Effect of infrastructure design on commons dilemmasin social−ecological system dynamicsDavid J. Yua,b,c,d,1, Murad R. Qubbaje, Rachata Muneepeerakulf, John M. Anderiesc,e,g, and Rimjhim M. Aggarwalc,e

aLyles School of Civil Engineering, Purdue University, West Lafayette, IN 47907; bDepartment of Political Science, Purdue University, West Lafayette, IN47907; cCenter for Behavior, Institutions, and the Environment, Arizona State University, Tempe, AZ 85287; dCenter for the Environment, Purdue University,West Lafayette, IN 47907; eSchool of Sustainability, Arizona State University, Tempe, AZ 85287; fAgricultural and Biological Engineering Department,University of Florida, Gainesville, FL 32611; and gSchool of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287

Edited by Stephen Polasky, University of Minnesota, St. Paul, MN, and approved September 16, 2015 (received for review June 8, 2014)

The use of shared infrastructure to direct natural processes for thebenefit of humans has been a central feature of human social orga-nization for millennia. Today, more than ever, people interact withone another and the environment through shared human-made in-frastructure (the Internet, transportation, the energy grid, etc.).However, there has been relatively little work on how the designcharacteristics of shared infrastructure affect the dynamics of social−ecological systems (SESs) and the capacity of groups to solve socialdilemmas associated with its provision. Developing such understand-ing is especially important in the context of global change wheredesign criteria must consider how specific aspects of infrastructureaffect the capacity of SESs to maintain vital functions in the face ofshocks. Using small-scale irrigated agriculture (the most ancient andubiquitous example of public infrastructure systems) as a modelsystem, we show that two design features related to scale andthe structure of benefit flows can induce fundamental changesin qualitative behavior, i.e., regime shifts. By relating the requiredmaintenance threshold (a design feature related to infrastructurescale) to the incentives facing users under different regimes, ourwork also provides some general guidance on determinants of ro-bustness of SESs under globalization-related stresses.

social−ecological system | infrastructure | robustness | resilience | irrigation

Many modern social−ecological systems (SESs) depend heavilyon shared infrastructure. How such critical infrastructure

mediates social and human−environment interactions is thus cen-tral to many pressing sustainability challenges in contemporary SESs(1). For example, the robustness of urban systems to natural hazardsoften depends on engineered structures such as levees, roads, orbuildings. Similarly, global food security depends on irrigation in-frastructure through which farmers obtain water. In infrastructure-mediated SESs, the very presence and the design features ofinfrastructure fundamentally shape the dynamics of coupled socialand natural processes (2). A major puzzle for sustainability in thisera of global change rests on a deep understanding of interactionsamong social, natural, and built components and the effects of suchinteractions on the robustness of SESs to unexpected shocks. Howcan the design of infrastructure affect the capacity of SESs tomaintain vital functions in the face of shocks? What are designcriteria for infrastructure for more robust SESs? This study exam-ines these questions using a simple model of a community irrigationsystem—a classic case of a SES in which shared infrastructure isthe key interface between social and natural processes.Community (or farmer-managed) irrigation systems are wide-

spread in Asia and, even today, serve a significant portion of thetotal irrigated area (3). These systems provide an excellent testingground for exploring how infrastructure affects SESs. Farmersneed a reliable supply of water to produce food and typically divertwater from its source through weirs, headgates, and canals. Twostrong empirical regularities emerge from a long-term compara-tive case analysis of robustness of such systems. First is the criticalimportance of infrastructure maintenance and the collective ac-tion problems associated with it (4). A study of 50 irrigation sys-tems in Nepal found that farmer-managed systems typically have

cruder infrastructure than agency-managed systems in the form oftemporary headworks and unlined canals that demand greatermobilization of collective labor or investment each year to main-tain functionality (5). Farmers thus face a threshold public gooddilemma. Second is the challenge of fair water distribution, whichcan be undermined by upstream−downstream asymmetry stem-ming from the canal layout (an asymmetric commons dilemma)(4,6). Because community irrigation systems contain the key basicfeatures of most SESs, they are, for our study of SES sustainability,a model system in a similar sense to fruit fly as a model organismin evolutionary biology (7).Small-scale irrigation infrastructure, critical for the food se-

