reframing human subsistence systems as emergent outcomes of complex adaptive processes in a nonlinear system suggests that it is useful to identify potential controlling variables. Such variables would point the way forward for further theoretical development.

SI Text S2: Change in Nonlinear Systems

Because of their nonlinearity, cause-and-effect logic is difficult to apply toward understanding change in dynamical systems. There currently exists no integrative theory of change in these types of systems. There have been, however, some useful approaches to understanding how complex systems change over time. The RT idea of the “adaptive cycle” is one of these approaches. Originally envisioned as a 2D diagram (Fig. S1A), it has since been expanded into three dimensions (Fig. S1B) (83). It is a heuristic diagram for temporal change, with axes corresponding to system potential, system connectedness, and system resilience. The potential of a system is a measure of its capacity (customarily measured in terms of accumulated resources), the connectedness of a system is a measure of the amount of integration present in the system (typically viewed as the tightness of the coupling between elements of the system), and the resilience of a system is a measure of its ability to adapt to new conditions (generally understood as its flexibility or adaptability, and measured in terms of things like degree of specialization, etc.). The “figure 8” diagram of the adaptive cycle is formed as the state of the system proceeds through time in the three-dimensional space of potential, connectedness, and resilience. Although there is an extensive literature about the adaptive cycle and its four phases, the most important concept is that system resilience fluctuates over time in roughly inverse proportionality to its potential and connectedness. RT suggests that systems can undergo rapid change when resilience is reduced and potential and connectedness are high. The system may then either reemerge into a totally new niche³, or remain in the same niche, but returned to its initial, less complex state (i.e., the system exhibits “boom/bust” temporal dynamics). [Although we use the term “niche” here in a semantically similar manner to its use in ecology (i.e., an “ecological niche”), we want to be clear that we mean “niche” in a wider sense, similar to how the term is used in dual-inheritance and niche-construction theory.] This cycling repeats over time, as the system stays in motion because “there is a fundamental trade-off between being adaptive and being efficient” (ref. 39, p. 78). In other words, increased resilience can be had only at the expense of decreased potential.

Holling and coworkers have envisioned a system of interconnection between adaptive cycles at different scales, which they term “panarchy” (83). The panarchy concept is a way of understanding the emergence and feedback of hierarchically arranged systems from heterarchical processes. A main idea of the panarchy is that system components scale logarithmically as a function of time and space so that smaller adaptive phenomena (e.g., an individual or family group) exist as independent cycles within larger adaptive phenomena (e.g., a society) (Fig. S1C). Each scale of adaptive phenomenon will have an areal footprint and a “cycle width” (length of time between boom/bust dynamics). There are two types of possible feedback connections between adjacent scales, termed “remember” and “revolt” (Fig. S1D). The important thing is that the panarchy hypothesis predicts a negative feedback (remember) from larger, slower adaptive cycles to faster, smaller adaptive cycles, and a positive feedback (revolt) from faster, smaller adaptive cycles to larger, slower adaptive cycles. These two forces are terms in a balancing equation that determines the stability state of the entire panarchy. [This idea is similar to the concept of “metastable” equilibrium in traditional systems theory (e.g., ref. 90).] Although conceptually simple, complexity is achieved as a function of the differences in the cycle width of all of the different scales of adaptive phenomena in the panarchy and the relative alignment of the adaptive states of the adaptive phenomena at each scale. Thus, small-scale stability or growth can be maintained via large-scale remember feedback, even if local conditions should seem to require release and reorganization (e.g., individual families may maintain a subsistence lifeway out of tradition or greater social pressure). Conversely, larger scale system structures can change (in a potentially punctuated way) via an amalgamation of small-scale revolt negative feedback events in the subsystem (e.g., an accumulation of individuals/families making subsistence transitions), even if the larger scale cycles were nominally stable.

To see how we can apply these ideas to a dynamical systems concept of human ecology, we plot our expectations for change in system potential, connectedness, or resilience as a time series in which we can produce a different heuristic plot of the adaptive cycle that shows how it plays out over time (Fig. S2). These heuristic graphs can be used to help analyze/explain patterning in real time series plots of various proxies for potential (e.g., population, number of farmed plots, crop yields, capital, infrastructure, etc.), connectedness (e.g., number of households in a community, heterogeneity of vegetation), and resilience (similar proxies as those for connectedness, but reversed metrics) over time.

Fig. S3 shows a heuristic time-series graph of system potential over several sequential boom/bust cycles of an adaptive system. Starting from time t1, the overall amount of system potential can increase, decrease, or remain constant over time, depending upon the current balance of negative to positive feedback forces. If positive feedback outbalances negative feedback, then the system experiences net growth of potential and connectedness over time (although at the expense of resilience), resulting in a pattern of compounding success. If negative feedback outbalances positive feedback, then the system experiences net reduction of potential and connectedness over time (but regains resilience), resulting in a pattern of cascading failure. If the positive and negative feedback forces are well-balanced between the various levels of the system (a phenomenon we suggest be called “remain”), then the panarchy experiences no (or insignificant) net change over time, resulting in a pattern of long-term stability. It is important to note that, at any time t, a new cycle begins, and the balance of the system can change. Thus, the trajectory from the system state at time t1 to any of the possible system states at time t4 is neither linear nor predictable, and it is impossible to predict which particular system state will be achieved at time t4. That is, given any set of initial conditions, there are multiple pathways to each possible system state at any later time, which is what makes the system “complex.” Furthermore, the contingencies of history matter in this scheme, in that the earlier pathways taken serve to limit the number and character of available future pathways. In other words, the probability of a particular system state being achieved at time t4 varies greatly depending upon the pathways taken at times t1–t3.

