Toward a theory of punctuated subsistence change

Toward a theory of punctuated subsistence changeIsaac I. T. Ullaha,1, Ian Kuijtb, and Jacob Freemanc

aSchool of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287-2402; bDepartment of Anthropology, University of Notre Dame,Notre Dame, IN 46556; and cDepartment of Sociology, Social Work and Anthropology, Utah State University, Logan, UT 84322-0730

Edited by Dolores R. Piperno, Smithsonian Institution, Fairfax, VA, and approved June 12, 2015 (received for review February 20, 2015)

Discourse on the origins and spread of domesticated species focuseson universal causal explanations or unique regional or temporaltrajectories. Despite new data as to the context and physicalprocesses of early domestication, researchers still do not understandthe types of system-level reorganizations required to transition fromforaging to farming. Drawing upon dynamical systems theory andthe concepts of attractors and repellors, we develop an understand-ing of subsistence transition and a description of variation in, andemergence of, human subsistence systems. The overlooked role ofattractors and repellors in these systems helps explain why the ori-gins of agriculture occurred quickly in some times and places, butslowly in others. A deeper understanding of the interactions of alimited set of variables that control the size of attractors (a proxyfor resilience), such as population size, number of dry months, netprimary productivity, and settlement fixity, provides new insights intothe origin and spread of domesticated species in human economies.

complex adaptive systems | subsistence change | origins of agriculture |social-ecological systems

Recent work highlights that the transition from foraging tofarming was nonlinear and heterogeneous (e.g., refs. 1–7). That

is, rather than an inevitability, early shifts to food production wereonly one of many possible outcomes that could have been reachedfor a given set of dynamically interacting social and ecologicalvariables. Although the forager–farmer transition is one of themost fundamental changes in human evolution, our understandingof the forager–farmer transition is theoretically fractious (1, 3–6,8–36), with scholarly discourse dominated by the assumption thatthe forager adoption of domesticates was driven either by sub-sistence necessity or because domesticates provided a desirableopportunity or assurance. Given our adaptive flexibility, however, itis clear that both options are possible, depending on the situation.The challenge is distinguishing the contextual settings in whichadoptions were linked to necessity versus opportunity. Simply put,there is currently no sufficient theory to explain the nonlinear andcontingent worldwide transitions from foraging to farming.In this paper, we use concepts from Dynamical Systems Theory

(SI Text S1) to model subsistence variation among contemporaryethnographic groups from an evolutionary perspective. We focuson a critical question: How can researchers use the concepts ofattractors and repellors—so integral to understanding many non-linear dynamical systems—to describe variation in the subsistencestrategies of human societies? This framing provides general in-sights into why transitions from foraging to farming, at a globalscale, exhibit nonlinearity and heterogeneity, and why the shift wassometimes gradual, and other times punctuated. Drawing uponcomparative ethnographic case studies, we formalize the use ofcross-cultural data in a theory-backed methodology to ascertainhow the attractor/repellor concept can be use to describe sub-sistence variation in human societies. Our analysis elucidatesbroad, multidimensional trends across the breadth of human sub-sistence practices and is a step toward developing a theory ofnonlinear subsistence change in human societies.

Dynamical Systems and Human EcologyWe start from the premise that human societies are complexadaptive systems, with heterogeneous agents at several levels oforganization, 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 dynamicalsystems in which the independent decisions and actions of in-dividual components of the system (i) self organize, (ii) changeover time, (iii) interact to derive novel emergent properties ofthe system, and (iv) may adapt to work in the interest of thesystem as a whole (37, 38). Viewing human societies as complexsystems 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 be-tween humans and their resources may lead to “attractors” and“repellors” that describe the variation in human subsistencesystems and that (ii) a small number of “controlling” variablesmay disproportionately affect change within subsistence systems.If these propositions have merit, then, using a few importantvariables, we should be able to identify clusters of societies in theethnographic record that occupy similar, although not iso-morphic, attractors. These clusters will be separated by economicvoids where subsistence strategies are unlikely to persist due tothe presence of repellors.In dynamical systems theory, attractors are system states toward

which (all else being equal) a complex adaptive system will tend toevolve, and, conversely, repellors are system states that the systemwill tend to avoid (39, 40). In other words, an attractor is a con-figuration of system subcomponents that are relatively stable overtime whereas a repellor is a configuration that is not. Thus, at anygiven time, a complex adaptive system is always evolving toward anattractor, but rarely reaches it (i.e., the system is never in “equi-librium”). Importantly, the size of an attractor determines itsresilience, which is how much environmental change a system cancope with before feedbacks between variables change (SI Text S2and Fig. S5) (41). Attractors emerge from these kinds of feedbacks,and our working supposition is that human subsistence attractorsemerge from cross-scale feedbacks between human and naturalresources in socio-natural systems.

Significance

The questions of how, when, and why humans transitionedfrom hunting and gathering to food production are importantto understand the evolution and sustainability of agriculturaleconomies. We explore cross-cultural data on human subsis-tence with multivariate techniques and interpret the resultsfrom the perspective of human societies as complex adaptivesystems. We gain insight into several controlling variables thatmay inordinately influence the possibilities for subsistencechange and into why the forager–farmer transition occurredquickly in some cases and more gradually in others.

Author contributions: I.I.T.U. designed research; I.I.T.U. performed research; I.I.T.U. contrib-uted new reagents/analytic tools; I.I.T.U., I.K., and J.F. analyzed data; and I.I.T.U., I.K., andJ.F. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Data deposition: The R code used to create all of the figures in the main text and theimputed SCCS datasets used in the analyses are made available as a free download at thefollowing persistent URL: figshare.com/articles/Cross_cultural_data_for_multivariate_analysis_of_subsistence_strategies/1404233.1To whom correspondence should be addressed. Email: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1503628112/-/DCSupplemental.

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Complex systems are usually in a dynamic state that is largelydominated by the force of a local attractor, but not solely con-trolled by it. Because these systems are dynamical, evolving, andopen, their attractors and repellors also change in strength andconfiguration as system subcomponents and emergent, macrolevelconditions change (Fig. S5). This property holds major implica-tions for how complex adaptive systems change over time. Aninteresting set of possibilities for change occurs when a system ispositioned between two or more attractors. Systems operating insuch intermediary locations are available to move from the sphereof influence of one attractor to another. These transitions canoccur either gradually or as very rapid-phase changes, dependingon the resilience of each of the attractors (SI Text S2 and Figs. S3and S4) (39). These properties also control whether the transitionis immediately reversible (i.e., related to choices of opportunity) orrepresents 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 ofattractors and repellors (42). Controlling variables are those thathave a disproportionate impact on the feedback between indiv-iduals and their use of resources and thus strongly affect thestructure of a system. For example, Holling (43) found that, fromhost–parasite, to lakes, to the boreal forest, only three to fourvariables control the structure of dynamical systems models ofecosystems. Similar observations have been made of dynamicalsystems models that describe socio-natural systems (e.g., refs. 44–49). In one of these examples, Freeman and Anderies (50) arguethat the ratio of population to resources controls a regime changefrom a mobile foraging to an intensive, property-based foragingattractor. The meta-insight that we pull from these models is thatreframing human subsistence systems as emergent outcomes ofcomplex adaptive processes in a nonlinear system suggests that it isuseful to identify potential controlling variables. Such variableswould point the way forward for further theoretical development.