curity of the bulk of the world’s poorest people, is in dire need ofmaintenance. This is especially true in South Asia, where much ofthis infrastructure built in the 1960s and 1970s has deterioratedrapidly, posing a major threat to food security in the region (8).Although a lack of funding is often identified as the reason for thedeterioration, studies have shown that reasons for underprovisionof shared infrastructure are numerous, and funding is not thepredominant problem (9). Rather, the subtle interplay betweensocial, technological, economic, and natural processes stronglyinfluences the capacity of groups to overcome the collective actionproblem that maintenance poses in farmer-managed systems. Here,we focus on this interplay by characterizing the structure of incen-tives that users face under different infrastructure design con-ditions and tracing the dynamics that follow. Our focus on theinteractions between the infrastructure design and the incen-tives facing user groups opens doors to alternative ways ofthinking about solutions to the maintenance problem, beyondthe budgetary considerations. This problem is highly relevant tocurrent discussions on global food security. Nearly 90% of farms

Significance

Recent years have witnessed an explosion of interdisciplinary re-search on social−ecological systems (SESs), which has typicallyviewed SESs as self-organized systems. This view, however, maybe incomplete in that many modern SESs are in fact part designedand part self-organized, i.e., the coupled processes in most SESs aremediated by consciously designed infrastructure. We examinedhow design features of infrastructure shape the long-term dy-namics of SESs, using a model of an irrigation system (an exem-plary case of a partly designed SES). We show that two designfeatures common to many SESs—the structure of benefit flowsand the scale of effort needed to maintain infrastructure—can in-duce fundamental changes in qualitative behavior as well as al-tered robustness characteristics.

Author contributions: D.J.Y., R.M., and J.M.A. designed research; D.J.Y. and M.R.Q. per-formed research; D.J.Y., M.R.Q., R.M., and R.M.A. analyzed data; and D.J.Y., R.M., J.M.A.,and R.M.A. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: davidyu@purdue.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1410688112/-/DCSupplemental.

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worldwide are operated by smallholder farmers who cultivate lessthan 2 ha of land (10). A significant proportion of these small-holders practice irrigated agriculture, which consumes roughly70% of global developed water supplies and produces nearly 40%of global agricultural output (11). It is imperative to understandhow these smallholders can continue to maintain cooperationand, with it, critical infrastructure in the face of climate- andglobalization-related shocks.We address the question of how infrastructure design affects

SES sustainability in two stages. First, we explore the effects ofdesign variations on long-term system behavior in our model sys-tem. We examine two types of distribution infrastructure, one withand one without upstream−downstream asymmetry, and differentthreshold characteristics of infrastructure maintenance. Second, weevaluate how these design variations influence the robustness ofsystem function to an economic shock. Our model results suggestthat infrastructure design features can generate the potential forregime shifts, i.e., fundamental changes in qualitative system be-havior. Three different SES regimes (sustainable, sustained butunequal, and collapsed) emerged, expanded, or shrunk as we variedinfrastructure design features. We also observed that infrastructuredesign can influence the sensitivity of system performance to so-cioeconomic shocks such as an increase in the attractiveness of al-ternative livelihood opportunities. Before presenting the details ofthe model and analysis, it is important to clarify that our goal is notto accurately model the dynamics of a particular irrigation system.Rather, we studied stylized model SES to better understand themechanisms that may underlie empirical regularities observed infield settings and behavioral studies, and to explore system dy-namics under different design conditions.What emerges from our analysis is the need to ensure that the

role of shared infrastructure is properly accounted for in studies ofSESs. This can be achieved by conceptualizing “ecologies” in SESsmore broadly to include both built and natural elements, as inindustrial ecology (12), or simply thinking in terms of coupled in-frastructure systems (CIS) of which SESs are special cases wherenatural infrastructure plays a key role (2). This broader view, builton earlier conceptualizations of the role of hard infrastructure (13)and soft infrastructure in SES governance (14), helps us considerthe links among social, natural, and built elements more explicitly.