Feedback processes also can lead to punctuated change. Scheffer and coworkers (39, 86, 87, 91–93) center a DST approach to rapid system change—“critical transitions” around the idea of alternative stable states. Fig. S4 shows three different patterns of system state change to major indexing variables. Fig. S4A shows steady-state change where there is a linear relationship between the system state (y axis) and some critical variable (x axis). Fig. S4B shows a more complex relationship between the system state and the critical variable, where change is more rapid over some subsection of variable values, and less rapid in others. In this figure, the steeper zone of the curve is less stable than the flatter portions, but there is still a fixed relationship between the critical variable and the state of the system (i.e., if one is known, the other can be predicted). Fig. S4C shows yet another relationship between the system state where there is a “zone of vulnerability” where two alternative systems states are possible for the same value of the critical variable. Scheffer and coworkers label this type of curve a “catastrophe curve.” The dashed portion of the curve cannot be traveled smoothly so, at critical points F1 and F2, the system state jumps from one portion of the curve to the other (Fig. S4D). An important aspect of this type of curve is that, even if the critical variable returns to its value from before the critical transition (e.g., point F2), the system remains in the alternative system state and will remain there until the other critical threshold is surpassed (e.g., point F1). In fact, it is possible for the system to enter into a cyclical recurrence between these two stable states as the critical resource varies between the two critical thresholds, which is called “hysteresis” (39).

Scheffer and coworkers use another heuristic—the “stability landscape”—to provide more detail on this phenomenon (Fig. S5). A stability landscape is a graph where the slope of the line represents the rate of change (39). Thus, if the slope is zero, the rate of change is zero. Scheffer uses the analogy of a “ball in a cup,” such that, if the stability landscape is concave, the ball will always fall to the bottom of the “trough.” Such troughs can thus be thought of as basins of attraction or, more formally, attractors. Attractors are essentially the stable state of the system under a specific set of conditions (i.e., the conditions that set the current stability landscape). Where the stability landscape is convex, the ball will always fall away from the “peak.” Such peaks can thus be thought of as repellors. If conditions are such that there is only one stable system state, there will be only one attractor (or none at all) on the stability landscape. In the case of two (or more) possible stable system states, then there will be two (or more) attractors, separated by a repellor. Thus, if the perturbation is large enough to overcome the force of the separating repellor, it is possible for the system state (the ball) to fall into one or the other attractor. It is this dual attraction and repulsion that results in the rapid pace of change across critical transitions.

Furthermore, the width and depth of the basins of attraction can be thought of as measures of the system resilience under the given conditions (Figs. S5 and S6). Thus, a deep, wide attractor is highly resilient, and even large perturbations will not “knock the ball out of the cup” (Fig. S6A). However, a shallow, narrow attractor is highly vulnerable to change, and a relatively minor perturbation may be sufficient to induce system state change (Fig. S6B). This concept is exemplified in Fig. S5, which shows a series of stability landscapes for different positions on a catastrophe curve: as the system nears the critical transition point (F2), the resilience of the original attractor reduces, and the amount of perturbation required to switch to the alternate attractor lessens. Related to this idea, systems that are vulnerable to critical transitions are also characterized by higher degrees of subsystem homogeneity and connectivity (93). Ironically, these homogeneous and highly connected systems are actually more stable in the short term because they continually act to resist change until the critical threshold is surpassed.

Fig. S6.

Twenty sample biplots from bootstrap randomized versions of the SCCS data used in our analyses. Each plot represents a novel row-wise recombination of the SCCS input variables that was then subjected to cluster analysis and NMMDS. The lack of patterning in these biplots indicates that the variation in the real SCCS societies is not due to random chance.

Materials and Methods

All explanations for subsistence change in archaeology are built on an understanding of ethnographically documented societies (e.g., refs. 17, 23, 45–49, 51, and 52). Much of this knowledge derives from traditional ethnoarchaeological research from the last century that provided case studies of human groups living traditional, or near-traditional, lifeways (SI Text S3). These studies often resulted in models designed to address specific archaeological problems (e.g., refs. 53 and 54) or to relate archaeological phenomena to theories of human behavior (e.g., ref. 55). Comparative ethnoarchaeology, on the other hand, attempts to identify global patterns of human behavior to either generate new hypotheses or to evaluate ecological models (e.g., refs. 47, 50, 51, and 56–58).

In the tradition of comparative approaches, in this study, we used automated multidimensional techniques to identify patterns in human subsistence variability with which to assess the attractor/repellor hypothesis. We examined subsistence, mobility, economic, demographic, and environmental data for the 186 societies of the Standard Cross-Cultural Sample (SCCS) (SI Text S3 and Tables S1 and S2) (59). We supplemented these data with information about Net Primary Production (NPP) from the Atlas of the Biosphere (60, 61) (SI Text S3 and Table S2). We address issues of missing data, potential autocorrelation (i.e., “Galton's problem”), and alternative explanations of patterning within the SCCS data in SI Text S4 and SI Text S5. Our workflow followed Le Roux and Rouanet's (62) “geometric data analysis” (SI Text S6) and was designed to graphically identify and intuit natural divisions in cross-cultural data by combining the result of multivariate clustering with dimensional reduction analyses. Specifically, we used K-medoids clustering paired with nonmetric multidimensional scaling (NMMDS) or canonical correspondence analysis (CCA). We used the workflow to plot societies in a phase space created by the ordination routine, which condenses many dimensions of subsistence activities, mobility characteristics, settlement types, and so on, into a biplot. We used plot symbology to thematically display the relationship between the spatial patterning of societies within that phase space to the input variables, other variables, or other data analyses. We used these techniques to ascertain whether the global SCCS sample of subsistence systems is characterized by clusters and gaps that might be analogous to attractors and repellors. All analyses were undertaken in R, using the “cluster” and “vegan” multidimensional analysis modules. We include our imputed datasets and R code as supplemental data (SI Text S7).

Table S1.