Materials and MethodsAll explanations for subsistence change in archaeology are built on an un-derstanding of ethnographically documented societies (e.g., refs. 17, 23,45–49, 51, and 52). Much of this knowledge derives from traditional eth-noarchaeological research from the last century that provided case studiesof human groups living traditional, or near-traditional, lifeways (SI Text S3).These studies often resulted in models designed to address specific archae-ological problems (e.g., refs. 53 and 54) or to relate archaeological phe-nomena to theories of human behavior (e.g., ref. 55). Comparativeethnoarchaeology, on the other hand, attempts to identify global patternsof human behavior to either generate new hypotheses or to evaluate eco-logical models (e.g., refs. 47, 50, 51, and 56–58).

In the tradition of comparative approaches, in this study, we used auto-mated multidimensional techniques to identify patterns in human sub-sistence variability with which to assess the attractor/repellor hypothesis. Weexamined subsistence, mobility, economic, demographic, and environmentaldata for the 186 societies of the Standard Cross-Cultural Sample (SCCS) (SIText S3 and Tables S1 and S2) (59). We supplemented these data with in-formation about Net Primary Production (NPP) from the Atlas of the Bio-sphere (60, 61) (SI Text S3 and Table S2). We address issues of missing data,potential autocorrelation (i.e., “Galton’s problem”), and alternative expla-nations of patterning within the SCCS data in SI Text S4 and SI Text S5. Ourworkflow followed Le Roux and Rouanet’s (62) “geometric data analysis” (SIText S6) and was designed to graphically identify and intuit natural divisionsin cross-cultural data by combining the result of multivariate clustering withdimensional reduction analyses. Specifically, we used K-medoids clusteringpaired with nonmetric multidimensional scaling (NMMDS) or canonicalcorrespondence analysis (CCA). We used the workflow to plot societies in aphase space created by the ordination routine, which condenses many di-mensions of subsistence activities, mobility characteristics, settlement types,and so on, into a biplot. We used plot symbology to thematically display therelationship between the spatial patterning of societies within that phasespace to the input variables, other variables, or other data analyses. We usedthese techniques to ascertain whether the global SCCS sample of subsis-tence systems is characterized by clusters and gaps that might be analogousto attractors and repellors. All analyses were undertaken in R, using the“cluster” and “vegan” multidimensional analysis modules. We include ourimputed datasets and R code as supplemental data (SI Text S7).

ResultsOur multivariate analysis of human subsistence identified fourdiscrete clusters consistent with attractors separated by gapsthat may be repellors (Fig. 1A). These clusters are as follows:intensive agriculture, extensive agriculture, pastoralism, andhunting or gathering terrestrial or marine resources. Data depthanalysis (via hierarchical convex hulls) of these clusters (Fig. 1B)delimits a potential range of influence and resilience of each hy-pothesized subsistence attractor (i.e., society clusters) and revealsthe potential location of repellors (i.e., gaps) that may separatethem. There is weak cluster separation between intensive andextensive agricultural groups, but stronger separation of hunter–gatherers and extensive agriculturalists, hunter–gatherers andherders, and herders and intensive agriculturalists. Herders clusterquite distantly from extensive agriculturalists, as do hunter–gath-erers from intensive agriculturalists. Comparison of the clusterresults with traditional ethnographic subsistence classification ofeach SCCS society (Fig. 1A) suggests that there exists smaller scalevariation within the clusters surrounding each macrolevel attrac-tor, which larger samples may help illuminate. Fig. 1B illustratesthe variables that influence the positioning and internal configu-ration of the clusters. Different configurations of subsistence ac-tivities, settlement fixity, and population density seem to be majorfactors “pulling” the clusters apart from one another.CCA allows us to constrain the axes to be linear combinations

of a subset of the analyzed variables and evaluate the importanceof particular variables in the clustering results. Mobility anddemographic variables (Fig. 2A) account for 27.6% of the totalvariability, with the variation roughly split along two axes: mo-bility (settlement pattern and settlement fixity) and demography(total population, population density, and community size). En-vironmental variables (Fig. 2B) account for 18.3% of the totalvariability, with the variability again split between two axes: tem-perature seasonality (absolute latitude, average temperature, andnumber of frost months) and water availability (number of drymonths, average precipitation, coefficient of variation in pre-cipitation, and NPP). Subsistence variables (Fig. 2C) account for18% of the total variability, with three major axes aligned to de-gree of reliance on agriculture, herding and trade, and hunting–gathering–fishing, respectively.Finally, we can gain insight into how clustering is reconfigured

as variables change by dividing and analyzing subsets of theoriginal dataset partitioned by cutoffs in NPP, absolute latitude,residential mobility, and total population. Viewing the resultstogether (Fig. 3) facilitates several unintuitive observations: (i) Notall of the macrolevel clusters are present in each partition, sug-gesting potential clinal variation in attractors. (ii) Our analysisseparates hunter–gatherers from fishers in some partitions, sug-gesting that the two may be weakly distinct attractors. (iii) Fishingshares some of the same tensions of extensive agriculture, implyingthat people intensively using an abundant wild resource (such asfish) may face pressures similar to those relying on extensivemanagement of cultivated resources. (iv) Cluster separation (i.e.,the resilience of attractors) in the partitioned phase spaces changesbetween partitions. This separation illustrates the interplay be-tween a set of highly influential constraints of mutually in-compatible variables. For example, a high degree of residentialmobility is largely incompatible with a very large population, anda high degree of residential sedentism conflicts with a high re-liance on animal products. These incompatibilities seem to shapethe resilience of subsistence attractors in different environments.Following societies across the partitioned datasets provides

insight into the conditions in which societies transition betweensubsistence systems. For example, the Ainu, Nama, and Chiri-cahua graph variably near two or more different clusters as thedataset is parsed. These groups can be thought of as in a systemstate that is far from any one local attractor, or, perhaps, haveindividuals who are capable of moving between attractors. TheNama—Khoisan-speaking hunter–herders in the Western Caperegion of South Africa—began to adopt some agriculture whenunder pressure from European settlers in the late 19th and early

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20th centuries (63, 64). At the time of study, the Ainu werehunter–fishers who had traded with feudal Japanese merchants forat least 200 y. The trade had severely depleted important gameanimals, and the Ainu had begun small-scale swidden horticultureto supplement wild foods (65). In these two cases, the transitionphase seems to have been rapid and not very stable. The Chiri-cahua, although under similar pressures, may be a case in whichindividuals opportunistically moved between foraging and agri-culture subsistence attractors. Although the central and westernChiricahua bands were foragers, Opler’s informant from theeastern band was clear that maize was a favorite food and that itwas obtained for planting whenever possible (66). He relates,“Only about six or seven families out of the hundred in a bigencampment might plant corn....The seeds came from the Mexi-cans, and many didn’t plant because they didn’t have seeds” (ref.66, p. 374). The presence of a stable agricultural system on thelandscape made the opportunity available for individuals to ex-periment in some years without abandoning a foraging economy.