Study SystemIrrigation systems can both enhance yields and stabilize productiondespite variability in annual precipitation. However, these benefitscome at a cost: Users of farmer-managed irrigation systems mustmaintain shared infrastructure, and create and enforce governingrules to coordinate the infrastructure maintenance and water dis-tribution processes (4). Without effective rules for coordination,monitoring, and enforcement, farmers can free-ride by taking irri-gated water without contributing to infrastructure maintenance.Likewise, upstream farmers, by virtue of their location, can over-appropriate, leading to an unfair distribution of water for down-stream users. Interestingly, provision and distribution are ofteninterdependent because infrastructure maintenance often requiresa critical mass of labor, so upstream farmers usually cannot carryout the task without help from downstream farmers (4, 15). Thisinterdependency often reduces the likelihood that upstream farm-ers will overappropriate water, because downstream farmers whodo not get enough water can retaliate by reducing their contributionto maintaining infrastructure (6).Despite the many challenges facing farmers, field studies have

shown several irrigation communities that have successfully main-tained their infrastructure and achieved fair water distribution forhundreds of years (16, 17). These long-lived systems typically havewell-tuned rules to govern user behavior (16). Behavioral experi-ments have supported field study findings by demonstrating thatindividuals in small groups (say, five players) can endogenously solverelatively complex commons dilemmas associated with irrigation ifallowed to communicate (6). These studies provide evidence thatplayers were willing to tolerate some inequality in the amountof appropriated water as long as there was some proportional

equivalence between investments in and benefits from infrastructure(6). This tolerance declined when the system was exposed to greaterexternal variability (18).Recent studies stress that contextual variables, such as the na-

ture of the built environment, the availability of exit options, orpower asymmetries, influence human decisions in SES collectiveaction situations (19, 20). A related question that we address hereis how these factors combine to affect SES robustness. We use adynamic model to help answer these questions. Specifically, howdo maintenance thresholds and asymmetric access interact to in-fluence collective action outcomes and system robustness in thelong run?

Basic Model Structure. Suppose N farming households are spreadacross two villages (village 1 and village 2) that manage a sharedirrigation infrastructure. There are N1 and N2 households in eachvillage, respectively, with N1 +N2 =N. Each farmer is endowedwith the same amount of available labor (l) each year and thesame acreage (a). A farmer may appropriate (q) units of waterfrom the system and allocate labor among three activities: farming(lf), maintaining infrastructure (lm), and outside employment (le)at wage rate w, i.e., l= lf + lm + le. Then, a farmer’s income isπ = pf ðlf , q, aÞ+wle, where f ðlf , q, aÞ is the production function foragricultural output, p is the price per unit of agricultural output,and wle is the employment income. The aggregate income of thetwo villages is given by Π= pFðLf ,Q,AÞ+wLe, where uppercasesymbols represent aggregate-level quantities.To deliver irrigation water, farmers must maintain the in-

frastructure each year (canals must be cleaned of silt and debris,and water diversion structures must be repaired). If farmers’ ag-gregate maintenance labor (Lm) exceeds the maintenance thresh-old, the system can continue to deliver water. If too few farmerscontribute labor, the infrastructure delivers little or no water. Thismaintenance threshold is a design parameter that depends on thecharacteristics of the biophysical and built environments. For ex-ample, if a weir is located in the shallow reaches of a river wherethe cross-section is wide, there is greater accumulation of silt andthus greater need for maintenance (21). There is a minimumamount of labor required to remove the silt in a short window oftime before the planting season begins, i.e., there is a maintenancethreshold. We represent this threshold behavior with a piece-wiselinear function IðLmÞ (Fig. 1A). The parameter ψ is the half-sat-uration point of Lm, yielding half of the maximum infrastructureefficiency. The parameter « controls the maintenance requirementand steepness of IðLmÞ. The volume of irrigation water, Q, thesystem can deliver is then Q= IðLmÞSðtÞ, where SðtÞ representsresource availability, e.g., volume of river discharge in this case.Governance is represented in our model system by the following

formal rules. The expected maintenance labor contribution isproportional to the farmer’s acreage (assumed to be the same forall farmers in this analysis). Water allocations are also proportionalto acreage, but only among the water rights holders. Only farmerswho contributed labor to the infrastructure before the plantingseason obtain water rights. Reflecting on Ostrom’s institutionaldesign principles for long-lived commons (16), these rules ensurethat the benefits and costs borne by a farmer are proportionate toeach other.Farmers choose between two strategies: group conformist

(G) and opportunist (O). The model tracks the fraction of Gs invillage i denoted by Xi =NG

i =Ni and the resulting performance ofthe irrigation system. We define the total number of Gs as NG =NG