Table of SCCS societies used in the macroscale analysis, organized by SCCS variable 858, “Subsistence Type-Ecological Classification”

Society Name	Code	Society Name	Code	Society Name	Code	Society Name	Code	Society Name	Code
Kung Bushmen	1 □	Gros Ventre	5 +	Natchez	7 ◊	Nicobarese	9 ◊	Callinago	11 *
Hadza	1 □	Comanche	5 +	Huichol	7 ◊	Orokaiva	9 ◊	Inca	11 *
Mbuti	1 □	Chiricahua	5 +	Miskito	7 ◊	Kwoma	9 ◊	Kaffa (Kafa)	12 *
Semang	1 □	Abipon	5 +	Bribri	7 ◊	New Ireland	9 ◊	Konso	12 *
Tiwi	1 □	Tehuelche	5 +	Cuna (Tule)	7 ◊	Trobrianders	9 ◊	Amhara	12 *
Aranda	1 □	Nama Hottentot	6 ×	Yanomamo	7 ◊	Siuai	9 ◊	Riffians	12 *
Pomo (Eastern)	1 □	Kikuyu	6 ×	Carib (Barama)	7 ◊	Tikopia	9 ◊	Egyptians	12 *
Paiute (North.)	1 □	Pastoral Fulani	6 ×	Saramacca	7 ◊	Pentecost	9 ◊	Hebrews	12 *
Shavante	1 □	Masai	6 ×	Mundurucu	7 ◊	Mbau Fijians	9 ◊	Babylonians	12 *
Vedda	2 ○	Somali	6 ×	Cubeo (Tucano)	7 ◊	Marquesans	9 ◊	Turks	12 *
Copper Eskimo	2 ○	Bogo	6 ×	Jivaro	7 ◊	Western Samoans	9 ◊	Gheg Albanians	12 *
Montagnais	2 ○	Teda	6 ×	Amahuaca	7 ◊	Gilbertese	9 ◊	Romans	12 *
Micmac	2 ○	Tuareg	6 ×	Aymara	7 ◊	Marshallese	9 ◊	Basques	12 *
Slave	2 ○	Rwala Bedouin	6 ×	Nambicuara	7 ◊	Trukese	9 ◊	Irish	12 *
Siriono	2 ○	Lapps	6 ×	Trumai	7 ◊	Yapese	9 ◊	Russians	12 *
Botocudo	2 ○	Yurak Samoyed	6 ×	Timbira	7 ◊	Palauans	9 ◊	Kurd	12 *
Aweikoma	2 ○	Abkhaz	6 ×	Tupinamba	7 ◊	Cayapa	9 ◊	Punjabi (West)	12 *
Lengua	2 ○	Basseri	6 ×	Cayua	7 ◊	Lozi	11 *	Santal	12 *
Andamanese	3 ∆	Toda	6 ×	Thonga	8 ◊	Nyakyusa	11 *	Uttar Pradesh	12 *
Badjau	3 ∆	Kazak	6 ×	Mbundu	8 ◊	Bambara	11 *	Burusho	12 *
Manus	3 ∆	Khalka Mongols	6 ×	Suku	8 ◊	Tallensi	11 *	Lolo	12 *
Ainu	3 ∆	Chukchee	6 ×	Bemba	8 ◊	Songhai	11 *	Lepcha	12 *
Gilyak	3 ∆	Goajiro	6 ×	Luguru	8 ◊	Hausa	11 *	Burmese	12 *
Yukaghir	3 ∆	Mao	7 ◊	Nkundo Mongo	8 ◊	Massa (Masa)	11 *	Vietnamese	12 *
Saulteaux	3 ∆	Garo	7 ◊	Banen	8 ◊	Fur (Darfur)	11 *	Khmer	12 *
Kaska	3 ∆	Lakher	7 ◊	Tiv	8 ◊	Otoro Nuba	11 *	Siamese	12 *
Yokuts (Lake)	3 ∆	Lamet	7 ◊	Ibo	8 ◊	Kenuzi Nubians	11 *	Negri Sembilan	12 *
Kutenai	3 ∆	Iban	7 ◊	Fon	8 ◊	Armenians	11 *	Javanese	12 *
Warrau	3 ∆	Toradja	7 ◊	Ashanti	8 ◊	Tanala	11 *	Balinese	12 *
Yahgan	3 ∆	Tobelorese	7 ◊	Mende	8 ◊	Kimam	11 *	Chinese	12 *
Ingalik	4 ∆	Alorese	7 ◊	Wolof	8 ◊	Ajie	11 *	Manchu	12 *
Aleut	4 ∆	Kapauku	7 ◊	Azande	8 ◊	Ifugao	11 *	Koreans	12 *
Eyak	4 ∆	Maori	7 ◊	Shilluk	8 ◊	Hidatsa	11 *	Japanese	12 *
Haida	4 ∆	Atayal	7 ◊	Gond	8 ◊	Zuni	11 *	Mapuche	12 *
Bellacoola	4 ∆	Pawnee	7 ◊	Rhade	8 ◊	Havasupai	11 *
Twana	4 ∆	Omaha	7 ◊	Popoluca	8 ◊	Papago	11 *
Yurok	4 ∆	Huron	7 ◊	Quiche	8 ◊	Aztec	11 *
Klamath	4 ∆	Creek	7 ◊	Ganda	9 ◊	Haitians	11 *

1, gathering; 2, hunting and/or marine animals; 3, fishing; 4, anadromous fishing; 5, mounted hunting; 6, pastoralism; 7, shifting cultivation, with digging sticks or wooden hoes; 8, shifting cultivation, with metal hoes; 9, horticultural gardens or tree fruits; 10, advanced horticulture, with metal hoes; 11, intensive agriculture, with no plow; 12, intensive agriculture, with plow. Plotting symbols follow number codes.

Table S2.

Table of SCCS variables included in the analyses, using the abbreviations used in the text and figures

Variable name	Variable no.	Variable name	Variable no.
Main variables		ag_importance	814
trade_food	1	herd_importance	815
ag_contrib	3	fish_importance	816
herd_contrib	5	hunt_importance	817
herd_animals	6	gath_importance	818
fish_contrib	7	trade_importance	819
fish_type	8	total_pop	1122
hunt_contrib	9	ag_staple1	1123
hunt_animals	10	ag_stape2	1125
gath_contrib	11	plow2	1127
gath_foods	12	crop_index	1128
food_stor	20	subsis_ecolo*	858
settle_fixity	61	Environmental variables
settle_compact	62	temperature	186
commun_size	63	precip	189
pop_dens	64	num_dry_mon	196
gath_depend	203	num_wet_mon	199
hunt_depend	204	latitude	1905
fish_depend	205	coef_var_precip†	192 and 193
herd_depend	206	Social variables‡
ag_depend	207	region	200
cultiv_intens	232	lang_fam	1859
maj_crop	233	lang_subfam1	1860
settle_pattern	234	lang_subfam2	1861
plow	243	num_neighbors	1864
herd_type	244	religion	2002
milking	245

^*Used only to determine plotting symbols, and not used in any statistical analyses.