Discussion and ConclusionA Dynamical Systems Approach to Human Subsistence. The transi-tion from foraging to farming seems nonlinear and heteroge-neous at a global scale. Why? Our goal in this paper has beento widen our perspective from this particular transition andoutline how concepts from nonlinear dynamical systemstheory—attractors and repellors—help us describe variation andchange in human subsistence systems. The spatial clustering and

separation apparent in multidimensional plots are consistentwith the presence of attractors and repellors in cross-culturaldata (Figs. 1–3), and the nature of these attractors and repellorsmay relate to zones of stability and instability within the totalspectrum of food procurement strategies in coupled human andnatural systems. Detailed dynamic models will help us to un-derstand the feedback processes that are likely to control theemergence and resilience of subsistence attractors and repellors.We must also advance by investigating alternative explanationsfor the clustered patterning in the SCCS. We have determinedthat some of these potential alternatives, such as randomness,sociocultural autocorrelation, or observer biases are unlikely toproduce the observed variation (SI Text S5 and Fig. S6). Twoother alternatives—the effect of competitive exclusion andsampling bias—warrant further consideration. The former re-quires investigation as an important controlling variable in itsown right, and the second requires an expanded set of inputsocieties that also includes prehistoric case studies (SI Text S5).Nonetheless, we suggest that the interaction of socio-naturalforces keeps the subsistence practices of human societies near anattractor. Populations may make a transition to a new sub-sistence mode when system conditions change enough to erodethe resilience of their former attractor. But under many systemconfigurations, societies may remain near an attractor even in theface of increasing pressures that might otherwise induce gradualchange. In these cases, dynamical systems theory suggests thatcritical thresholds may exist that, once surpassed, propagate quick

Fig. 1. The results of nonmetric multidimensionalscaling (NMMDS) and subsequent K-medoids clusteranalysis of subsistence, mobility, and demographicSCCS variables. (A) Biplot showing four macrolevelclusters. Clusters are represented by point color andtwo levels of hierarchical convex hulls. They mayreflect subsistence attractors for hunter–gatherer–fishers, herders, extensive agriculture, and intensiveagriculture. Point symbology represents SCCS sub-sistence labels (v858). Selected societies are labeled.(B) The same biplot, but showing the weightings ofinput variables instead of input cases, indicatingtheir importance in determining clusters.

Fig. 2. The results of canonical correspondence analysis (CCA) and subsequent K-medoids cluster analysis. In all biplots, colors and hierarchical convex hulls rep-resent clusters, symbology represents SCCS v858, and select societies are labeled. (A) This biplot shows the results of a CCA conducted where the axes were con-strained to be linear combinations of variables related to subsistence economy. (B) This biplot shows the results of a CCA conducted where the axes were constrainedto environmental variables. (C) This biplot shows the results of a CCA conducted where the axes were constrained to variables related to mobility and demography.

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phase changes from one attractor (and period of stability) to an-other, which are difficult to recoup (39). This possibility allows forboth gradual and rapid transition, and explains why a transitioncould occur quickly or slowly.The four potential macroscale subsistence attractors identified

by our analysis (pastoralism, hunting/gathering/fishing, extensiveagriculture, and intensive agriculture) (Fig. 1) are influenced by asmall group of controlling variables, including temperature andprecipitation seasonality, environmental productivity, degree ofresidential mobility, and population size. Mobility and popula-tion size may be the most influential (Fig. 2). Other variables—including social ones—likely become more important in themanifestation of smaller scale patterning, but, at either scale, so-cieties seem to coalesce around general ways of doing things dueto the inherent incompatibilities between important limiting var-iables. For example, our analysis shows that relatively high pop-ulations can be sustained in low-productivity environments in oneof two ways: pastoralism or agriculture (Fig. 3 C and J). However,pastoralism requires a high degree of residential mobility, whichcauses a fundamental tension between the two lifeways in thatenvironmental context. Transitioning between the two would re-quire considerable impetus (e.g., total devastation of flocks orharvests). This idea feeds back into the issue of opportunity versusnecessity in subsistence transition.As conditions change—particularly in major controlling vari-

ables—different subsistence transitions may become more or lesspossible than others. For example, intuitively, a horticultural

society already familiar with domestic plants might opportunis-tically transition to an intensive agricultural strategy, but only ifenvironmental productivity is high enough to allow it. It is alsoimportant to consider, however, that not every macroscale clus-ter was present in the phase space when the data were parti-tioned across major variables (Fig. 3). Although the samerelative patterning of attractors and repellors persisted wherepresent, the overall strength of the different attractors changedbetween partitions. We infer from this consistency that it is easierto make certain subsistence transitions under some socio-envi-ronmental conditions than others. For example, a transition fromhorticulture to intensive agriculture may be more possible in thetropics than it would be in a temperate climate region (holdingpopulation constant) (Fig. 3 D and E), and a transition fromhunting–gathering to shifting cultivation may be easier in lowNPP environments (Fig. 3C). Extrapolating these insights overarchaeological time scales, the interplay of climate or environ-mental change, technological changes, population change, andchanges to the abundance of resources can all affect the resil-ience of particular subsistence attractors and, thus, subsistencetransitions. The key is that controlling variables, like residentialmobility (67, 68) and resource seasonality (69), may have a muchgreater affect on an attractor’s resilience than others and so evensubtle 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 evaluatingwhether and how subsistence attractors emerge in socio-natural

Fig. 3. The results of multiple NMMDS and K-medoids cluster analyses, where the 186 societies were divided into unique subsets by partitions in importantstructuring variables (indicated below). In all of the biplots, clusters are represented by point color, point symbology represents SCCS v858, and two levels ofhierarchical 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) Partitionedby cutoffs in residential mobility (G, “impermanent” and “permanent” settlements; H, “rotating” and “semisedentary” settlements; I, “migratory” and “semi-nomadic” settlements). (J–L) Partitioned by cutoffs in total population (J, population > 10,000; K, 10,000 > population ≥ 1,000; L, 1,000 > population).