1 +NG2 . Accordingly, the fraction of Os in village i is 1−Xi =

NiO=Ni (we use the notational convention that subscripts and su-

perscripts refer to village and agent type, respectively). Gs followand enforce the rules, and strive to maximize the total welfare ofthe two villages. Each G assumes everyone will contribute to theshared infrastructure and contribute their proportionate share(1=N) of the socially optimal maintenance labor (Lp

m), attempts totake only the allocated share (1=NG) of the total irrigated water(Q), and allocates labor between farming and employmentto maximize the total income. Lp

m is the maintenance labor that

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maximizes the total welfare of the two villages via optimal pro-duction of Q, as would be prescribed by a village leader acting as abenevolent social planner. Further, Gs monitor for rule violationsin their own village i and the other village j, and punish violators ata cost to themselves. The cost of enforcement for a G increaseswith the frequencies of Os.Os, in contrast to Gs, break the rules. They contribute zero

maintenance labor, and thus do not hold water rights. Nevertheless,they appropriate an amount of water and split labor betweenfarming and wage labor to maximize individual net income. Theamount of appropriated water and the labor allocation to farmingare based on a balance between the cost of being sanctionedcompared with farming income and the benefits to be gained fromthe outside employment. The probability of being caught andsanctioned increases with NG. The sanction varies by situation: Itincreases with the amount of water stolen but decreases with waterabundance in the system. When water is abundant, rule violationsare tolerated because farmers have little incentive to concernthemselves with equity issues (19, 22). Critical for the emergence ofself-governance is the competition between the G and O strategies.We use replicator equations (23) to model the dynamics of thesestrategies within each village (seeMaterials and Methods for details).

Infrastructure Design. The infrastructure is characterized by itsmaintenance threshold, captured by two design parameters, ψ and« (Fig. 1A) The threshold could be high and sharp (small «,ψ − «  ≈ψ) or low and gentle in slope (large «, ψ − «  ≈ 0). Thefirst case would characterize a system with a large-scale productionstructure coupled with long distribution networks, such as themajor irrigation systems found in the plain regions of India (17).The second case might represent a scalable system with small-scaleproduction units and shorter distribution networks, such as thosefound in the hilly terrains of Nepal (5) and Taiwan and SouthKorea (24).

Another infrastructure feature is upstream−downstream asym-metry. Without upstream−downstream asymmetry (Fig. 1B), we havea situation in which two villages have equal access to a common-poolresource (for simplicity, let us assume that within each village,farmers have equal access to water). This occurs in what theirrigation engineering literature refers to as a “bifurcated” canallayout, and is observed in several traditional irrigation systems(25). In this setting, farmers have equal access to water and areendowed with the same levels of available labor, technology, andskills. It follows that if all farmers are to rush and compete forwater, Os and Gs will face, on average, the same constraint on theamount of water they can obtain (≤Q=N). Several studies haveexamined SES dynamics in such a symmetric context (26, 27). Themore likely scenario for most irrigation systems is one in whichwater is accessed sequentially (Fig. 1C), which is referred togenerally as a “hierarchical” layout design in irrigation engineeringliterature. Farmers in village 1 can access water before those invillage 2 and, as a result, are less constrained in the amount ofwater they can appropriate than in the symmetric case (see Sup-porting Information for more details).With the components of the model now defined, we turn to our

analysis. Our analysis focuses on the two key infrastructure char-acteristics just discussed and proceeds in two parts. In part I, weexplore several scenarios related to the maintenance thresholdand asymmetry in distribution to understand how infrastructuredesign affects qualitative system behavior. In part II, we leveragethe analysis in part I to explore the robustness characteristics ofthe system in the long run.

