ORIGINAL ARTICLE

Modeling the decline of labor-sharing in the semi-desert regionof Chile

Andres Baeza1,2 & Marco A. Janssen2

Received: 25 March 2017 /Accepted: 23 October 2017 /Published online: 22 November 2017# The Author(s) 2017. This article is an open access publication

Abstract The rapid environmental changes currently under-way in many dry regions of the world, and the deep uncertain-ty about their consequences, underscore a critical challengefor sustainability: how to maintain cooperation that ensuresthe provision of natural resources when the benefits ofcooperating are variable, sometimes uncertain, and often lim-ited. In this work, we present the case of a group of ruralcommunities in a semi-desert region of Chile, where cooper-ation in the form of labor-sharing has helped maintain higheragriculture yields, group cohesion, and identity. Today, thesecommunities face the challenge of adapting to recurrentdroughts, extreme rainfall, and desertification. We formulatedan agent-based model to investigate the consequences of re-gional climate changes on the fate of these labor-exchangeinstitutions. The model, implemented in the framework ofprospect theory, simulates the economic decisions of house-holds to engage, or not, in labor-sharing agreements underdifferent scenarios of water supply, water variability, andsocio-environmental risk. Results show that the number offulfilled labor-sharing agreements is reduced by water scarcity

and environmental variability. More importantly, defectionsthat involve non-fulfillment of these agreements are more like-ly to emerge at the intermediate level of environmental vari-ability and water supply stress. These results underscore theneed for environmental policy instruments that consider theeffects of regional climate changes on the social dynamics ofthese communities.

Keywords Cooperation . Rainfall . Drought . Agent-basedmodel . Labor-sharing . Risk

Introduction

Cooperative behavior among multiple actors of a society iscritical to ensure the provision of resources and other ecosys-tem services (Daily et al. 2000; Anderies 2015). Given theinherent complexity of socio-ecological systems, however,decisions to build and maintain trustworthy cooperative insti-tutions are often made under deep uncertainty about the po-tential costs and benefits associated with these agreements(Herman et al. 2014). A critical question is therefore how togenerate and maintain sustainable cooperative behavior formanaging natural resources, when the long-term benefits ofengaging in those enterprises are not well defined, often lim-ited, and under high levels of risk and uncertainty (Janssenet al. 2007). This work contributes to this body of literature bysimulating the decisions to cooperate made by households inagricultural communities of the semi-desert region ofNorthern Chile. In these communities, informal cooperationinstitutions in the form of labor-sharing agreements haveemerged, in an environment that today is forced by climaticuncertainty, long-lasting droughts, and extreme rainfallevents. We are particularly interested in understanding how

Editor:Diana Sietz.

Electronic supplementary material The online version of this article(https://doi.org/10.1007/s10113-017-1243-0) contains supplementarymaterial, which is available to authorized users.

* Andres Baezaandres.baeza@gmail.com

Marco A. JanssenMarco.Janssen@asu.edu

1 National Socio-Environmental Synthesis Center, University ofMaryland, College Park, MD, USA

2 Present address: School of Sustainability, Arizona State University,Wrigley Hall, 800 Cady Mall, Tempe, AZ 85281, USA

Reg Environ Change (2018) 18:1161–1172https://doi.org/10.1007/s10113-017-1243-0

the regional climatic changes currently underway in this semi-desert region influenced these labor-sharing agreements.

Labor-sharing refers to the exchange of labor betweenindividuals or households without relying on money(Suehara 2006; Debebe 2010). This is a common practiceamong many peasant societies around the world, and it is animportant strategy for reducing marginal and wage-relatedcosts, as well as for increasing household income and laborefficiency (Gilligan 2004; Gerichhausen et al. 2009). Froma social perspective, labor-sharing helps communitiesmaintain social bonds and collective identity while enhanc-ing cohesion (Downey 2010). While the evolutionary ori-gin of these institutions seems to be related to kinship prox-imity (Hames 1987), their structure—that is, the number ofmeaningful and successful cooperative interactions be-tween members—is shaped by multiple direct and indirectreciprocal interactions that over time shape group identityand social capital (Suehara 2006; Waring 2006). It is pos-sible then that over long temporal scales, these agreementsmay be influenced by changes in the biophysical environ-ment that in turn shape many of the short-term economicdecisions.

For rural communities living in dry environments, the com-bination of long dry seasons and extreme variability in rainfallregarding the water supply results in risky economic condi-tions due to the uncertainties around water supply (Reynoldset al. 2007). These precarious prospects of future outcomescause farmers to undertake multiple strategies to cope withuncertainty, aimed at maintaining economic viability over lon-ger periods of time (McAllister et al. 2006). If, therefore, so-cial interactions are modulated by changes in the socio-ecological environment, how do resource scarcity, its variabil-ity over time, and the inherent socio-ecological uncertainty atthe moment of decisions influence the stability of these coop-erative labor-sharing agreements?