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systems. The centrality of residential mobility in our resultssuggests that the evolutionary ecology of time allocation may beimportant to understand the emergence of subsistence attractorsfrom human-resource feedbacks. For example, changing resil-ience of a hunting and gathering attractor may feedback into theratio of search time to handling costs, creating critical thresholdswhere it suddenly becomes more profitable to remain sedentarythan to search and travel. Another possibility is that the evolu-tion of complex social structures is a response to fundamentaltrade-offs in time allocation. Historic Tuareg pastoralistsinhabited the heart of the Sahara, but they had a complex castesystem of nobles, serfs, slaves, and freedmen that solved the timeconflicts necessary to allow them to do agriculture near oaseswhile also engaging in mobile pastoralism and long-distancetrade of salt and other market resources (70). Dynamic systemsmodels of the ideal despotic distribution are particularly in-teresting for exploring such possibilities (71).

The Transition to Food Production. There is evidence that terminalPleistocene hunter–gatherer groups were intensively managinglandscapes in many parts of the world (72, 73), including in areasthat would become centers of early agriculture (2, 74). It isnatural to envision the origins of food production as an extensionof this management, which, in many ways, it was. Our analysisillustrates that the transition was not simple, however, nor needit have been gradual. It is unlikely that food production wouldalways have emerged from the same initial conditions, but it isclear that significant socio-natural changes must have accrued topredicate the transition. Landscape management practices byLate Pleistocene hunters, such as moving species to new terri-tories (73) and management of woodlands by burning (72, 73),combined with socio-technical changes, such as decreased resi-dential mobility and increased storage (52), all may have weak-ened the resilience of hunting–gathering attractors by changingconstraints on human subsistence and human-resource feedbacks.It is also possible that increasing population densities or climaticchanges may also have narrowed the resilience of hunting andgathering attractors in some areas, increasing the chance of acritical transition (SI Text S2). All of these changes would havealso increased the temporal stability of subsistence practices thatincorporated management of central predomesticated plants.These processes in and of themselves were likely not enough tohave induced a full transition. Exemplifying this complexity, wenote that the intensive wild resource users in the SCCS (e.g., thefisher societies), although likely at the margins of the zone of in-fluence for the hypothesized hunting macroscale attractor, none-theless clustered with hunters in most of our analyses. It is,therefore, likely that, whereas prior system reorganization wasrequired, the actual transition to food production itself occurredonce critical thresholds in the optimal allocation of time for

subsistence tasks or other important constraining variables weresurpassed, and the everyday requirements for a hunter–gathererlifeway could no longer be met. The pathways of individual groupsacross this threshold were likely unique and related to stochasticevents as well as system-component interaction and the feedbackeffects of accumulated change. But once they transitioned, itwould have been difficult to recover a hunting and gathering wayof life.Viewing human subsistence systems as complex adaptive

phenomena provides a unique opportunity to define both in-ternal and external mechanisms for subsistence change, withoutgiving 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 somecenters of early agriculture, but not for others. Dynamical sys-tems theory combines with evolutionary perspectives to offer aset of governing mechanisms that help to show how majortransitions would occur under particular conditions. Importantly,these mechanisms do not preclude the inclusion of historicalcontingency in explanatory models of subsistence transition. In-deed, under this framework, we can seek to better understandhow each case of novel transition was predicated in system-levelchanges to major controlling variables, their incompatibilities,currencies, and the thresholds that existed before the change.Homo sapiens have been remarkably creative in the de-

velopment and adoption of different subsistence practices in arange of global prehistoric and historic contexts. For many de-cades, anthropologists have studied adaptive subsistence variation,and much headway has been made in describing, categorizing, andmodeling the breadth of diverse economic practices in the humanpast. Researchers have developed a general framing of humansubsistence through time, have shown that humans can undertakevery different subsistence strategies in similar physical environ-ments, and have developed a reasonably good understanding ofthe timing and general circumstances of major subsistence tran-sitions, such as the shift to plant and animal domestication aroundthe world. Drawing on the growing awareness that the transitionfrom foraging to farming was gradual in some places and punc-tuated in others, we have put forth a nonlinear theory of sub-sistence transition, including the transition from foraging tofarming. We argue that modeling the emergence of alternativeattractors and repellors helps define subsistence system variationand may help us understand why the transition from foraging tofarming was at times gradual or punctuated.

ACKNOWLEDGMENTS. Advice from C. Michael Barton, J. Marty Anderies, andLoukas Barton helped us to orient our thoughts. Comments from twoanonymous reviewers helped improve the paper. The University of PittsburghCenter for Comparative Archaeology provided support for some of the research.

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Supporting InformationUllah et al. 10.1073/pnas.1503628112SI Text S1: Dynamical Systems Theory, Complex AdaptiveSystems, Social-Ecological Systems, and Resilience TheoryDynamical systems theory (DST) (often also referred to as“complex systems theory” or “complexity theory”) is a body oftheory that has evolved out of the work of researchers across avariety of disciplines (but particularly physicists, ecologists, andcomputer scientists) who, in the latter half of the 20th century,began to rethink previously accepted notions about the linearnature of natural phenomena (75). They challenged the idea thatthe outcome of a series of stimulus events on natural systemscould be accurately predicted, if only the “correct” equationcould be found. In other words, researchers began to questionthe validity of the quest for unified causal explanations. A re-examination of the linkages between stimuli and results, largelyinformed by the advent of computer-based simulation modeling,led to the idea of feedback loops and uncertainty; “pre-dictability” was replaced by “emergent properties” as the epit-omizing factor of natural systems (76).Complex adaptive systems (CAS) are a special subset of dy-

namical systems. The CAS concept is, in essence, a framework forinvestigating how the independent decisions and actions of in-dividual components of a system (i) self organize, (ii) are dynamicand change over time, (iii) interact to derive novel, unpredictable,emergent properties of the system, and (iv) may adapt to work inthe interest of the system as a whole (37, 38). The focus of CASresearch has been to use alternative methods of analysis—par-ticularly simulation with agent-based models—to understandthese properties in a variety of complex systems, including humansocial 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 “coupledhuman and natural systems” or “socio-natural systems”). SES aredefined by Glaser et al. (ref. 77, p. 4) as “complex, adaptivesystem[s] consisting of a bio-physical unit and its associated socialactors and institutions. The spatial or functional boundaries of thesystem delimit a particular ecosystem and its problem context.”Importantly, this defines SES as “real,” tangible things that exist inthe physical world with distinct boundaries in time and space, andso can be observed and studied empirically. Thus, SES can bestudied as regionally distinct analytical units (78). This propertyis particularly helpful for archaeologists, who are accustomed toconducting research at regional scales.Considerable debate exists about whether DST is truly an in-

tegrative or unified paradigm (37, 38, 40, 79–81). This confusionis, in large part, a consequence of the widely varying nomen-clature used by DST researchers. In addition to complexitytheory, CAS, and SES, there is also “resilience theory” (RT)[conceived by C. S. Holling (first described in ref. 41) and pop-ularized by two edited volumes (82, 83)], which is frequentlyconsidered as intellectually distinct from DST. The RT approachmay not be very well-integrated with the CAS/SES approaches,but there is much methodological and conceptual overlap be-tween them because both derive from similar early DST roots.More importantly to the research presented here, both are usefulsources of ideas for a dynamical systems view of change in hu-man systems. In particular we use (i) the interrelated ideas of theadaptive cycle, resilience, and “panarchy” (42, 82–85) and (ii)the parallel ideas of critical transitions, catastrophic regimeshifts, “tipping points,” “basins of attractions,” and alternativestable states (39, 76, 86–89). We use these and other concepts inour discussion of change in nonlinear systems in SI Text S2.

