Agent-Based Modeling for Community Resource Management: Acequia-based Agriculture

Abstract Water management is a major concern across the world. From northern China to the Middle East to Africa to the United States, growing populations can stress local water resources as they demand more water for both direct consumption and agriculture. Irrigation based agriculture draws especially heavily on these resources and usually cannot survive without them; however, irrigation systems must be maintained, a task individual agriculturalists cannot bear alone. We have constructed an agent-based model to investigate the significant interaction and cumulative impact of the physical water system, local social and institutional structures which regulate water use, and the real estate market on the sustainability of traditional farming as a lifestyle in the northern New Mexico area. The regional term for the coupled social organization and physical system of irrigation is “acequias”. The results of the model show that depending on the future patterns of weather and government regulations, acequia-based farming may continue at near current rates, shrink significantly but continue to exist, or disappear altogether. Keywords: agent-based modeling, land-use, integrated models

1 Introduction Water has been an important resource throughout human history. It is crucial not only for

direct human consumption but also for agriculture, especially in marginally arable

regions. Irrigation is correlated with social complexity, as everything from government

bureaucracies (Lees, 1994) to new legal formalisms (Butzer et al., 1985) have sprung up

to maintain and manage water systems. Ancient Egyptian irrigation was quite

sophisticated, and China has records of irrigation from as far back as 1600 BCE (Chang-

Qun et al., 1998). The need for these systems continues into the present day and across

the world. In modern China, (Jowett, 1986) widely across the Middle East and Africa,

(Giordano et al., 2002) and various places within the United States (Postel, 2000)

growing populations are placing enormous stress on local water resources. Irrigation

based agriculture draws heavily on these resources; however, irrigation systems must be

maintained, a task individual agriculturalists cannot bear alone. A great deal of research

has been devoted to the problem of irrigation management and water usage (e.g. Schluter

& Pahl-Wostl, 2007; Janssen, 2007; van Oel, 2009).

In arid northern New Mexico, water is a scarce and precious commodity. A traditional

local system of water management has evolved, which involves landowners collectively

maintaining and managing ditches which distribute water among the properties. This

system of the physical ditches and the maintaining organization together is known as an

acequia, and the landowners who maintain it are called parciantes. Acequias are

especially interesting to researchers because of the developed common property regimes

they require to function.

The water carried by the ditches is a shared resource, and the complex management

system of the acequia has evolved to avoid Hardin’s Tragedy of the Commons with

regard to natural resources in the sense that it prevents the resource from being overused

or under-maintained to the detriment of everyone (Hardin, 1968). Ostrom (1990) has

extensively studied the process of sharing such resources, investigating the structures set

in place to preserve them. In “Governing the Commons”, her book on common pool

resources and human-ecosystem interactions, she suggests a set of characteristics that

define stable communal social mechanisms. These characteristics include the presence of

environment-appropriate rules governing the use of collective goods and the efficacy of

individuals in the system. These rules do exist in the acequia system, although there have

of late been legal battles to define the distinction between owning land and owning water

and how this distinction impacts the right of an individual to participate in the community

decision-making process. Brown and Rivera (2000) in particular highlight how changes

in the social and political environment have lead to tensions between the collective nature

of acequias and private property rights.

Despite the historical strengths of the system, parciantes are increasingly pressured to

convert farmland into residential space. Any effort to protect this traditional form of

agriculture relies on researchers and policy makers developing an understanding how the

different parts of the system interact and how rigorous the system is to perturbation. The

simulation presented here seeks to model land-use in acequia-dependent areas as it is

determined by a combination of physical, economic, and social factors. The goal of this

paper is to construct a tool that will help explore these relationships and their

interdependencies, allowing a researcher or policy-maker to interact with the systems and

understand them in an intuitive fashion. To this end, an agent-based model of the

acequia-irrigated land around the county of Taos, New Mexico, has been constructed.

Roughly 40km2 of the 400km2 of land in the Taos valley is acequia irrigated (Cox &

Ross, 2011). Figure 1 displays a map of some of the tracts of land associated with this

form of agriculture to give a sense of the interplay between and morphology of acequia

tracts and the water system. Local pressure to use farmland for non-agricultural purposes

is mainly the result of in-migration and the building of single-family residences,

condominiums, and mobile homes (Cox & Ross, 2011).