Analysis I: Effects of Design VariationsAsymmetric Access. Fig. 2A is a phase space representation of theoverall cooperation level in the system with asymmetry thatsummarizes our analysis. The system exhibits three possible re-gimes: (i) system collapse (ALL-Os), (ii) a sustainable situationin which most farmers adopt strategy G in village 1 and all adoptG in village 2 (MOSTLY-Gs), and (iii) a decoupled situation inwhich the two villages stop collaborating to maintain infra-structure, Gs come to dominate in village 1, and Os prevail invillage 2 (DECOUPLED). In the absence of asymmetry, only tworegimes emerge for most parameters explored: all Os (X1 = 0 andX2 = 0) and all Gs (X1 = 1 and X2 = 1).Fig. 2B compares the three regimes in the asymmetric case in

terms of infrastructure efficiency and inequality in total income.At ALL-Os, no water is supplied, and everyone is equally bad off.At MOSTLY-Gs, water is almost fully supplied, and the two vil-lages have a roughly equal total income (but the income of village1 is somewhat higher than that of village 2). At DECOUPLED,some water is supplied, but considerable income inequality existsat the village level because only farmers in village 1 obtain irri-gated water. Farmers in village 2 leave agriculture and resort tooutside employment.A closer look at the MOSTLY-Gs and DECOUPLED regimes in

the asymmetric case reveals that the total income of village 1 ishigher than that of village 2 in both regimes, but inequality is muchmore severe in DECOUPLED. This outcome is consistent withexisting knowledge of irrigation systems (4, 6, 28). At MOSTLY-Gs,some Os exist in village 1, but all are Gs in village 2. This slightlyunfair regime occurs because Os in village 1 are less constrained inthe amount of water they appropriate than Os in village 2. That is,upstream Os in the asymmetric case face a higher upper bound onthe amount of water they can obtain (≤Q=N1) compared with theupper bound in the symmetric case (≤Q=N). This advantage enablessome Os to survive in village 1 in the asymmetric case. The systemconverges to DECOUPLED when enough Gs exist in village 1 butfew Gs exist in village 2 at the outset. Because water rights holders(Gs) are few in village 2, village 2 is allocated with only a little water,which becomes subject to fierce competition between many Os andfew Gs in that village. Because of this competition for scarce water,the amount of water that downstream Os get is decided by the limitof available water rather than by the penalty they face. It follows,then, that Gs and Os in village 2 end up obtaining an equal amount

A

B

C

Fig. 1. (A) Infrastructure efficiency IðLmÞ as a function of maintenance laborLm. The half-saturation point of labor (ψ) and half-width of the thresholdslope («) determine the threshold of maintenance (ψ − «). When «  = 0, slopeis infinite and no water is generated until Lm =ψ. When «  =ψ, the amount ofwater increases linearly with Lm until Lm =ψ + «. In our discussion, wesometimes refer to a small « as a sharp threshold, and a large « as a lowthreshold or scalable infrastructure. (B and C) Two types of distribution in-frastructure. In B, two villages have equal access to water. In C, village 1 hasadvantage over village 2 in water access.

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of water. Eventually, Os prevail in village 2 because they are pe-nalized little (because they obtain only a meager amount of wa-ter), appropriate the same amount of water asGs, and free-ride onmaintenance labor. In contrast to village 2, Gs win over Os invillage 1—a substantial amount of water is available upstream, andGs obtain more payoff than Os by means of enforcement. Hence,the system converges to theDECOUPLED regime in the long run.It is important to note that theMOSTLY-Gs and DECOUPLED

regimes are resilient: The system is sustained even though in-come inequality lingers on. Our findings are concordant withempirical studies. Behavioral experiments have shown thatplayers in irrigation dilemma games may be willing to toleratesome degree of inequality, as long as there is some proportionalequivalence between investments in and benefits from infrastructure(i.e.,MOSTLY-Gs) (6). Field studies also observed that downstreamfarmers may exit from comanaging a system if there is too muchincome inequality (i.e., DECOUPLED) (28).

Maintenance Thresholds. As discussed above, we distinguish be-tween two empirically motivated cases: (i) systems that dependon large-scale infrastructure that requires that a minimum crit-ical amount of maintenance work be completed each year beforewater is delivered and (ii) scalable systems in which collections ofsmall-scale infrastructure can deliver water at much smallermaintenance inputs and increase delivery with increasing inputs.Fig. 2 C and D summarizes our analysis of how the “high and

sharp” threshold or “low-threshold, scalable” nature of infrastruc-ture maintenance affects the potential for regime shifts in thesymmetric and asymmetric access systems, respectively.Fig. 2D shows that in the asymmetric system, as the threshold gets