SI Text S2: Change in Nonlinear SystemsBecause of their nonlinearity, cause-and-effect logic is difficult toapply toward understanding change in dynamical systems. Therecurrently exists no integrative theory of change in these types ofsystems. There have been, however, some useful approaches tounderstanding how complex systems change over time. The RTidea of the “adaptive cycle” is one of these approaches. Origi-nally envisioned as a 2D diagram (Fig. S1A), it has since beenexpanded into three dimensions (Fig. S1B) (83). It is a heuristicdiagram for temporal change, with axes corresponding to systempotential, system connectedness, and system resilience. The po-tential of a system is a measure of its capacity (customarilymeasured in terms of accumulated resources), the connectednessof a system is a measure of the amount of integration present inthe system (typically viewed as the tightness of the couplingbetween elements of the system), and the resilience of a system isa measure of its ability to adapt to new conditions (generallyunderstood as its flexibility or adaptability, and measured interms of things like degree of specialization, etc.). The “figure 8”diagram of the adaptive cycle is formed as the state of the systemproceeds through time in the three-dimensional space of po-tential, connectedness, and resilience. Although there is an ex-tensive literature about the adaptive cycle and its four phases,the most important concept is that system resilience fluctuatesover time in roughly inverse proportionality to its potential andconnectedness. RT suggests that systems can undergo rapidchange when resilience is reduced and potential and connect-edness are high. The system may then either reemerge into atotally new niche3, or remain in the same niche, but returned toits 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-in-heritance and niche-construction theory.] This cycling repeatsover time, as the system stays in motion because “there is afundamental trade-off between being adaptive and being effi-cient” (ref. 39, p. 78). In other words, increased resilience can behad only at the expense of decreased potential.Holling and coworkers have envisioned a system of in-

terconnection between adaptive cycles at different scales, whichthey term “panarchy” (83). The panarchy concept is a way ofunderstanding the emergence and feedback of hierarchicallyarranged systems from heterarchical processes. A main idea ofthe panarchy is that system components scale logarithmically as afunction of time and space so that smaller adaptive phenomena(e.g., an individual or family group) exist as independent cycleswithin larger adaptive phenomena (e.g., a society) (Fig. S1C).Each scale of adaptive phenomenon will have an areal footprintand a “cycle width” (length of time between boom/bust dynam-ics). There are two types of possible feedback connections be-tween adjacent scales, termed “remember” and “revolt” (Fig.S1D). The important thing is that the panarchy hypothesis pre-dicts a negative feedback (remember) from larger, sloweradaptive cycles to faster, smaller adaptive cycles, and a positivefeedback (revolt) from faster, smaller adaptive cycles to larger,slower adaptive cycles. These two forces are terms in a balancingequation that determines the stability state of the entire pan-archy. [This idea is similar to the concept of “metastable”equilibrium in traditional systems theory (e.g., ref. 90).] Al-though conceptually simple, complexity is achieved as a functionof the differences in the cycle width of all of the different scales

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of adaptive phenomena in the panarchy and the relative align-ment of the adaptive states of the adaptive phenomena at eachscale. Thus, small-scale stability or growth can be maintained vialarge-scale remember feedback, even if local conditions shouldseem to require release and reorganization (e.g., individual fami-lies may maintain a subsistence lifeway out of tradition or greatersocial pressure). Conversely, larger scale system structures canchange (in a potentially punctuated way) via an amalgamation ofsmall-scale revolt negative feedback events in the subsystem (e.g.,an accumulation of individuals/families making subsistence tran-sitions), 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 insystem potential, connectedness, or resilience as a time series inwhichwe can produce a different heuristic plot of the adaptive cyclethat shows how it plays out over time (Fig. S2). These heuristicgraphs can be used to help analyze/explain patterning in real timeseries 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, het-erogeneity of vegetation), and resilience (similar proxies as thosefor 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 canincrease, decrease, or remain constant over time, dependingupon the current balance of negative to positive feedback forces.If positive feedback outbalances negative feedback, then thesystem experiences net growth of potential and connectednessover time (although at the expense of resilience), resulting in apattern of compounding success. If negative feedback out-balances positive feedback, then the system experiences net re-duction of potential and connectedness over time (but regainsresilience), resulting in a pattern of cascading failure. If thepositive and negative feedback forces are well-balanced betweenthe various levels of the system (a phenomenon we suggest becalled “remain”), then the panarchy experiences no (or in-significant) net change over time, resulting in a pattern of long-term stability. It is important to note that, at any time t, a newcycle begins, and the balance of the system can change. Thus, thetrajectory from the system state at time t1 to any of the possiblesystem states at time t4 is neither linear nor predictable, and it isimpossible to predict which particular system state will be ach-ieved at time t4. That is, given any set of initial conditions, thereare multiple pathways to each possible system state at any latertime, which is what makes the system “complex.” Furthermore,the contingencies of history matter in this scheme, in that theearlier pathways taken serve to limit the number and character ofavailable future pathways. In other words, the probability of aparticular system state being achieved at time t4 varies greatlydepending 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 ap-proach to rapid system change—“critical transitions” around theidea of alternative stable states. Fig. S4 shows three differentpatterns of system state change to major indexing variables. Fig.S4A shows steady-state change where there is a linear relation-ship between the system state (y axis) and some critical variable(x axis). Fig. S4B shows a more complex relationship between thesystem state and the critical variable, where change is more rapidover some subsection of variable values, and less rapid in others.In this figure, the steeper zone of the curve is less stable than theflatter portions, but there is still a fixed relationship between thecritical variable and the state of the system (i.e., if one is known,the other can be predicted). Fig. S4C shows yet another re-lationship between the system state where there is a “zone ofvulnerability” where two alternative systems states are possiblefor the same value of the critical variable. Scheffer and coworkers