^†The coefficient of variation of precipitation was calculated from the two SCCS variables indicated (maximum and minimum precipitation).

^‡Social variables were used only to test whether they significantly affected the results of the main analyses (i.e., Galton's problem).

SI Text S3: The Standard Cross-Cultural Sample and Supplemental Data

The dataset used in this analysis is the Standard Cross-Cultural Sample (59), which is a unique database of over 2,000 cultural variables coded for 186 societies. The greater part of the SCCS variables pertain to specific social characteristics or socially ordained behaviors. Because our interests are in those aspects of human behavior related to making a living, we focused on those variables related to subsistence, mobility, demography, and, especially, those that seem to be more consistent with the kinds of data that can be recovered archaeologically. Table S1 lists the names of the 186 societies of the SCCS and the plotting codes used to display how ethnographers characterized their subsistence. Table S2 lists the core set of subsistence, mobility, and demographic variables that were included in our analyses, as well as the supplemental environmental and social variables that were used in additional analyses. See SI Text S4 for completeness criteria also used when choosing the variables used in our analyses.

Although the SCCS data are appropriate for the problem being investigated, they are not without limitations. For example, although the SCCS was developed to cover a maximum of human diversity and the best-studied human groups (59), it is nonetheless numerically biased toward groups studied by ethnographers in the modern era, and, thus, rather than being a true representative sample of all traditional human lifeways, it is a sample of traditional human lifeways after the effects of global post-17th century colonialism/imperialism. Further, although the SCCS was compiled purposefully to minimize the effects of cultural, spatial, or environmental autocorrelation (see SI Text S5), there may nevertheless still exist auto-correlative relationships that could skew perceived relationships between variables (94). And, finally, because the data for each group included in the database were collected by many different researchers through time, the data are not necessarily coeval. SCCS coders have tried to ameliorate this problem by coding most of the variables either as interval-scale data at a very coarse resolution or as nominal-scale data, but there are still many missing values throughout the database. (Although the resolution of these data can be considered coarse by ethnographic standards, their resolution is actually on par with, or better than, most archaeological data.) These problems are serious issues, but are unfortunately all-to-familiar to archaeologists who are used to dealing with coarse, fragmentary, and biased data. These properties can be viewed as virtues, however, and, if analyzed with methods appropriate for these data types and quality (SI Text S6), can still yield interesting and far-reaching insight into human variability. The SCCS data are, in large part, on par with most archaeological data and can be treated exactly like archaeological data so insights derived from it are directly applicable to archaeological inquiry.

Estimates of net primary production (NPP) were obtained from outside of the SCCS database. We obtained these estimated NPP values by using the latitude and longitude reported in the SCCS for each society to query a global map of NPP. We used the global 1-km resolution dataset provided by Kucharik et al. (60), and, to account for error in the coordinates and localized variation in NPP, we uploaded the maximum NPP value in a three-cell radius around the SCCS coordinates for each of the 186 societies. In some cases (coastal or island societies), the SCCS coordinates were above ocean, and so we had to manually enter coordinates for the nearest land.

SI Text S4: Multiple Imputation

Due to the nature of ethnographic data and research, many of the SCCS variables do not contain information for all of the186 SCCS societies. We handled these data gaps via multiple imputation (MI), which is an accepted method for managing missing data in statistical analysis of the SCCS data and has been shown to provide better results than list-wise deletion in traditional regression and correlation-based analyses (95). Imputation is a statistical procedure that “fills in” missing data based on a function of all other variables and cases in the dataset. MI differs from standard imputation in that it introduces a controlled degree of randomness into the imputation process and iteratively repeats the imputation process to create i imputed datasets, each of which contains slightly different imputations of missing data cases. Traditionally, MI is used in such a way that each imputed dataset is used to undertake a statistical test (e.g., MANOVA), and the results of each are then recombined to get a final estimate of the statistical test that also approximates the error in the analysis associated with the missing data. This traditional approach is not possible with our geometric data analysis workflow, which requires visual approximation of clustering results (SI Text S6). We chose to use the mean values of the i imputed datasets as input into the routine and gained an understanding of the potential for error derived from the imputation process through the SE of the imputed values across all i imputed datasets. During this process, we discovered that imputation error was minimal when variables had fewer than about 8% missing cases (i.e., when data existed for at least 171 of the 186 SCCS societies), and so we limited our analysis to variables that met this criterion (Table S2). This culling resulted in a final imputed dataset that contained the maximum possible number of variables related to subsistence, economy, mobility, and demography, without introducing unnecessary variability due to many missing data cases. Finally, MI is most effective when related extra variables (i.e., variables not intended to be used in the final analysis) are included. These extra variables are also indicated in Table S2. The imputation was carried out in the R statistical language using the “mi” package. Imputed datasets used in this research are made available as described in SI Text S7.

SI Text S5: Alternative Explanations for Observed Patterning

Although we believe that the spatial patterning we observed in our analysis is consistent with the idea of attractors and repellors, there are other possible forces that could have induced structure on the data. We address four of the more apparent possibilities here.