To provide insight into this question, we developed andanalyzed an agent-based model inspired by the labor-sharing documented in the rural communities of NorthernChile. Our aim is to understand how labor-sharing agree-ments have been influenced by the extreme variability andscarcity in water supply these communities face, and howuncertainty about this supply prospect influences the fulfill-ment of these agreements. These communities are locatedin a transitional climatic zone, where regional changes inatmosphere and oceanic patterns of the subtropical Pacificregion have influenced regional rainfall trends, causing theChilean side of the Andes to confront longer inter-annualperiods of drought in summer and more extreme rainfallevents in winter (Minetti et al. 2003; Souvignet et al.2010). These communities face the challenge of adaptingto these environmental and climate changes by varyingtheir economic decisions over time (Alexander 2008;Salas et al. 2012).

The agents in the model are households of a community.Each household makes decisions as to whether to engage inthe production of a rain-fed crop, whose productivity dependson the availability of water that is assumed to be variable andunknown. Under this climatic uncertainty, households mustdecide if they will engage in informal agreements to sharelabor with other households. The decisions to share labor(cooperate) are made on the bases trust and reputation of thehouseholds. Trust is defined as the probability that a house-hold will cooperate based on previous direct interactions, andreputation is defined as the average trust of a household in thecommunity based on the interactions with other households(Mui et al. 2002; Janssen 2008).

The decision-making process of the households is imple-mented using the framework of prospect theory (Kahnemanand Tversky 1979). Prospect theory (PT) introduces impor-tant aspects from cognitive psychology into moreBtraditional^ econometric models, including considerationsof risk perception and risk attitude, which cause it to deviatefrom standard expected utility approaches (Wakker 2010).It describes in mathematical terms how people make deci-sions, not just by choosing among alternative options thatinvolve probabilistic events but also by assuming that peo-ple make behavioral choices that are biased by the context,social or physical, to avoid losses or to seek gains (Hastieand Dawes 2010). The theory has been used to understandhuman decisions in multiple arenas to represent uncertainand ambiguous alternatives, such as international relation-ships (Goldgeier and Tetlock 2001), financial risk manage-ment (Fiegenbaum 1990), and insurance markets (Sydnor2010), and it has been applied recently to problems relatedto natural resource management in variable environments(Podestá et al. 2009). We use PT to represent the risk be-havior and perception of gains and losses when householdsdecide to establish cooperation agreements and make finaldecisions that involve environmental ambiguity and socialrisk based on trust and reputation.

In the next section, we briefly summarize the institution-al arrangements of the agricultural communities of thenorth of Chile, the type of environmental variability towhich these communities are exposed, and the strategiesthat have emerged over the past 50 years to cope with andadapt to these environmental conditions. We then describethe structure of the agent-based model and the numericalexperiments constructed to test the effects of water scarcityand water variability on the cooperative decisions of thecommunity in conditions of social and climatic risk. Weend the paper by discussing our results in the context ofempirical research needed to test the influence of socio-environmental risk, along with the potential implicationsof the results for moving forward with environmental pol-icies to halt the environmental degradation affecting thesemi-desert region of Chile.

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Agricultural communities in the semi-desert regionsof Chile

In the semi-desert territory of Chile, between the AtacamaDesert and the fertile, wine-producing valleys of centralChile, 178 agricultural communities occupy more than10,000 km2 of three administrative regions. Each of thesecommunities is composed of a group of households with in-dividual rights to use community land for individual produc-tive purposes (Ministerio de Bienes Nacionales 2017). Themost common purpose the community assigns to the land isthe production of crops, of which the most commonly plantedis wheat. Common land within the community is designatedand managed by the community members themselves. On thiscommon land, many households engage in pastoral activitiesfor the production of cheese, milk, meat, and leather. Besidesagriculture and livestock activities, members of the communi-ties also engage in off-farm activities, which mostly take theform of work in mining, construction, or large-scaleagriculture.

These kinship-based communities can be traced back to the1800s, when the rights to the land were passed down to thedescendants of Spanish colonists (Silva et al. 1978). Since1932, the Chilean government has recognized them as self-governing units, which means that each of them has a gover-nance structure to manage their natural resources. Today, eachcommunity is governed internally by institutions that definethe rights to common land, designating resting areas and ani-mal quotas for livestock, and determining the needs and pri-orities of the community regarding investment in publicgoods, such as irrigation systems. Social organizations arealso present, overseeing cultural traditions like group harvest-ing and cheese production, as well as organizing sportingevents and social gatherings (Rocha Pérez 2006).

The environment in which these agricultural communitiesare located is defined as a semi-desert and with Mediterraneanclimate, with dry summers and a short rainy season in winter.The land is mostly classified as Bel secano,^ which is definedby its low productivity, high susceptibility to erosion, and lowcarrying capacity for livestock. Most of the households inthese communities do not have access to surface water forirrigation (Hearne and Donoso 2014). In consequence, theeconomic return is highly variable and strongly dependenton rainfall and ground water, forcing the farmers to rely onfast-cash rain-fed crops such as wheat. However, the produc-tion of these crops is uncertain and dependent on the amountof water the rainy season will bring.