label this type of curve a “catastrophe curve.” The dashed portionof the curve cannot be traveled smoothly so, at critical points F1and F2, the system state jumps from one portion of the curve tothe other (Fig. S4D). An important aspect of this type of curve isthat, even if the critical variable returns to its value from beforethe critical transition (e.g., point F2), the system remains in thealternative system state and will remain there until the othercritical threshold is surpassed (e.g., point F1). In fact, it is possiblefor the system to enter into a cyclical recurrence between thesetwo stable states as the critical resource varies between the twocritical 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 linerepresents the rate of change (39). Thus, if the slope is zero, therate of change is zero. Scheffer uses the analogy of a “ball in acup,” such that, if the stability landscape is concave, the ball willalways fall to the bottom of the “trough.” Such troughs can thusbe thought of as basins of attraction or, more formally, attractors.Attractors are essentially the stable state of the system under aspecific set of conditions (i.e., the conditions that set the currentstability landscape). Where the stability landscape is convex, theball will always fall away from the “peak.” Such peaks can thus bethought of as repellors. If conditions are such that there is onlyone stable system state, there will be only one attractor (or none atall) on the stability landscape. In the case of two (or more) pos-sible stable system states, then there will be two (or more) at-tractors, separated by a repellor. Thus, if the perturbation is largeenough to overcome the force of the separating repellor, it ispossible for the system state (the ball) to fall into one or the otherattractor. It is this dual attraction and repulsion that results in therapid 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 thegiven conditions (Figs. S5 and S6). Thus, a deep, wide attractor ishighly resilient, and even large perturbations will not “knock theball out of the cup” (Fig. S6A). However, a shallow, narrow at-tractor is highly vulnerable to change, and a relatively minorperturbation may be sufficient to induce system state change(Fig. S6B). This concept is exemplified in Fig. S5, which shows aseries of stability landscapes for different positions on a catas-trophe curve: as the system nears the critical transition point(F2), the resilience of the original attractor reduces, and theamount of perturbation required to switch to the alternate at-tractor lessens. Related to this idea, systems that are vulnerableto critical transitions are also characterized by higher degrees ofsubsystem homogeneity and connectivity (93). Ironically, thesehomogeneous and highly connected systems are actually morestable in the short term because they continually act to resistchange until the critical threshold is surpassed.

SI Text S3: The Standard Cross-Cultural Sample andSupplemental DataThe dataset used in this analysis is the Standard Cross-CulturalSample (59), which is a unique database of over 2,000 culturalvariables coded for 186 societies. The greater part of the SCCSvariables pertain to specific social characteristics or sociallyordained behaviors. Because our interests are in those aspects ofhuman behavior related to making a living, we focused on thosevariables related to subsistence, mobility, demography, and, es-pecially, those that seem to be more consistent with the kinds ofdata that can be recovered archaeologically. Table S1 lists thenames of the 186 societies of the SCCS and the plotting codesused to display how ethnographers characterized their subsis-tence. Table S2 lists the core set of subsistence, mobility, anddemographic variables that were included in our analyses, as wellas the supplemental environmental and social variables that were

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used in additional analyses. See SI Text S4 for completeness cri-teria 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, al-though the SCCS was developed to cover a maximum of humandiversity and the best-studied human groups (59), it is nonethelessnumerically biased toward groups studied by ethnographers in themodern era, and, thus, rather than being a true representativesample of all traditional human lifeways, it is a sample of tra-ditional human lifeways after the effects of global post-17thcentury colonialism/imperialism. Further, although the SCCS wascompiled purposefully to minimize the effects of cultural, spatial,or environmental autocorrelation (see SI Text S5), there maynevertheless still exist auto-correlative relationships that couldskew perceived relationships between variables (94). And, fi-nally, because the data for each group included in the databasewere collected by many different researchers through time, thedata are not necessarily coeval. SCCS coders have tried toameliorate this problem by coding most of the variables either asinterval-scale data at a very coarse resolution or as nominal-scaledata, but there are still many missing values throughout the da-tabase. (Although the resolution of these data can be consideredcoarse by ethnographic standards, their resolution is actually onpar with, or better than, most archaeological data.) These prob-lems are serious issues, but are unfortunately all-to-familiar toarchaeologists 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 datatypes and quality (SI Text S6), can still yield interesting and far-reaching insight into human variability. The SCCS data are, inlarge part, on par with most archaeological data and can betreated exactly like archaeological data so insights derived from itare directly applicable to archaeological inquiry.Estimates of net primary production (NPP) were obtained from

outside of the SCCS database. We obtained these estimated NPPvalues by using the latitude and longitude reported in the SCCSfor each society to query a global map of NPP.We used the global1-km resolution dataset provided by Kucharik et al. (60), and, toaccount for error in the coordinates and localized variation inNPP, we uploaded the maximum NPP value in a three-cell radiusaround the SCCS coordinates for each of the 186 societies. Insome cases (coastal or island societies), the SCCS coordinateswere above ocean, and so we had to manually enter coordinatesfor the nearest land.

SI Text S4: Multiple ImputationDue to the nature of ethnographic data and research, many of theSCCS variables do not contain information for all of the186 SCCSsocieties. We handled these data gaps via multiple imputation(MI), which is an accepted method for managing missing data instatistical analysis of the SCCS data and has been shown toprovide better results than list-wise deletion in traditional re-gression and correlation-based analyses (95). Imputation is astatistical procedure that “fills in” missing data based on afunction of all other variables and cases in the dataset. MI differsfrom standard imputation in that it introduces a controlled de-gree of randomness into the imputation process and iterativelyrepeats the imputation process to create i imputed datasets, eachof which contains slightly different imputations of missing datacases. Traditionally, MI is used in such a way that each imputeddataset is used to undertake a statistical test (e.g., MANOVA),and the results of each are then recombined to get a final esti-mate of the statistical test that also approximates the error in theanalysis associated with the missing data. This traditional ap-proach is not possible with our geometric data analysis workflow,which requires visual approximation of clustering results (SI TextS6). We chose to use the mean values of the i imputed datasetsas input into the routine and gained an understanding of the

potential for error derived from the imputation process throughthe SE of the imputed values across all i imputed datasets.During this process, we discovered that imputation error wasminimal when variables had fewer than about 8% missing cases(i.e., when data existed for at least 171 of the 186 SCCS socie-ties), and so we limited our analysis to variables that met thiscriterion (Table S2). This culling resulted in a final imputeddataset that contained the maximum possible number of vari-ables related to subsistence, economy, mobility, and demography,without introducing unnecessary variability due to many missingdata cases. Finally, MI is most effective when related extra vari-ables (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 usingthe “mi” package. Imputed datasets used in this research are madeavailable as described in SI Text S7.