The first possibility is that the patterning occurs by chance in this dataset. To test this possibility, we conducted a bootstrapped, iterative rerandomization of the SCCS data used in our study. In this procedure—a kind of Monte Carlo method—the data in each column (SCCS variable) were independently shuffled at each iteration, to make 186 new sample “societies.” We repeated the shuffling many times, creating many novel combinations of potential societies from the pool of real SCCS data values. For each of these combinations of fictitious societies, we conducted NMMDS and K-medoids cluster analyses. Fig. S6 shows 20 sample biplots of some of the shuffled datasets. None of the biplots for the reshuffled datasets displayed the kind of clustering and cluster separation that we observed in the real SCCS sample societies. That the reshuffled datasets all produced randomized patterning in NMDS space indicates that the patterns we observe in the main text are not likely to occur—i.e., some process has introduced structure.

The second major alternative explanation is the effect of Galton's problem (social, spatial, and/or environmental autocorrelation). Although the 186 societies of the SCCS were chosen specifically to reduce this effect (59), Dow and Eff (94) have shown that a significant amount of autocorrelation does remain in the SCCS data. Our geometric data analysis workflow (SI Text S6) is less susceptible to autocorrelative errors than are regression-based techniques (such as ANOVA or MANOVA), but we nevertheless need to understand the effect of autocorrelation or other biases in our analyses. Attempts to understand the impact of autocorrelation are complicated by the fact that (spatially autocorrelated) environmental conditions may, in fact, be very important structuring elements in defining the human subsistence attractors and repellors that we are looking for. Because we are explicitly interested in the effect of environmental factors on the patterning of human subsistence variability in the SCCS, we do not want to “correct” for their effects. Our approach is to separate environmental variables into a discrete dataset (Table S2) that can be combined or withheld from any analysis. This approach allows us to assess the effect of adding these variables, without necessarily controlling for their influences. Our analyses did find that certain environmental variables, such as seasonality and environmental productivity, are important structuring components of the patterning we observed. We do not find this result to be inconsistent with our hypothesis of subsistence attractors.

Social or cultural autocorrelation is more difficult to assess and is more likely to be a substantial alternative structuring influence on the observed patterning. Although we did conduct preliminary investigations of the influence of social variables (e.g., language, religion) on the patterning of societies in some of our analyses (e.g., in exploratory multidimensional analyses), we were unable to include them in the final analysis in ways that were heuristically meaningful. The particular social variables of interest (Table S2) were coded in the SCCS as categorical variables that cannot be ordered on a gradient (a fundamental requirement for use as controlling variables in a CCA routine). In the limited tests that we did perform, we noticed no significant influence of social variables to the observed subsistence patterns.

Observer biases are another potentially important alternative explanation for the patterning that we observed. These biases might be inherent in the SCCS data (SI Text S3), and it may be that 19th and 20th century ethnographers projected their own beliefs about subsistence possibilities into the data that they collected. Although it is probable that widely held, preconceived divisions of economic subtypes influenced the work of these ethnographers to some degree, it is unlikely (i) that these biases would have similarly affected the reporting of all the different types of empirical data used in this study (Table S2) and (ii) that all of the researchers would have been affected in the same way, or to the same degree, by these biases. Further, clusters created solely by these biases should be very discretely defined, with very high cluster separation, and CCA analyses using environmental or mobility data to constrain the axes should show that these variables contribute relatively little to the spatial patterning. Our analyses do not show these trends so we conclude that ethnographer biases, although likely present, do not inordinately affect the outcome of the research.

There could also be bias introduced by the coding process itself because individuals coded data from several ethnographies for comparison. Although care was taken to try to avoid this possibility during the creation of the SCCS, coders could have subconsciously lumped cases so that clusters of societies are an artifact of coding judgments. More work is needed to address this possibility. Larger sample sizes of one subsistence type, for example, should help sort this problem out.

The process of competitive exclusion could also explain some of the observed patterning. Competition for limited resources with sedentary, agricultural societies has, over time, constrained less-populous, more-mobile societies to less-productive lands. It could be that the observed correlations between environmental productivity (and seasonality) are due to this more recently induced process and do not reflect the relationship between subsistence and environment as it existed in the past (e.g., at the Pleistocene–Holocene transition). However, a substantial number of the smaller scale SCCS societies lived in regions that now support substantial sedentary agricultural populations but did not at the time of ethnographic study (e.g., California and Australia). Further, although processes of competitive exclusion may affect the subsistence patterning seen in the SCCS data, the process of intersocial competition is not at odds with our hypotheses about the formation of subsistence attractors. Indeed, competitive exclusion may well be one of the important controlling variables that help to shape attractors—and their resilience—over time. Although we did not explicitly study the effect of competition on the patterns observed in the SCCS, it is a potentially fruitful future research direction.

Finally, sampling biases may also be responsible for some of the patterning we observed. Because the societies included in the SCCS were, for the most part, studied in the last 200 y, there is a chance that they do not represent the full breadth of all possible human subsistence strategies. It could be that the observed gaps in the cluster results are less the product of repellors than they are a product of an incomplete sample of subsistence systems. Sampling error is a significant issue, and not one that is easily dismissed. The obvious solution is to increase the sample size and expand the sampling criteria to include prehistoric peoples. Archaeological data are the only source of information about the economic activities of prehistoric populations, but the incomplete nature of the archaeological record, and their derivation from proxy measures instead of direct observation, make it difficult (although not impossible) to extend the sample to include societies from many different times. We acknowledge that sample size is an issue for the current dataset.

SI Text S6: Geometric Data Analysis Workflow for Cross-Cultural Data

Following established methods of geometric data analysis (62), we prefer to examine multivariate data as “clouds of points” in multidimensional space, rather than to extract minimal sets of variables to analyze with more traditional, but dimensionally limited, comparative statistical tests. Thus, the workflow we use in this research begins with multidimensional techniques to reduce the high number of initial attribute dimensions to a lower number of eigenvectors that can be displayed in two- or three-dimensional plots.