This strong dependency on water is critical for understand-ing the decisions and strategies of these communities. Beforethe rainy season, agreements to share labor are designed tohelp each other with activities related to agriculture, such aspreparation of the land, seeding, or planting, and the expecta-tion for help continues until the end of the agricultural season

with the harvesting of the production (Alexander 2008).However, during the rainy season before the harvest, a house-hold must decide whether to continue investing time in thecommunity or diversify its portfolio of options given the cur-rent water situation it faces. The most common of these op-tions is for one or two members of the household to leave thecommunity temporarily to work off-farm, seasonal jobs, mostoften in the wine and liquor production industry, mining, andconstruction. Another diversification option is to take the an-imals and rent land from other communities or private land-owners in areas with better conditions for animals to feed andsurvive (Alexander 2008). In both situations, water availabil-ity determines the need for households to choose betweenstaying in the community and leaving for better opportunities.

The decision to leave the community would imply, in prin-ciple, a reduction of the amount of time individuals wouldhave to fulfill their labor-sharing agreements, at the time inthe season when the help would be most critically needed forharvesting the crops. Because the most common crop plantedis wheat, the harvest season is short and has to be carried out ata specific point in time before the grains dry out. Because ofthis, labor during harvesting is intensive, and the help fromothers is essential for completing the work on time. Moreover,labor-sharing during this time generates higher yields that oth-erwise would not be possible if the household members workby themselves. Not receiving this type of help can be extreme-ly detrimental. However, when households rely heavily onothers for maintaining production without reciprocating a fairamount of time contributing to the agricultural needs of others,they are seen as Bfree riders,^ which thereby reduces theirtrustworthiness and the overall reputation of the household(Alexander 2008).

The model

The community

A community is defined as a group ofN households of farmersproducing agriculture in a water-driven environment. Eachyear, households must decide to either set an agreement withother households to share labor to increase the production ofboth farms or leave the community and use the time to work inpaying (wages) jobs. These agreements, however, are madeunder conditions of uncertainty about how much water theseason will bring, and they must be validated after the house-holds have more information regarding the availability of wa-ter (Fig. 1).

Agriculture production and utility function

When a household decides to stay in the community, it willproduce and harvest a crop. We assume that the Bannual^

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harvested crop Hi,t is influenced by the amount of land Ai; thetotal labor for production, Li,H; and a seasonal (variable) cli-matic, rainfall effect xt, such that,

Hi;t ¼ φxtAiLi;H ; ð1Þwhere φ is the factor of cooperation. This is a parameter that isgreater than 1 when both households decide to engage inlabor-sharing, and φ = 1 if not. This is the benefit ofcooperation.The total labor for production for household i,Li,H, is defined as

Li;H ¼ Li−Li;C þ Lj;C−Li;W ; ð2Þ

where Li is the total labor of a household i, Li,W is thetime a household spends working outside the farm in pay-ing jobs, and Li, C is the labor provided by household i to

household j and Lj, C the labor received from household jto household i. We assumed that in an agreement setting,households share the same amount of time; therefore, Li, Cand Lj, C cancel each other out in a fulfilled agreement asboth families help each other. However, this symmetrybreaks down if one of the families does not fulfill theagreement (see Table 1).The utility of household i at timet, Ui, t, is defined as the sum of the gains obtained fromthe private farm (Hi, t) and from off-farm wages, W, suchthat

Ui;t ¼ Hi;t þWLi;W; ð3Þ

where W is the off-farm wage per unit of labor investedby household i in working off-farm, Li,W.

Fig. 1 Flow diagram ofhouseholds’ decisions. Thedecision to cooperate and sharelabor is made in two steps: beforeand after the rainy season. Beforethe rainy season, a decision ismade under climatic uncertaintyas to whether to set an agreement.After the rainy season, a seconddecision is made as to whether tofulfill the agreement, and it ismade under uncertainty as towhether or not the other familywill cooperate. Circles representthe environmental and socialuncertainties

Table 1 Possible outcomes for household i to decide if engaging or not in a labor-sharing agreement, given the possible decisions of household j

Household jHousehold i

c: Stay in the community, work on farm, and share laborwith household i

d: Divide time working on farm and off farm, but do not engage inlabor-sharing

C: Stay in the community, work on farm, and share labor withhousehold j UCc

it ¼ φxtAiLi UCdi;t ¼ xtAi Li−Li;C

� �D: Divide time working on farm and off farm, but do not

engage in labor-sharing UDci;t ¼ φxtAi Li þ Lj;C−Li;W

� � þwLi;W UDdi;t ¼ xtAi Li−Li;W

� � þwLi;W

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Modeling variability of water

Equation 1 includes variable xt to represent inter-seasonalchanges in yield related to water availability. For the sake ofthe argument, the model assumes that the communitywould experience only good (wet) or bad (dry) years ofwater availability, and the difference between a good rainyyear, RW, and a bad dry year, RD, is represented by Rvar, suchthat

xt ¼ 1þ Rvar ¼ RW

1−Rvar ¼ RD:

�

Thus, the larger the value of parameter Rvar, the big-ger the difference is between a drought and a highlyproductive year. Therefore, water variability in this workis defined as the magnitude of the difference between agood and a bad year.