SI Text S5: Alternative Explanations for Observed PatterningAlthough we believe that the spatial patterning we observed in ouranalysis is consistent with the idea of attractors and repellors, thereare other possible forces that could have induced structure on thedata. 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. Inthis procedure—a kind of Monte Carlo method—the data ineach column (SCCS variable) were independently shuffled ateach iteration, to make 186 new sample “societies.”We repeatedthe shuffling many times, creating many novel combinations ofpotential societies from the pool of real SCCS data values. Foreach of these combinations of fictitious societies, we conductedNMMDS and K-medoids cluster analyses. Fig. S6 shows 20sample biplots of some of the shuffled datasets. None of thebiplots for the reshuffled datasets displayed the kind of cluster-ing and cluster separation that we observed in the real SCCSsample societies. That the reshuffled datasets all produced ran-domized patterning in NMDS space indicates that the patternswe observe in the main text are not likely to occur—i.e., someprocess has introduced structure.The second major alternative explanation is the effect of

Galton’s problem (social, spatial, and/or environmental auto-correlation). Although the 186 societies of the SCCS were cho-sen specifically to reduce this effect (59), Dow and Eff (94) haveshown that a significant amount of autocorrelation does re-main in the SCCS data. Our geometric data analysis workflow(SI Text S6) is less susceptible to autocorrelative errors than areregression-based techniques (such as ANOVA or MANOVA),but we nevertheless need to understand the effect of autocor-relation or other biases in our analyses. Attempts to understandthe impact of autocorrelation are complicated by the fact that(spatially autocorrelated) environmental conditions may, in fact,be very important structuring elements in defining the humansubsistence attractors and repellors that we are looking for.Because we are explicitly interested in the effect of environ-mental factors on the patterning of human subsistence variabilityin the SCCS, we do not want to “correct” for their effects. Ourapproach is to separate environmental variables into a discretedataset (Table S2) that can be combined or withheld from anyanalysis. This approach allows us to assess the effect of addingthese variables, without necessarily controlling for their in-fluences. Our analyses did find that certain environmental vari-ables, such as seasonality and environmental productivity, areimportant structuring components of the patterning we ob-served. We do not find this result to be inconsistent with ourhypothesis of subsistence attractors.Social or cultural autocorrelation is more difficult to assess and

is more likely to be a substantial alternative structuring influenceon the observed patterning. Although we did conduct preliminary

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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 unableto include them in the final analysis in ways that were heuristicallymeaningful. The particular social variables of interest (Table S2)were coded in the SCCS as categorical variables that cannot beordered on a gradient (a fundamental requirement for use ascontrolling variables in a CCA routine). In the limited tests thatwe did perform, we noticed no significant influence of socialvariables to the observed subsistence patterns.Observer biases are another potentially important alternative

explanation for the patterning that we observed. These biasesmight be inherent in the SCCS data (SI Text S3), and it may bethat 19th and 20th century ethnographers projected their ownbeliefs about subsistence possibilities into the data that theycollected. Although it is probable that widely held, preconceiveddivisions of economic subtypes influenced the work of theseethnographers to some degree, it is unlikely (i) that these biaseswould have similarly affected the reporting of all the differenttypes of empirical data used in this study (Table S2) and (ii) thatall of the researchers would have been affected in the same way,or to the same degree, by these biases. Further, clusters createdsolely by these biases should be very discretely defined, with veryhigh cluster separation, and CCA analyses using environmentalor mobility data to constrain the axes should show that thesevariables contribute relatively little to the spatial patterning. Ouranalyses do not show these trends so we conclude that ethnog-rapher biases, although likely present, do not inordinately affectthe outcome of the research.There could also be bias introduced by the coding process itself

because individuals coded data from several ethnographies forcomparison. Although care was taken to try to avoid this possi-bility during the creation of the SCCS, coders could have sub-consciously lumped cases so that clusters of societies are anartifact of coding judgments. More work is needed to address thispossibility. Larger sample sizes of one subsistence type, for ex-ample, should help sort this problem out.The process of competitive exclusion could also explain some of

the observed patterning. Competition for limited resources withsedentary, agricultural societies has, over time, constrained less-populous, more-mobile societies to less-productive lands. It couldbe that the observed correlations between environmental pro-ductivity (and seasonality) are due to this more recently inducedprocess and do not reflect the relationship between subsistenceand environment as it existed in the past (e.g., at the Pleistocene–Holocene transition). However, a substantial number of thesmaller scale SCCS societies lived in regions that now supportsubstantial sedentary agricultural populations but did not at thetime of ethnographic study (e.g., California and Australia).Further, although processes of competitive exclusion may affectthe subsistence patterning seen in the SCCS data, the process ofintersocial competition is not at odds with our hypotheses aboutthe formation of subsistence attractors. Indeed, competitive ex-clusion may well be one of the important controlling variablesthat help to shape attractors—and their resilience—over time.Although we did not explicitly study the effect of competition onthe patterns observed in the SCCS, it is a potentially fruitfulfuture research direction.Finally, sampling biases may also be responsible for some of the

patterning we observed. Because the societies included in theSCCS were, for the most part, studied in the last 200 y, there is achance that they do not represent the full breadth of all possiblehuman subsistence strategies. It could be that the observed gaps inthe cluster results are less the product of repellors than they are aproduct of an incomplete sample of subsistence systems. Sam-pling error is a significant issue, and not one that is easily dis-missed. The obvious solution is to increase the sample size andexpand the sampling criteria to include prehistoric peoples. Ar-

chaeological data are the only source of information about theeconomic activities of prehistoric populations, but the incompletenature of the archaeological record, and their derivation fromproxy measures instead of direct observation, make it difficult(although not impossible) to extend the sample to include societiesfrom many different times. We acknowledge that sample size is anissue for the current dataset.

SI Text S6: Geometric Data Analysis Workflow for Cross-Cultural DataFollowing establishedmethods of geometric data analysis (62), weprefer to examine multivariate data as “clouds of points” inmultidimensional space, rather than to extract minimal sets ofvariables to analyze with more traditional, but dimensionallylimited, comparative statistical tests. Thus, the workflow we usein this research begins with multidimensional techniques to re-duce the high number of initial attribute dimensions to a lowernumber of eigenvectors that can be displayed in two- or three-dimensional plots.Nonmetric multidimensional scaling (NMMDS) is a dimen-

sional reduction procedure with appropriate techniques foranalysis of categorical data types. It is designed to help re-searchers understand the structure of a multidimensional datasetby scaling the variability present in that dataset to a smallernumber of dimensions (in this case, two) (96). The input datapoints are projected into the space created by the two mostdominant NMMDS dimensions and can be viewed as a scatterplot where the physical proximity of the projected points denotesa multidimensional affinity (i.e., the closer two points are on theNMMDS plot, the more similar their input variables are).NMMDS is often used in analysis of ecological datasets as a kindof “indirect” gradient analysis to identify previously unknowninternal or external structural constraints on plant and animalcommunities. We therefore find it useful to start our dataanalysis as a workflow using NMMDS ordinationCanonical correspondence analysis (CCA) is similar to