Nonmetric multidimensional scaling (NMMDS) is a dimensional reduction procedure with appropriate techniques for analysis of categorical data types. It is designed to help researchers understand the structure of a multidimensional dataset by scaling the variability present in that dataset to a smaller number of dimensions (in this case, two) (96). The input data points are projected into the space created by the two most dominant NMMDS dimensions and can be viewed as a scatter plot where the physical proximity of the projected points denotes a multidimensional affinity (i.e., the closer two points are on the NMMDS plot, the more similar their input variables are). NMMDS is often used in analysis of ecological datasets as a kind of “indirect” gradient analysis to identify previously unknown internal or external structural constraints on plant and animal communities. We therefore find it useful to start our data analysis as a workflow using NMMDS ordination

Canonical correspondence analysis (CCA) is similar to NMMDS in that it projects multivariate data into 2D space, but it constrains the ordination according to one or more known (or suspected) gradients (97). It is therefore often used as a kind of “direct” gradient analysis of ecological data to better understand known or hypothesized constraints within different ecological communities (97). CCA plots allow the researcher to understand how a small group of preidentified variables constrain or affect the patterning of all other measured variables and thus provides a kind of loose hypothesis test for ideas about structuring relationships within the dataset.

The results of both NMMDS and CCA can be graphically displayed as biplots, on which are plotted the input case studies (in this case, SCCS societies) and/or the input variables (in this case, variables related to human subsistence, mobility, demography, etc.) in the phase space created by the first two dimensions of the dimensional reduction. The plotted location of the input variables in relationship to the input cases (SCCS societies) is important; each input variable can be considered as a vector with distance and direction relative to the origin, such that their “pull” on the input cases is what creates the 2D spatial patterning of the input cases on the biplots. In other words, the biplots also provide a graphical representation of the amount of influences that each input variable has on the creation, separation, and character of each of any clustering.

To further highlight any extant spatial patterning, the dimensionally reduced dataset is subjected to a K-medoids clustering routine. K-medoids is similar to the better known K-means routine in that it iteratively assigns input data points to one of a predefined number of clusters based on a distance metric (in this case, Manhattan) and an iteratively defined cluster center; but, whereas K-means uses the mean of the coordinates of all input data points included in a cluster as the cluster center (i.e., a “centroid”), K-medoids uses the most centrally located of the input data points in the cluster (i.e., a “medoid”) (98). This property is advantageous because clustering routines that rely on calculating an “average,” such as K-means, cannot be used with categorical data types (99) and are also more susceptible to outliers and “noise” in the input dataset (98, 99).

By manipulating the color and symbology of points on the resulting plots, we can also thematically represent up to two external variables to see how they relate to the spatial patterning of input societies and variables on the biplot. We have chosen to represent the results of the K-medoids clustering routine as colors and to use the point symbology to represent the economic classification of the society as determined by the SCCS coders from the ethnographic data. Hierarchical convex hulls provide a graphical representation of the degree of cluster separation (the amount of empty space between clusters), the tightness of the clustering itself (the physical proximity of points within each cluster), the uniformity of each cluster (the overall size and shape of the cluster), and how well the cluster analysis corresponds to traditional anthropological classification by ethnographers.

We formalized the workflow outlined above as a script for the R statistical package. We make this script available as described in SI Text S7.

SI Text S7: SCCS Datasets and R Script for Geometric Data Analysis

The R code used to create all of the figures in the main text and the imputed SCCS datasets used in the analyses are made available as a free download at the following persistent URL: figshare.com/articles/Cross_cultural_data_for_multivariate_analysis_of_subsistence_strategies/1404233. They are citable as a collection (100), with the following unique digital object identifier (doi) number: 10.6084/m9.figshare.1404233. The imputed datasets and R code are released under the Creative Commons and MIT licenses, respectively (free to use and modify for any purpose, provided credit is given).

Results

Our multivariate analysis of human subsistence identified four discrete clusters consistent with attractors separated by gaps that may be repellors (Fig. 1A). These clusters are as follows: intensive agriculture, extensive agriculture, pastoralism, and hunting or gathering terrestrial or marine resources. Data depth analysis (via hierarchical convex hulls) of these clusters (Fig. 1B) delimits a potential range of influence and resilience of each hypothesized subsistence attractor (i.e., society clusters) and reveals the potential location of repellors (i.e., gaps) that may separate them. There is weak cluster separation between intensive and extensive agricultural groups, but stronger separation of hunter–gatherers and extensive agriculturalists, hunter–gatherers and herders, and herders and intensive agriculturalists. Herders cluster quite distantly from extensive agriculturalists, as do hunter–gatherers from intensive agriculturalists. Comparison of the cluster results with traditional ethnographic subsistence classification of each SCCS society (Fig. 1A) suggests that there exists smaller scale variation within the clusters surrounding each macrolevel attractor, which larger samples may help illuminate. Fig. 1B illustrates the variables that influence the positioning and internal configuration of the clusters. Different configurations of subsistence activities, settlement fixity, and population density seem to be major factors “pulling” the clusters apart from one another.

Fig. 1.

The results of nonmetric multidimensional scaling (NMMDS) and subsequent K-medoids cluster analysis of subsistence, mobility, and demographic SCCS variables. (A) Biplot showing four macrolevel clusters. Clusters are represented by point color and two levels of hierarchical convex hulls. They may reflect subsistence attractors for hunter–gatherer–fishers, herders, extensive agriculture, and intensive agriculture. Point symbology represents SCCS subsistence labels (v858). Selected societies are labeled. (B) The same biplot, but showing the weightings of input variables instead of input cases, indicating their importance in determining clusters.

CCA allows us to constrain the axes to be linear combinations of a subset of the analyzed variables and evaluate the importance of particular variables in the clustering results. Mobility and demographic variables (Fig. 2A) account for 27.6% of the total variability, with the variation roughly split along two axes: mobility (settlement pattern and settlement fixity) and demography (total population, population density, and community size). Environmental variables (Fig. 2B) account for 18.3% of the total variability, with the variability again split between two axes: temperature seasonality (absolute latitude, average temperature, and number of frost months) and water availability (number of dry months, average precipitation, coefficient of variation in precipitation, and NPP). Subsistence variables (Fig. 2C) account for 18% of the total variability, with three major axes aligned to degree of reliance on agriculture, herding and trade, and hunting–gathering–fishing, respectively.

Fig. 2.