We also considered that these climatic events could be cor-related in time. By following Caswell (2001), we define theprobability of having a bad or a good spell, conditional on thelast rainfall event, using the following expressions:

P xt ¼ RW jxt−1 ¼ RDð Þ ¼ 1−ρ−P xt−1 ¼ RDð Þ 1−ρð Þ ð4Þ

and

P xt ¼ RDjxt−1 ¼ RWð Þ ¼ P xt−1 ¼ RDð Þ 1−ρð Þ; ð5Þ

where P(xt = RD) is the unconditional probability of having abad, dry year, and ρ is the temporal correlation between rainfallevents. When ρ = 0, these conditional probabilities become theunconditional probabilities P(xt = RW) = 1 − P(xt = RD).

Using these expressions and setting parameters Rvar and ρto particular values, we generated random realizations of xt.Scenarios with higher probability of a good year representenvironments with low levels of hydric stress, and scenarioswith higher values for parameter Rvar are environments withhigh variability of water between years.

Prospect theory

Before explaining how the labor-sharing agreements and thefinal decisions are made, we need to explain the main assump-tions of prospect theory (PT) that will mathematically definethe choices (prospects) under environmental and social risk.The main assumption of prospect theory is that people evalu-ate options based on their perception of loss and gain; theirattitude toward risk; and, finally, the probability of those op-tions. What differentiates a loss from a gain is a threshold or,more precisely, a reference point that is a reflection of people’sexpectations or beliefs about past outcomes or the outcomes ofothers. In addition, PTassumes people have an attitude towardrisky behavior that weighs gains and losses differently. It is

important to note that in PT risk, attitude can represent differ-ent types of behavior, such as risk aversion, relentlessness, orindifference to the perceived risk (Wakker 2010). Moreover,in PT, people weigh events differently based on the probabilitythat such events will happen. Commonly, people underesti-mate events that are less commonly observed, such as extremestorms that happen once every 100 years. Less often, peopleoverestimate events occurring more frequently. Placing themodel in the framework of PT allows for the evaluation ofthe importance that risk attitude may have on the social struc-ture of these communities when confronted with a variableand unpredictable environment.

In the next two sections, we define the decision-makingprocess of households in these communities using the mathe-matic formulation of PT for both the agreements made beforethe rainy season and the final decisions. We compare the re-sults obtained with PT against a modified model that does notconsider risk attitude and instead evaluates the agreements andfinal decisions using absolute quantities rather than a relativemeasure of gain and losses. This modified model is called theBExpected Utility^ (EU) formulation. The modifications tothe model along with the simulation results are presented inthe Online resources document (Expected Utility formula-tion). A graphical comparison of the results obtained underPT and EU is also presented in fig. 3.

Agreement under environmental risk

At the beginning of the planting season, before the rains havefallen, each household must decide if it will engage in ex-changing labor with other households in the community(Fig. 1). Households are paired with probability proportionalto the trust both households have in each other and their rep-utation based on previous interactions with other households.After households have been paired, they mutually evaluatetwo possibilities: first, they can stay in the community, workon their farms, and share labor. This decision is one that leadsto both staying in the community, BCC^, and it can happenduring a good year with abundant water, in which case theutility obtained is labeled UCC

W . Alternatively, they can coop-erate in a bad year with low water, in which case the utility is

UCCD . The second option is that they can mutually decide not

to share labor and instead work on their own farms and off-farm. This decisionwould giveUDD

W in conditions of abundant

water, with BDD^ as the agreement to not cooperate, andUDDD

in the case of a dry year. The following equations provide thefour possible prospects to evaluate:

UCCW;t ¼ φRW AiLi þ AjLj

� � ð6Þ

UCCD;t ¼ φRD AiLi þ AjL j

� �L ð7Þ

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UDDW;t ¼ RW Ai Li−Lwð Þ þ Aj L j−Lj;w

� �� �þ WLi;W þWLj;W� � ð8Þ

UDDD;t ¼ RD Ai Li−Lwð Þ þ Aj L j−Lj;w

� �� �þ WLi;W þWLj;W� �

; ð9Þ

In general terms Ugy;t with g = {CC,DD}, and y = {W,D}.

The valuation of these four prospects by a household incor-porates considerations of the subjective perception of gainsand losses with respect to a reference point. Here, we as-

sume that this reference point for family i, Urefi;t , is defined

as the average of the utility obtained in the five previoustime-steps, or

Ure fi;t ¼ 1

Δt∑t−Δt

t−1Ui;t:

A difference measure between the prospect and a referencepoint for an agreement is constructed using

ΔUgy;t ¼ Ug

y;t− Urefi;t þ Uref

j;t

� �: ð10Þ

A positive outcome ofΔU is perceived as a gain. Using thissubjective evaluation of gains (and losses whenΔUg

y;t < 0 ), a

value function v is constructed using the probabilities of theseprospects:

V U ;π; gð Þ ¼ Ω πWð Þv ΔUgW ;t

� �þ Ω πDð Þ*v ΔUg

D;t

� �: ð11Þ

The form of function v is such that it considers the riskbehavior of the farmers to evaluate the gains and losses Ug

y;t.