NMMDS in that it projects multivariate data into 2D space, but itconstrains the ordination according to one or more known (orsuspected) gradients (97). It is therefore often used as a kind of“direct” gradient analysis of ecological data to better understandknown or hypothesized constraints within different ecologicalcommunities (97). CCA plots allow the researcher to understandhow a small group of preidentified variables constrain or affectthe patterning of all other measured variables and thus providesa kind of loose hypothesis test for ideas about structuring re-lationships within the dataset.The results of both NMMDS and CCA can be graphically

displayed as biplots, on which are plotted the input case studies (inthis 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 thedimensional reduction. The plotted location of the input variablesin relationship to the input cases (SCCS societies) is important;each input variable can be considered as a vector with distanceand direction relative to the origin, such that their “pull” on theinput cases is what creates the 2D spatial patterning of the inputcases on the biplots. In other words, the biplots also provide agraphical representation of the amount of influences that eachinput variable has on the creation, separation, and character ofeach of any clustering.To further highlight any extant spatial patterning, the di-

mensionally reduced dataset is subjected to a K-medoids clus-tering routine. K-medoids is similar to the better known K-meansroutine in that it iteratively assigns input data points to one of apredefined number of clusters based on a distance metric (in thiscase, Manhattan) and an iteratively defined cluster center; but,whereas K-means uses themean of the coordinates of all input datapoints included in a cluster as the cluster center (i.e., a “centroid”),

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K-medoids uses the most centrally located of the input data pointsin the cluster (i.e., a “medoid”) (98). This property is advanta-geous because clustering routines that rely on calculating an “av-erage,” such as K-means, cannot be used with categorical datatypes (99) and are also more susceptible to outliers and “noise” inthe input dataset (98, 99).By manipulating the color and symbology of points on the

resulting plots, we can also thematically represent up to twoexternal variables to see how they relate to the spatial patterningof input societies and variables on the biplot. We have chosen torepresent the results of the K-medoids clustering routine as colorsand to use the point symbology to represent the economicclassification of the society as determined by the SCCS codersfrom the ethnographic data. Hierarchical convex hulls provide agraphical representation of the degree of cluster separation (theamount of empty space between clusters), the tightness of theclustering itself (the physical proximity of points within eachcluster), the uniformity of each cluster (the overall size and shape

of the cluster), and how well the cluster analysis corresponds totraditional 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 inSI Text S7.

SI Text S7: SCCS Datasets and R Script for Geometric DataAnalysisThe R code used to create all of the figures in the main text and theimputed SCCS datasets used in the analyses are made available as afree 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 followingunique digital object identifier (doi) number: 10.6084/m9.figshare.1404233. The imputed datasets and R code are releasedunder the Creative Commons and MIT licenses, respectively (freeto use and modify for any purpose, provided credit is given).

Fig. S1. (A) A 2D representation of the adaptive cycle showing how system potential and connectedness change over time. (B) A 3D representation of theadaptive cycle, which adds an axis of resilience. (C) An illustration showing how different adaptive systems exist at different scales. (D) An illustration of theconcept 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, orresilience. The solid green line shows the expected pattern for system potential, the dashed green line shows the expected pattern for system connectednessover time, and the dashed red line shows the expected pattern for resilience over time.

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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 forcontinual remember, revolt, or remain, but note that multiple pathways (combinations of remember, revolt, or remain between any time t) could have beentaken 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 morecomplex 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.

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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 thesystem 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 stablestate is achieved. The depth of the basin of attraction indicates the amount of system resilience. Modified from ref. 86, with permission from Elsevier.

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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.

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Table S1. Table of SCCS societies used in the macroscale analysis, organized by SCCS variable 858, “Subsistence Type-EcologicalClassification”

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 Δ Toda 6 × Thonga 8 ◊ Nyakyusa 11 * Uttar Pradesh 12 *Badjau 3 Δ Kazak 6 × Mbundu 8 ◊ Bambara 11 * Burusho 12 *Manus 3 Δ Khalka Mongols 6 × Suku 8 ◊ Tallensi 11 * Lolo 12 *Ainu 3 Δ Chukchee 6 × Bemba 8 ◊ Songhai 11 * Lepcha 12 *Gilyak 3 Δ Goajiro 6 × Luguru 8 ◊ Hausa 11 * Burmese 12 *Yukaghir 3 Δ Mao 7 ◊ Nkundo Mongo 8 ◊ Massa (Masa) 11 * Vietnamese 12 *Saulteaux 3 Δ Garo 7 ◊ Banen 8 ◊ Fur (Darfur) 11 * Khmer 12 *Kaska 3 Δ Lakher 7 ◊ Tiv 8 ◊ Otoro Nuba 11 * Siamese 12 *Yokuts (Lake) 3 Δ Lamet 7 ◊ Ibo 8 ◊ Kenuzi Nubians 11 * Negri Sembilan 12 *Kutenai 3 Δ Iban 7 ◊ Fon 8 ◊ Armenians 11 * Javanese 12 *Warrau 3 Δ Toradja 7 ◊ Ashanti 8 ◊ Tanala 11 * Balinese 12 *Yahgan 3 Δ Tobelorese 7 ◊ Mende 8 ◊ Kimam 11 * Chinese 12 *Ingalik 4 Δ Alorese 7 ◊ Wolof 8 ◊ Ajie 11 * Manchu 12 *Aleut 4 Δ Kapauku 7 ◊ Azande 8 ◊ Ifugao 11 * Koreans 12 *Eyak 4 Δ Maori 7 ◊ Shilluk 8 ◊ Hidatsa 11 * Japanese 12 *Haida 4 Δ Atayal 7 ◊ Gond 8 ◊ Zuni 11 * Mapuche 12 *Bellacoola 4 Δ Pawnee 7 ◊ Rhade 8 ◊ Havasupai 11 *Twana 4 Δ Omaha 7 ◊ Popoluca 8 ◊ Papago 11 *Yurok 4 Δ Huron 7 ◊ Quiche 8 ◊ Aztec 11 *Klamath 4 Δ 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 diggingsticks or wooden hoes; 8, shifting cultivation, with metal hoes; 9, horticultural gardens or tree fruits; 10, advanced horticulture, with metal hoes; 11, intensiveagriculture, with no plow; 12, intensive agriculture, with plow. Plotting symbols follow number codes.

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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 814trade_food 1 herd_importance 815ag_contrib 3 fish_importance 816herd_contrib 5 hunt_importance 817herd_animals 6 gath_importance 818fish_contrib 7 trade_importance 819fish_type 8 total_pop 1122hunt_contrib 9 ag_staple1 1123hunt_animals 10 ag_stape2 1125gath_contrib 11 plow2 1127gath_foods 12 crop_index 1128food_stor 20 subsis_ecolo* 858settle_fixity 61 Environmental variablessettle_compact 62 temperature 186commun_size 63 precip 189pop_dens 64 num_dry_mon 196gath_depend 203 num_wet_mon 199hunt_depend 204 latitude 1905fish_depend 205 coef_var_precip† 192 and 193herd_depend 206 Social variables‡

ag_depend 207 region 200cultiv_intens 232 lang_fam 1859maj_crop 233 lang_subfam1 1860settle_pattern 234 lang_subfam2 1861plow 243 num_neighbors 1864herd_type 244 religion 2002milking 245

*Used only to determine plotting symbols, and not used in any statisticalanalyses.†The coefficient of variation of precipitation was calculated from the twoSCCS variables indicated (maximum and minimum precipitation).‡Social variables were used only to test whether they significantly affectedthe results of the main analyses (i.e., Galton’s problem).

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