The results of canonical correspondence analysis (CCA) and subsequent K-medoids cluster analysis. In all biplots, colors and hierarchical convex hulls represent clusters, symbology represents SCCS v858, and select societies are labeled. (A) This biplot shows the results of a CCA conducted where the axes were constrained to be linear combinations of variables related to subsistence economy. (B) This biplot shows the results of a CCA conducted where the axes were constrained to environmental variables. (C) This biplot shows the results of a CCA conducted where the axes were constrained to variables related to mobility and demography.

Finally, we can gain insight into how clustering is reconfigured as variables change by dividing and analyzing subsets of the original dataset partitioned by cutoffs in NPP, absolute latitude, residential mobility, and total population. Viewing the results together (Fig. 3) facilitates several unintuitive observations: (i) Not all of the macrolevel clusters are present in each partition, suggesting potential clinal variation in attractors. (ii) Our analysis separates hunter–gatherers from fishers in some partitions, suggesting that the two may be weakly distinct attractors. (iii) Fishing shares some of the same tensions of extensive agriculture, implying that people intensively using an abundant wild resource (such as fish) may face pressures similar to those relying on extensive management of cultivated resources. (iv) Cluster separation (i.e., the resilience of attractors) in the partitioned phase spaces changes between partitions. This separation illustrates the interplay between a set of highly influential constraints of mutually incompatible variables. For example, a high degree of residential mobility is largely incompatible with a very large population, and a high degree of residential sedentism conflicts with a high reliance on animal products. These incompatibilities seem to shape the resilience of subsistence attractors in different environments.

Fig. 3.

The results of multiple NMMDS and K-medoids cluster analyses, where the 186 societies were divided into unique subsets by partitions in important structuring variables (indicated below). In all of the biplots, clusters are represented by point color, point symbology represents SCCS v858, and two levels of hierarchical convex hulls are shown. Select SCCS societies are labeled in each plot. (A–C) Partitioned by cutoffs in net primary production (NPP) (A, NPP > 4; B, 4 > NPP ≥ 1.5; C, NPP < 1.5). (D–F) Partitioned by cutoffs in absolute latitude (D, latitude ≤ ±23.5°; E, ±23.5° < latitude ≤ ±50°; F, ±50° < latitude). (G–I) Partitioned by cutoffs in residential mobility (G, “impermanent” and “permanent” settlements; H, “rotating” and “semisedentary” settlements; I, “migratory” and “seminomadic” settlements). (J–L) Partitioned by cutoffs in total population (J, population > 10,000; K, 10,000 > population ≥ 1,000; L, 1,000 > population).

Following societies across the partitioned datasets provides insight into the conditions in which societies transition between subsistence systems. For example, the Ainu, Nama, and Chiricahua graph variably near two or more different clusters as the dataset is parsed. These groups can be thought of as in a system state that is far from any one local attractor, or, perhaps, have individuals who are capable of moving between attractors. The Nama—Khoisan-speaking hunter–herders in the Western Cape region of South Africa—began to adopt some agriculture when under pressure from European settlers in the late 19th and early 20th centuries (63, 64). At the time of study, the Ainu were hunter–fishers who had traded with feudal Japanese merchants for at least 200 y. The trade had severely depleted important game animals, and the Ainu had begun small-scale swidden horticulture to supplement wild foods (65). In these two cases, the transition phase seems to have been rapid and not very stable. The Chiricahua, although under similar pressures, may be a case in which individuals opportunistically moved between foraging and agriculture subsistence attractors. Although the central and western Chiricahua bands were foragers, Opler's informant from the eastern band was clear that maize was a favorite food and that it was obtained for planting whenever possible (66). He relates, “Only about six or seven families out of the hundred in a big encampment might plant corn....The seeds came from the Mexicans, and many didn't plant because they didn't have seeds” (ref. 66, p. 374). The presence of a stable agricultural system on the landscape made the opportunity available for individuals to experiment in some years without abandoning a foraging economy.

Discussion and Conclusion

A Dynamical Systems Approach to Human Subsistence.

The transition from foraging to farming seems nonlinear and heterogeneous at a global scale. Why? Our goal in this paper has been to widen our perspective from this particular transition and outline how concepts from nonlinear dynamical systems theory—attractors and repellors—help us describe variation and change in human subsistence systems. The spatial clustering and separation apparent in multidimensional plots are consistent with the presence of attractors and repellors in cross-cultural data (Figs. 1–3), and the nature of these attractors and repellors may relate to zones of stability and instability within the total spectrum of food procurement strategies in coupled human and natural systems. Detailed dynamic models will help us to understand the feedback processes that are likely to control the emergence and resilience of subsistence attractors and repellors. We must also advance by investigating alternative explanations for the clustered patterning in the SCCS. We have determined that some of these potential alternatives, such as randomness, sociocultural autocorrelation, or observer biases are unlikely to produce the observed variation (SI Text S5 and Fig. S6). Two other alternatives—the effect of competitive exclusion and sampling bias—warrant further consideration. The former requires investigation as an important controlling variable in its own right, and the second requires an expanded set of input societies that also includes prehistoric case studies (SI Text S5). Nonetheless, we suggest that the interaction of socio-natural forces keeps the subsistence practices of human societies near an attractor. Populations may make a transition to a new subsistence mode when system conditions change enough to erode the resilience of their former attractor. But under many system configurations, societies may remain near an attractor even in the face of increasing pressures that might otherwise induce gradual change. In these cases, dynamical systems theory suggests that critical thresholds may exist that, once surpassed, propagate quick phase changes from one attractor (and period of stability) to another, which are difficult to recoup (39). This possibility allows for both gradual and rapid transition, and explains why a transition could occur quickly or slowly.