We used the formulation from Wakker (2010):

v ΔUgy;t

� �¼ λ ΔUg

y;t

��� ���a.(12).Using this formulation and specific parameter values, two

types of communities were specified: a community composedof gain-seeking farmers and another with loss-averse farmers.Gain-seeking farmers do not pay much attention to losses andoutweigh gains. In such case, the value function v is parame-terized using

λ ¼ 1; a > 1 if ΔUgy;t ≥0

−1 < λ < 0; a ¼ 1 if ΔUgy;t < 0

�:

In the other case, loss-averse farmers outweigh losses andpay little attention to gains. In such cases, function v is param-eterized with

λ ¼ 1; 0 < a < 1 if ΔUgy;t ≥0

λ < −1; a ¼ 1 if ΔUgy;t < 0

�.

The perception of risk is also subjective with regard to theevaluation of these possibilities. That is, farmers do not rely onthe objective probability of an event. This subjectivity can be

captured by a parametric form of a weighting function pro-posed by Kahneman and Tversky (1979):

Ω πð Þ ¼ πc

πc þ 1−πð Þcð Þ1c; ð13Þ

where π is the probability of the next rainfall event (RWor RD).Given the assumption of environmental risk, households cal-culate the prospects using π = P(xt = RW | xt = RD) (Eqs. 4 and5).

Final decision under social risk

As stated in the introduction, the agreements made by thehouseholds in a community are informal, that is, there is nolegal bond that ensures fulfillment. Therefore, we assume thatas the season proceeds, the households can update an agree-ment according to the environmental information obtained(Fig. 1). This is implemented by assuming that the final deci-sion is made with farmers knowing the true environmentaloutcome, i.e., xt. However, the calculation of the expectedgains or losses is now made under the uncertainty that theother household will fulfill its agreement (Fig. 1). Table 1shows the possible outcomes of each decision from the pointof view of one household, given the possible final decisions ofanother household.The expected utility of household i underthe risky prospect that the other household will fulfill theagreement is calculated using

ViC ¼ Ω I i; j;t

� �v ΔUi;t

Cc� �þ Ω 1−I i; j;t� �

v ΔUi;tCd� � ð14Þ

and

ViD ¼ Ω I i; j;t

� �v ΔUi;t

Dc� �þ Ω 1−I i; j;t� �

v ΔUi;tDd� � ð15Þ

Function v is the value function evaluated for the individualreference point of household i for each one of the four possiblefinal decisions,ΔUi, t

f, with f = {Cc,Cd,Dc,Dd}. Ii, j, t is theexpectation from household i that household j will fulfill theagreement, and it is represented by the image of the house-hold, a function of the trust household i has in household j, andthe reputation of household j (see below). This is the socialrisk associated with the final decision. Thus, when Vi

C > ViD,

the household will stay in the community, work on its ownland, and engage in sharing labor.

Trust, reputation, and expectation of cooperative behavior

Trust and reputation influence the image each household hasfrom each other, and this image defines the expectation that agiven household will fulfill an agreement. Formally, the imagethat household i has of household j is defined by

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I i; j;t ¼ ετ i; j;t þ 1−εð ÞRj;t; ð16Þ

where τi, j, t is the level of trust household i has in household jat time t, and Rj, t is the reputation of household j. Parameter εrepresents the importance households give to direct (trust) andindirect (reputation) interactions. The level of trust householdi has in household j is

τ i; j;tþ1 ¼ 1−μð Þτ i; j;t þ μSi; j; ð17Þ

where μ is a parameter that defines the memory of the house-hold. Si, j is the score of the interaction of household i withhousehold j. The trust a household has in others changes overtime according to the outcome of this interaction between thehouseholds. The following score sheet was used to define theoutcome of each interaction:

Si; j ¼

0 if g ¼ CC and f of j ¼ d1

3if g ¼ DD and f of j ¼ d

2

3if g ¼ DD and f of j ¼ c

1 if g ¼ CC and f of j ¼ c:

8>>>><>>>>:

where Si, j represents the score that household i assigns tohousehold j after a single interaction, by comparing the finaldecision made by household j against the agreement madebetween the two before the rainfall season.

Thus, a household would score better when both the initialagreement and the final decision were to stay and share labor,and the score would be the lowest when the agreement was toshare labor BCC^, but the final decision was to leave the com-munity, Bd^. A household does not rely solely on direct trust-worthy interactions to define an image; it also relies on theinteractions of others. We define this as the Breputation^ of ahousehold. Reputation is defined as the average trust otherhouseholds have in a household, such that

Rj;t ¼ 1

N−1ð Þ ∑k¼N

k¼1τk; j;t: ∀k∈∁ : k≠ j

� ; ð18Þ

where ∁ is the set of households in a community of size N.

Numerical experiments

We simulated the model using different levels of water abun-dance and environmental variation. We constructed scenariosof water abundance by varying P(xt = RW), which ranges from0.1 to 0.8.We also constructed scenarios with different levelsof variability between dry and rainy years, from no variability,Rvar = 0, to a highly variable environment, Rvar = 0.8. We sim-ulated each scenario under different levels of temporal corre-lation between events, from ρ = 0 to ρ = 0.8. Finally, weconstructed scenarios to explore the effects of external eco-nomic incentives, by varying the wages received per unit of

time, from W = 1 to W = 4. Each simulation was conductedassuming households have different types of risk perception: acommunity composed of gain-seeking farmers and a commu-nity composed of loss-averse households. A gain-seekingcommunity was constructed using parameters λ = 1 anda = 1.5 for gains and λ = − 0.5 and a = 1 for losses. A loss-averse community was composed using λ = 1 and a = 0.5 forgains and λ = − 1.5 and a = 1 for losses. We also simulated themodel without considering risk attitude, using the ExpectedUtility formulation.