lower and gentler in slope (« approaches ψ), ALL-Os loses resilience(its basin of attraction shrinks) and the MOSTLY-Gs basin emergesand expands. However, this regime shift occurs at the cost ofemergence of the DECOUPLED regime. The opposite is true whenthe threshold gets higher and sharper in slope (« approaches zero).These results suggest that in asymmetric systems, low-thresholdscalable infrastructures (i.e., «≈ψ) are less likely to collapse but aremore prone to inequality. Conversely, infrastructures with a high and

sharp threshold (i.e., «≈ 0) are less likely to have inequality issuesbut are more prone to collapse. In the symmetric system, only tworegimes are possible: MOSTLY-Gs and DECOUPLED (Fig. 2C).When the threshold is high and sharp (small «) in asymmetric

systems, little or no water is generated until most of the populationis comprised of Gs. In such a situation, DECOUPLED cannot bestable because upstream farmers alone cannot maintain the in-frastructure, i.e., strong interdependency exists between villages 1and 2. When the threshold is extremely sharp, MOSTLY-Gs alsobecomes unstable because it is too vulnerable to opportunism. Thepath toward sustainability is much narrower in systems with highand sharp thresholds because most farmers need to participate incollective action each year just to make the system work.In contrast, with the low-threshold scalable infrastructure,

(«≈ψ), the water supply starts to increase almost linearly even atsmall labor inputs. Hence, ALL-Os has smaller resilience—as soonas some Gs are introduced, it is better for some farmers to co-operate and get some water than to quit farming (unless, of course,outside wage rates are sufficiently high). However, this departurefrom ALL-Os is accompanied by a higher likelihood of inequalityin the system because of the emergence of the DECOUPLED re-gime. AtMOSTLY-Gs, downstream farmers continue to cooperatedespite some inequality because the infrastructure generates sub-stantial benefits that trickle down to them. At DECOUPLED,however, the system functions poorly, with considerable incomeinequality. Because low thresholds weaken the upstream−down-stream interdependency, upstream farmers cooperate only amongthemselves to obtain enough water, i.e., they do not need laborinputs from downstream farmers.

Analysis II: Robustness of System Performance to ShocksField studies have found that, as globalization proceeds, ruralcommunities tend to depend more on nonfarm work; suffershortages of labor for maintaining shared infrastructure; andexperience erosion of social norms for collective action, espe-cially among younger generations (22, 28). Hence, we introducedinto our model system a sudden rise in wage rates (Fig. 3A) tomimic the pressures of globalization processes. Four types of

A

B

C D

Fig. 2. Effects of asymmetric access and maintenance thresholds. In A, the x and y axes show the fractions of Gs in village 1 (X1) and village 2 (X2), respectively.Red dots represent stable equilibrium points of the dynamics. Arrows represent the flows of dynamics from particular initial states. Red and green lines representX1 and X2 nullclines, respectively. (A) Possible regimes under asymmetry:ALL-Os (light pink area),MOSTLY-Gs (light green area), and DECOUPLED (light blue area).At ALL-Os, the irrigation system collapses. AtMOSTLY-Gs, most farmers follow the rules, water is almost fully supplied, and some income inequality exists betweenthe villages. At DECOUPLED, farmers in village 2 leave farming, and considerable inequality in total income exists between villages 1 and 2. (B) A comparison ofthe three regimes shown inA (model with asymmetry) in terms of infrastructure efficiency and income inequality (gini-coefficient) between villages 1 and 2. C andD illustrate effects of infrastructure design on stability landscape. In C, distribution infrastructure is symmetric, and maintenance threshold is varied from «  = 0 to«  = 0.2. Inset graphs at far right show the shape of the infrastructure–labor relation for each value of «. In D, distribution infrastructure is asymmetric, andmaintenance threshold is varied across the same range. (See Supporting Information for the parameters used).

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wage shocks were applied by varying their duration (short andlong) and intensity (low and high).We exposed the MOSTLY-Gs regime to the shocks under two