The four potential macroscale subsistence attractors identified by our analysis (pastoralism, hunting/gathering/fishing, extensive agriculture, and intensive agriculture) (Fig. 1) are influenced by a small group of controlling variables, including temperature and precipitation seasonality, environmental productivity, degree of residential mobility, and population size. Mobility and population size may be the most influential (Fig. 2). Other variables—including social ones—likely become more important in the manifestation of smaller scale patterning, but, at either scale, societies seem to coalesce around general ways of doing things due to the inherent incompatibilities between important limiting variables. For example, our analysis shows that relatively high populations can be sustained in low-productivity environments in one of two ways: pastoralism or agriculture (Fig. 3 C and J). However, pastoralism requires a high degree of residential mobility, which causes a fundamental tension between the two lifeways in that environmental context. Transitioning between the two would require considerable impetus (e.g., total devastation of flocks or harvests). This idea feeds back into the issue of opportunity versus necessity in subsistence transition.

As conditions change—particularly in major controlling variables—different subsistence transitions may become more or less possible than others. For example, intuitively, a horticultural society already familiar with domestic plants might opportunistically transition to an intensive agricultural strategy, but only if environmental productivity is high enough to allow it. It is also important to consider, however, that not every macroscale cluster was present in the phase space when the data were partitioned across major variables (Fig. 3). Although the same relative patterning of attractors and repellors persisted where present, the overall strength of the different attractors changed between partitions. We infer from this consistency that it is easier to make certain subsistence transitions under some socio-environmental conditions than others. For example, a transition from horticulture to intensive agriculture may be more possible in the tropics than it would be in a temperate climate region (holding population constant) (Fig. 3 D and E), and a transition from hunting–gathering to shifting cultivation may be easier in low NPP environments (Fig. 3C). Extrapolating these insights over archaeological time scales, the interplay of climate or environmental change, technological changes, population change, and changes to the abundance of resources can all affect the resilience of particular subsistence attractors and, thus, subsistence transitions. The key is that controlling variables, like residential mobility (67, 68) and resource seasonality (69), may have a much greater affect on an attractor's resilience than others and so even subtle changes in them could lead to punctuated change.

We argue that dynamic optimal foraging models that include the process of niche construction will be useful in evaluating whether and how subsistence attractors emerge in socio-natural systems. The centrality of residential mobility in our results suggests that the evolutionary ecology of time allocation may be important to understand the emergence of subsistence attractors from human-resource feedbacks. For example, changing resilience of a hunting and gathering attractor may feedback into the ratio of search time to handling costs, creating critical thresholds where it suddenly becomes more profitable to remain sedentary than to search and travel. Another possibility is that the evolution of complex social structures is a response to fundamental trade-offs in time allocation. Historic Tuareg pastoralists inhabited the heart of the Sahara, but they had a complex caste system of nobles, serfs, slaves, and freedmen that solved the time conflicts necessary to allow them to do agriculture near oases while also engaging in mobile pastoralism and long-distance trade of salt and other market resources (70). Dynamic systems models of the ideal despotic distribution are particularly interesting for exploring such possibilities (71).

The Transition to Food Production.

There is evidence that terminal Pleistocene hunter–gatherer groups were intensively managing landscapes in many parts of the world (72, 73), including in areas that would become centers of early agriculture (2, 74). It is natural to envision the origins of food production as an extension of this management, which, in many ways, it was. Our analysis illustrates that the transition was not simple, however, nor need it have been gradual. It is unlikely that food production would always have emerged from the same initial conditions, but it is clear that significant socio-natural changes must have accrued to predicate the transition. Landscape management practices by Late Pleistocene hunters, such as moving species to new territories (73) and management of woodlands by burning (72, 73), combined with socio-technical changes, such as decreased residential mobility and increased storage (52), all may have weakened the resilience of hunting–gathering attractors by changing constraints on human subsistence and human-resource feedbacks. It is also possible that increasing population densities or climatic changes may also have narrowed the resilience of hunting and gathering attractors in some areas, increasing the chance of a critical transition (SI Text S2). All of these changes would have also increased the temporal stability of subsistence practices that incorporated management of central predomesticated plants. These processes in and of themselves were likely not enough to have induced a full transition. Exemplifying this complexity, we note that the intensive wild resource users in the SCCS (e.g., the fisher societies), although likely at the margins of the zone of influence for the hypothesized hunting macroscale attractor, nonetheless clustered with hunters in most of our analyses. It is, therefore, likely that, whereas prior system reorganization was required, the actual transition to food production itself occurred once critical thresholds in the optimal allocation of time for subsistence tasks or other important constraining variables were surpassed, and the everyday requirements for a hunter–gatherer lifeway could no longer be met. The pathways of individual groups across this threshold were likely unique and related to stochastic events as well as system-component interaction and the feedback effects of accumulated change. But once they transitioned, it would have been difficult to recover a hunting and gathering way of life.

Viewing human subsistence systems as complex adaptive phenomena provides a unique opportunity to define both internal and external mechanisms for subsistence change, without giving primacy to one over the other or requiring any one factor. It also provides a basis for understanding why long periods of “pre-domestication cultivation” (6) occur for some crops in some centers of early agriculture, but not for others. Dynamical systems theory combines with evolutionary perspectives to offer a set of governing mechanisms that help to show how major transitions would occur under particular conditions. Importantly, these mechanisms do not preclude the inclusion of historical contingency in explanatory models of subsistence transition. Indeed, under this framework, we can seek to better understand how each case of novel transition was predicated in system-level changes to major controlling variables, their incompatibilities, currencies, and the thresholds that existed before the change.

Homo sapiens have been remarkably creative in the development and adoption of different subsistence practices in a range of global prehistoric and historic contexts. For many decades, anthropologists have studied adaptive subsistence variation, and much headway has been made in describing, categorizing, and modeling the breadth of diverse economic practices in the human past. Researchers have developed a general framing of human subsistence through time, have shown that humans can undertake very different subsistence strategies in similar physical environments, and have developed a reasonably good understanding of the timing and general circumstances of major subsistence transitions, such as the shift to plant and animal domestication around the world. Drawing on the growing awareness that the transition from foraging to farming was gradual in some places and punctuated in others, we have put forth a nonlinear theory of subsistence transition, including the transition from foraging to farming. We argue that modeling the emergence of alternative attractors and repellors helps define subsistence system variation and may help us understand why the transition from foraging to farming was at times gradual or punctuated.