We generated 20 realizations for each combination of pa-rameters, and we ran the model for a period of 100 time-steps.We recorded the community average number of fulfilledagreements (interactions of the form BCc^); the number ofhouseholds that decided to leave (strategy BDd^); and thenumber of defections, represented by the number of unful-filled agreements of the form BCd.^ The name of the param-eters and the range of values used are presented in OnlineResources Table 1.

Code availability

The model was coded in Netlogo, version 5.2.1, and can beaccessed at https://github.com/abaezacastro/Cooperation_Chile, along with output files from the experiments and thescripts to rerun the analyses. The ODD protocol to describeagent- and individual-based models (Grimm et al. 2006) isincluded in the Online Resources, along with a detailed de-scription of the decision-making processes using the frame-workMoHub (Schlüter et al. 2017) (Online Resources Fig. 4).The model will be archived in the library of CoMSES.

Results

Effect of water scarcity

When comparing the number of fulfilled agreements within agradient of water availability, the results show that labor-sharing contracts are formed more commonly in scenarioswith high water abundance (Fig. 2a). More importantly, de-fections of the form Cd are more likely to be observed inenvironments that are neither extremely dry nor abundantbut in the middle of the range of water availability (Fig. 3a).Under a high degree of scarcity, more households leave thecommunity and, via mutual agreement, decide not to engagein labor-sharing, thereby increasing the number of interactionsof the form Dd (Fig. 2a). At the other extreme, when water isabundant, most of the households decide to stay and most ofthe contracts are fulfilled. Overall, in communities copingwith more stressful water conditions, more people move outof the community to work paying jobs (Online ResourcesFig. 2).

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Fig. 2 Relationship between fulfilled labor-sharing agreements andscenarios of water availability, variability, wages, and temporalcorrelation of events. In each panel, a point in the x, y plot representsresults from a single simulation, with the y-axis showing the yearlyaverage number of fulfilled agreements (BCc^) with respect to waterabundance in a, water variability in b, wages in c, and temporalcorrelation between good and bad years in d. a Shows that scenarioswith more abundance of water can incentivize farmers to invest moretime in helping each other. The colors red and blue display resultsassuming a community composed entirely of loss-averse and gain-seeking farmers, respectively. b Shows the negative relationship

between the magnitude of the difference between good and bad years ofwater supply and the number of agreements that were fulfilled. c Showshow increasing off-farm wages can reduce the number of fulfilledagreements. Both water variability and wages influence the number ofcooperative agreements in a non-linear way. d Displays the null effect ofthe temporal correlation between good and bad years. Overall, gain-seeking farmers are more likely to engage in cooperative agreementsthan loss-averse farmers. The solid lines represent the results of fitting alocal polynomial regression using the function Bgeom_smooth^ in thesoftware R

Fig. 3 Relationship between defections and scenarios of wateravailability and water variability. The plots show the yearly averagenumber of defections in the community. A defection is defined as aninteraction that begins as an agreement to share labor but ends with oneof the households leaving the community and not fulfilling the agreementstrategy BCd.^ In a, the number of defections are shown in a gradient ofwater abundance, which is represented by the probability of good years.In b, defections are plotted against the magnitude of the variability

between good and bad years. Larger numbers of defections areobserved in the middle range of variability and abundance and forscenarios with loss-averse farmers. The solid lines show the results offitting a local polynomial regression, using the function Bgeom_smooth^in R. The black lines are the fitting of the local polynomial regression tothe results obtained from the Expected Utility formulation. The full set ofresults from the EU formulation is presented in the Online Resourcesdocument (Online Resources Fig. 1)

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Significant differences are observed due to the risk behav-ior of the communities. Specifically, in communities com-posed of gain-seeking farmers, the number of fulfilled agree-ments increases linearly with the availability of water re-sources, whereas in scenarios with loss-averse farmers, thisrelationship, while still positive, is non-linear, suggesting thata large degree of water security is needed for farmers to startinvesting time in the community and helping others (Figs. 2and 3). As shown in Fig. 3a, more defections of the form Cdare observed in scenarios where farmers are loss-averse.Scenarios with gain-seekers show less defections and lesssensitivity to water availability.

Simulating the model using the Expected Utility formula-tion (Online Resources Fig. 1) generates fewer defections thansimulations from risk-adverse communities, though there are ahigher number of defections when compared to gain-seekercommunities (Fig. 3b).

Effect of water variability

The magnitude of the fluctuation between good and bad yearsof agricultural productivity, due to water variability, also in-fluences the social fabric of these communities. A negativeand non-linear relationship is observed between the numberof fulfilled agreements, Cc, and the level of environmentalvariation (Fig. 2b). An abrupt decay in labor-sharing agree-ments is observed when the variability in water crosses a cer-tain threshold (Rvar > 0.2). This non-linear decay in the num-ber of fulfilled agreements matches the rise of defections ofthe formDc, which correspond to interactions where an agree-ment was defined, but a final decision to leave was made (Fig.3b). The decay in fulfilled agreements and the rise of defec-tions also coincide with a decline in trust (Fig. 4a). This wan-ing of trust and, eventually, reputation among members of the

community reflects the tension that arises under environmen-tal ambiguity and the need to cope with rapid environmentalchanges.