different infrastructure designs: a high and sharp threshold systemand a low-threshold scalable system (both with asymmetry). Fig. 3B and C shows the sensitivity of infrastructure efficiency to shortand long wage shocks, respectively. It turns out that the low-threshold scalable system («= 0.2) is more sensitive (less robust) tothe shocks than is the high and sharp threshold system («= 0.1).This is because upstream Os have a greater advantage with thelow-threshold infrastructure because of the weakened upstream−downstream interdependency. Here, sharp increase in wage ratescan cause Os to surge in the upstream village because they stillaccess water while earning extra income from skipping mainte-nance work. As a result, downstream Gs progressively get lesswater despite their maintenance work and thus decline in numbergradually. At some point, a limit is crossed—downstreamGs beginto decline rapidly (the trajectory starting from point “a” in Fig.3D). Hence, in the absence of a high and sharp threshold, theinfrastructure efficiency of the MOSTLY-Gs regime is highlysensitive to the economic shocks. The high and sharp thresholdsystem («= 0.1) is less sensitive to the economic shocks. This re-duced sensitivity stems from the tight upstream−downstream in-terdependency associated with the maintenance work (i.e.,upstream users need labor inputs from downstream users to ob-tain sufficient water). Os surge initially upstream in response tothe wage shocks, but the resulting decline of downstream Gs feedsback to balance the rise of Os upstream (the trajectory startingfrom point “b” in Fig. 3D). Hence, the MOSTLY-Gs regime canbetter withstand wage shocks when higher thresholds exist.We also exposed the DECOUPLED regime (sustained but

highly unequal) to the shocks under the same design variations.Fig. 3 E and F shows the sensitivity of infrastructure efficiency tothe short and long wage shocks, respectively. A different pattern isobserved in the DECOUPLED regime: The high and sharpthreshold system («= 0.1) is more sensitive to the shocks than is

the low-threshold scalable system («= 0.2). The reason is that highand sharp threshold systems have lower infrastructure efficiency atthe DECOUPLED equilibrium. That is, upstream users alone toilto maintain the infrastructure, but obtain only a meager amount ofwater because of the tight upstream−downstream interdependency.Hence, upstream users react more sensitively to rises in wage. Low-threshold scalable systems («= 0.2) at DECOUPLED are less sen-sitive to the wage shocks because infrastructure efficiency is higher atthe DECOUPLED equilibrium.In sum, infrastructure design (different degrees of maintenance

threshold) can significantly affect the robustness of infrastructureefficiency to wage shocks in our model system. We observed thatthe MOSTLY-Gs regime with a high and sharp threshold («= 0.1)is less sensitive to the shocks because of the tight upstream−downstream interdependency. However, the same design was as-sociated with more sensitivity in the DECOUPLED regime. Theseresults suggest that design or technological fixes to SESs mustconsider the potential for regime shifts and altered robustnesscharacteristics.

ConclusionCommunity irrigation systems contain all of the basic features ofcomplex SES: hard human-made infrastructure (water diversionand conveyance structures), soft human-made infrastructure (in-stitutional arrangements and organizational forms), and naturalinfrastructure (watersheds and agricultural land). Understandinghow these infrastructures interact and respond to change is criticalfor maintaining food security for billions of people in the comingdecades. Using a model of an irrigation system, we have shown thatinfrastructure design can greatly influence SES sustainability byinducing regime shifts in collective action dynamics. When distri-bution infrastructure generates asymmetric access, three regimescan emerge: sustainable, sustained but unequal, and collapsed. Wealso observed that regime shifts occur as the maintenance thresh-old is varied. With a low-threshold scalable infrastructure, thelikelihood of system collapse is low. The tradeoff is a higher

A B C

D E F

Fig. 3. Robustness of system performance to wage shocks. (A) Profiles of four wage shocks (w). Black solid line represents a high shock (HS) in which w jumpsfrom 0.2 to 1.2. Black dashed line represents a low shock (LS) in which w jumps from 0.2 to 0.8. These shocks apply between T = 150 and T = 200. Gray linesrepresent the same shocks applied over a longer duration (between T = 150 and T =300). Along with the shocks, we perturb the fractions of X1 and X2 a bit atT = 151 to observe local stability properties. (B and C) Sensitivity of the infrastructure efficiency (IðLmÞ) at MOSTLY-Gs to the short and long wage shocks,respectively. Red and blue lines represent the system response when «  =0.2 and «  =0.1, respectively (both with ψ = 0.2). (D) Trajectories of X1 and X2 atMOSTLY-Gs when the short-duration high shock is applied. Two design scenarios are compared: «  = 0.2 (point a) and «  = 0.1 (point b). (E and F) Sensitivity ofIðLmÞ at DECOUPLED to the short (E) and long (F) wage shocks. Except for the focal parameters, the same default parameter values were used as in Fig. 2.