Similar to the effect of water abundance, the risk attitudeamong farmers also influenced the number of fulfilled agree-ments. Scenarios of communities composed of gain-seekerhouseholds generated more fulfilled agreements (Fig. 2b)and less defections (Fig.3b), when compared to loss-adversecommunities. This occurred more often when the variabilitywas extreme. It is in the mid-range of variability where simu-lations with gain-seekers differ the most from those with loss-averse farmers. Gain-seekers are willing to risk a major loss ifthe gain is larger and are more likely to stay in the communityunder intermediate levels of variability if they perceived thatgains from staying in the community and cooperating are po-tentially greater than working outside the community. Thesedecisions to stay allow them to accumulate larger amounts ofwealth (Online Resources, Fig. 3a, b) compared to scenarioswith loss-averse households. The influence of risk behaviorstarts to disappear under high levels of variability when therisk of a drought is extremely high, though the prospects ofgain in a good year are also high (Fig. 3b and OnlineResources Fig. 1b).

Results from simulating the model using the expected util-ity formulation demonstrate that both models produce similaroutcomes when farmers are loss-averse (Fig. 3a).

External economic incentives

Higher wages also result in a reduction of the time householdsspend in the community. As shown in Fig. 2c, strong non-linearity emerges as a result of the feedback between socialuncertainty, influenced by trust and reputation, and the exter-nal incentives that impact the decision to stay in the

Fig. 4 Relationship between trust and scenarios of water availability andwater variability. The figure in a shows the average level of trust in thecommunity, in a range of scenarios of water availability represented bythe probability of good years (P(xt = RW)). b Illustrates how the level of

trust decreases in a non-linear way, as the water variability, represented bythe magnitude of the difference between a good and a bad year (Rvar),increases. Trust in others is higher in scenarios with gain-seeking farmers

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community despite the level of climatic variation and wateravailability. In a closed community without external markets,that is, when parameterW = 0, 100% of the farmers engage inagriculture, including helping each other. As wages increase, asharp decay in agreements is observed as more people decideto leave in pursuit of better outcomes (Fig. 2c and OnlineResources Fig. 2).

Temporal correlation between events and environmentaluncertainty

The temporal correlation between good and bad years of wateravailability did not influence the number of fulfilled agree-ments (Fig. 2d). Finally, when comparing simulations withcomplete uncertainty about the future availability of waterversus scenarios in which households have knowledge of thetrue probability of an event, our results do not indicate signif-icant differences.

Discussion

Rural communities in areas of transition between desert andforests are significantly affected by rapid climatic changescurrently underway (Kepner et al. 2006; Huang et al. 2016).In particular, for the semi-desert region of Chile, significantchanges in rainfall patterns, along with other socio-environmental processes, have caused degradation (Leon2007) and impacted the productivity of the land.Agricultural communities have adapted to these variable con-ditions by diversifying their activities, which often involvesmaking the short-term decision of leaving the community insearch of other opportunities. In this work, we show the pos-sibility that these regional climate changes and short-term de-cision are exacerbating in the long-term the degradation of thesocial institutions and resource-based activities that havehelped these communities to maintain cultural bonds andgroup identity.

We are not the first to suggest a connection between theseregional climatic changes, the environmental degradation, andthe decline of social relationships of these communities.Castro and Bahamondes, for instance, analyzed narrativesfrom members of these communities about the effects thatclimate changes have had on their lives and on the socialorganizations that promote social bonds and cultural identity.They noted that many cultural traditions are disappearing inareas that suffer the most from water depletion, and they con-cluded that most of the activities and cooperative institutionsthat characterize the identity of these communities are current-ly only observed in the southernmost part of the region, wherethe land is more productive and water is more abundant(Castro and Bahamondes 1986).

Our study was limited by the lack of empirical data aboutthe time households in these communities have invested inlabor-sharing over time. In this context, the interpretation ofour results must be considered with caution and should not betranslated into policy interventions. They should be used asthe basis for hypotheses of future empirical studies on institu-tional analysis. Specifically, our results suggest that risk atti-tude can have important consequences for maintaining thenetwork of labor-sharing. In scenarios where gains were val-ued more heavily than avoiding losses, households were morewilling to stay in the community and cooperate, despite socialand environmental ambiguity. Maintaining social bonds and aperception of gain from these interactions can incentivize peo-ple to invest more time in their community to strengthen cul-tural bonds. Future studies should focus on understandinghow the composition of these communities, in terms of ageand gender, influences the perception of risk and the expecta-tions for maintaining trustworthy relationships within thecommunity and contributing to solving common problems.Empirical studies in rural communities of Africa, for instance,have shown that the perception of large losses in environmentswith scarcity can facilitate spiteful and competitive behavior(Prediger et al. 2013).