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likelihood that economic inequality will increase. With a high andsharp threshold infrastructure, SESs can attenuate the possibility ofinequality, but the tradeoff is that they become more prone tosystem collapse. The maintenance threshold also influences therobustness of SES to wage shocks. Under low thresholds, theMOSTLY-Gs regime is more sensitive to wage shocks. How-ever, the opposite pattern was observed with the DECOUPLEDregime—high and sharp thresholds make the system moresensitive to wage shocks.Although our purpose here has been to use this model to il-

lustrate the dynamics of SESs, rather than predict behavior, it isworth noting that our model results resonate with some notablecases of irrigation systems in the literature. For example, thecommunity irrigation systems in hilly regions of Nepal, as de-scribed by ref. 5, come close to the characterization of a low-threshold scalable system in aMOSTLY-Gs regime. These kinds ofsystems have been found to be highly sensitive to wage shocks inrecent decades (29). In contrast, irrigation systems in plain regionsof South India, for instance, the Kurnool Cuddapah canal systemstudied by Wade (17), are examples of DECOUPLED systemswith high and sharp thresholds. The Kurnool Cuddapah systemhas also been highly sensitive to wage shocks (17), consistent withour model results. Interestingly, though, some specific villagesunder this system that Wade (17) observed to have been successfulin developing local collective institutions fall under aMOSTLY-Gsregime with high and sharp threshold levels. A recent study (30)looking at the long-term dynamics of the villages with collectiveinstitutions found them to be remarkably robust to wage shocks,again consistent with our model.Our findings also have some policy relevance. Policy makers

must balance the increased robustness of maintaining cooperationand system function that scalable infrastructure (higher «) conferswith increased fragility to emerging inequality. Likewise, if bio-physical conditions favor large-scale infrastructure (low «, largeψ), policy makers must be aware of the increased propensity forsystem collapse and the increased robustness to economicinequality. Our results also suggest the need for anticipatoryapproaches—institutional considerations should not follow as de-rivatives from infrastructure after it has been built but as factors thatshould enter as part of project design itself to enhance robustness.These outcomes highlight the need to ensure that the role of

public infrastructure is made more central in SES research. This

can be achieved by expanding ecologies of SES to include bothbuilt and natural components or thinking in broader terms aboutCIS, of which SESs are examples. We suggest that viewing SESsas examples of CIS provides a better reflection of the sustainabilityproblem context in the modern era because of the prominence ofinfrastructure systems in contemporary SESs. It would also helpcross-fertilize knowledge between social and natural science-basedsustainability scholars and those based in the applied sciences ofarchitecture and engineering.Of course, our findings represent only a first step toward better

understanding the capacity of CIS to cope with global change. Ourstudy restricted the number of strategies to two: group conformistand opportunist. Additional strategies could be considered.Farmers could, for example, invest in the infrastructure but takemore water than their share. We assumed that the depreciationrate of infrastructure is fast, i.e., no water is provided unless theinfrastructure is repaired every year (true for small-scale systemsthat require annual maintenance). An alternative would be toassume a slower rate of depreciation, such that some water is stillprovided even if no repair is done in a given year. Finally, furthercase study analysis and empirical fieldwork, like that which moti-vated this modeling effort (see csid.asu.edu), are essential tosupport theoretical and practical results.

Materials and MethodsThe payoffs for G and O in village i are expressed as the following:

πGi =pf�lGf ,q

Gi , a

�+wlGe − γsð1−XiÞ− γo

�1−Xj

�

πOi =pf�lOf ,q

Oi ,a

�+wlOe − δ

0@1− σ

QðLmÞQ�L*m

�1AqO

�Xi +Xj

2

�

where j denotes the other village (i≠ j). See Supporting Information for moredetails on the equations. We used replicator equations to model the changesin the fraction of Gs ðXiÞ in village i: dXi=dt =Xi ½πGi − πi �, where πi is the av-erage payoff of a farmer in village i, i.e., πi = πGi Xi + πOi ð1−XiÞ. Our resultswere obtained from numerical simulation of the above system of equations.

ACKNOWLEDGMENTS. We thank Marco A. Janssen, Charles L. Redman, andKathryn Kyle for feedback and inspiration. All authors acknowledge financialsupport from the National Science Foundation (Grant GEO-1115054).

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