The model presented here therefore provides hypothesesthat position within the same decision-making frameworkthe economic decisions made by farmers, the behavioral fac-tors behind them, and environmental variability and socialuncertainty. By linking these processes in the context of re-gional environmental changes, our model illustrates the criti-cal feedback between resource variability and social risk thatleads to the erosion of trust and reputation and the subsequentdegradation of the institutions that support cultural bonds.According to Mehta, a failure to recognize the inherent cou-pling between social and environmental factors that influencethe structure of rural communities can lead to simplistic policyinterventions that can reduce the adaptive capacity of thesecommunities to maintain themselves in the face of environ-mental changes (Mehta et al. 1999). On the other hand, con-sidering the preservation of these institutions over time andusing strategies to cope with climate variability can providenew ways to combat desertification.

Our results also illustrate how external economic opportu-nities driven by global markets can influence the participationof farmers in cooperative institutions (Cárdenas et al. 2017).Access to other sources of income and more information caninfluence the perception that young people have of the pros-pect of living in rural areas, thereby incentivizing rural-urbanemigration patterns. These global forces acting in concert withclimate changes challenge the capacity of the system to main-tain stable communities that can adapt to the changes in theenvironment (Janssen et al. 2007; Montaña et al. 2016).Policies that aim to achieve land restoration—economic in-centives for reforestation, insurance schemes for climate-

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related disasters, or better prediction of rainfall—should con-sider the interactive nature of these socio-environmental pro-cesses in maintaining the cooperative institutions that shapethe social fabric of these groups.

Cooperative institutions based on the exchange of otherassets, such as land or water, have been observed in otherdry regions of the world subjected to water scarcity and ex-treme variability. In pastoral communities of Australia, coop-erative institutions known as Bagistment^ help rangers fromdistant communities share their land in order to reduce fluctu-ations in livestock size due to rainfall variability (McAllisteret al. 2006). In Kenya, informal insurance schemes were cre-ated between pastoral communities to transfer animals amongdistant regions to reduce losses in years of rainfall scarcity(Dixit et al. 2012). In both cases, these insurance schemesare also maintained by trust and reputation. A critical differ-ence between these strategies and the case of labor-sharing isthe spatial scale at which these cooperative interactions aremore likely to emerge in response to climatic variability. Inthe case of the insurance schemes in Kenya and the agistmentcontracts in Australia, the benefit of cooperation is obtained atlarge spatial scales, when the distance between the users of theresources (pastures) is large enough to generate sufficient spa-tial variability. In the case of labor-sharing, these decisionsoccur between closely located households that are similarlyaffected by climatic events. Both of these cooperative strate-gies (within and between communities) have been document-ed in Chilean communities (Alexander 2008), suggesting thatthey may be acting on and influencing the system at a moreregional scale. Given the large area these communities coverand their strategic importance for reducing regional degrada-tion (Leon 2007; Montaña et al. 2016), future research shouldaim to understand how these strategies, acting at multiplespatial and temporal scales, can lead to different social-economic and environmental outcomes.

Conclusions

Environmental changes in semi-desert regions of the world areimpacting the prosperity of many rural communities that de-pend on the availability of seasonal pulses of water for agri-culture and pastoralism. Farmers and pastoralists change theirstrategies to cope with prolonged droughts and extreme rain-fall events. The agent-based model proposed in this work wasdeveloped to provide awareness and theoretical insight onhow these environmental changes and strategies may haveimpacted the social fabric of these rural communities ofNorthern Chile and the ways they cooperate. The modelshows that increase in rainfall variability and scarcity can neg-atively impact cooperation among farmers.

High dependency on weather patterns for production, so-cial and environmental uncertainty, and strong external market

forces are not just processes underway in Chile but in manyother communities around the world. It is therefore critical forpolicy-makers, when designing and implementing policy in-struments aimed at reducing environmental degradation, toconsider the interaction between these processes and the per-ception and attitudes of people toward socio-environmentalrisk. An institutional analysis is needed to empirically validatethese results and thus to understand how these regional envi-ronmental changes are influencing the way people invest re-sources in collective actions, public goods, and communitybuilding. Such analysis should provide valuable informationfor decision-makers when creating these policy instruments inthis and other semi-arid regions. Furthermore, consideringinitiatives that can foster environmental restoration along withsocial cohesion and enhancement of collective institutionsshould provide more effective policies to combat desertifica-tion and land degradation in these fragile socio-ecologicalsystems.

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Acknowledgments We especially thank RyanMcAlister and the rest ofthe participants of the working group for their valuable comments duringour meetings in Annapolis and Leipzig.

Funding information This research was supported by the NationalSocio-Environmental Synthesis Center (SESYNC) [Grant No. DBI-1052875] through the Postdoctoral fellowship program to AB and theBModeling Human Decision-making^ working group with the GermanCenter for Integrative Biodiversity Research (iDiv) to MJ. We also ac-knowledge the support from the Project MEGADAPT [NSF Grant No.1414052].

Open Access This article is distributed under the terms of the CreativeCommons At t r ibut ion 4 .0 In te rna t ional License (h t tp : / /creativecommons.org/licenses/by/4.0/), which permits unrestricted use,distribution, and reproduction in any medium, provided you giveappropriate credit to the original author(s) and the source, provide a linkto the Creative Commons license, and indicate if changes were made.

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