The remainder of this paper is structured as follows. Section 2 outlines the rationale for

creating an agent-based model (ABM) loosely coupled to GIS in order to study acequia-

based agriculture; with this justification, Section 3 describes the model as it is

implemented. Results from this model are discussed in Section 4. Section 5 provides a a

summary of what has been presented and identifies further avenues of research.

2 Background Acequias have been the focus of a great deal of research because of their importance to

agriculture in New Mexico’s otherwise arid environment. Past research has focused upon

many different aspects of their persistence, building toward an understanding of the

social, political, legal, and physical structures which make up this complex environment

(see Cox, 2010; Cox & Ross, 2011 for reviews). To date, no other studies have focused

upon modeling such a system, but previous work highlights the complex nature of the

acequias system and motivates this research.

The simulation presented in this paper utilizes ideas from complexity theory within an

agent-based modeling context. This is particularly appealing in understanding acequias in

the sense that the processes involved in acequia use are not neatly decomposable into

separate subprocesses because of the critical importance of interactions and feedbacks

among them. This interplay between humans and the environment is a feature of many

complex social systems (Epstein & Axtell, 1996). The most important agents in the

system are the parciantes, who are farmers as well as land and water right holders who

utilize traditional forms of irrigation. Parciantes’ ability to grow crops depends upon the

maintenance of local acequias, and so their economic decisions directly shape the

morphology of the water network. Parciantes are also under pressure from developers

who want to convert agricultural land into residential space, which is in high demand

locally (Cox & Ross, 2011). Their choices about whether and when to sell land have long

term ramifications: land is a finite resource and, once converted from rural agricultural to

residential purposes, is difficult to convert back (it is easy to build a house on a flat field,

but more difficult to dig out the foundations of a building and reconnect it to a decayed

water network). Additionally, breaking up the land to use it for residential purposes tends

to subdivide the land, making it difficult to gather up all of the now-residential pieces and

forge them back into a piece of farmland large enough to justify farming again. The cost

of land conversion is therefore high when one is turning residential land into farmland

and quite low when moving in the opposite direction (Cox & Ross, 2011).

The functioning of the physical water network, the actions of parciantes, and the impact

of either of these processes on the other necessitate building an integrated model of the

acequia system. In the model described in Section 2, an economic model of land holders

rests atop the physical water flow model of the acequias themselves; this layering is

motivated by the fact that in the “real world”, land can be subdivided and subsequently

sold, sometimes without water rights to the acequias connected to it (Brown & Rivera,

2000). If the land is sold without water rights, it is impossible for the tenant of the land to

carry out agricultural work.

To capture the complexity of the system, we create an ABM. Agent-based modeling

focuses on representing heterogeneous populations of individuals and their interactions

with their environment or one another which result in emergent phenomena (Epstein &

Axtell, 1996). This approach relates to the notion of generative social science (Epstein,

2007) wherein we can exploit controlled “laboratory” conditions and grow a system from

the bottom up in order to isolate the sources of aggregate phenomena. Such a modeling

technique has been used in many disciplines, ranging from archaeology, economics,

ecology, geography, to political science, to name but a few (Crooks & Castle, 2012).

Agent-based modeling has the notable advantage of being one of the few modeling

techniques that allows researchers to incorporate the true heterogeneity of humans into

models (Axtell, 2000). With respect to this paper, this is to our knowledge the first model

to explore acequias; it builds upon a growing body of literature documenting the use of

ABMs to study agricultural practices (e.g. Parker et al., 2003; Schluter & Pahl-Wostl,

2007; van Oel, 2009). These ABMs have grown from more formal treatment of such

systems using statistical models, equation-based models, system models, expert models,

evolutionary models, cellular models, and hybrid models which explore farming and its

impact on the environment (e.g. Angelsen & Kaimowitz, 1999; Chuvieco, 1993;

Balmann, 1997, Briassoulis, 2000, Maatman et al., 2002). However, many such models

do not focus on human behavior per se. For example, statistical models play down the

role of individual decision making while equation-based models seek static or

equilibrium solutions, which can be problematic because systems tend to be far from such

states (Parker et al., 2003). Researchers have employed cellular automata to simulate

similar socially driven processes (e.g. Hegselmann, 1998; Balmann, 1997) or genetic

algorithms to tackle agricultural land market auction asking prices (Balmann & Happe,

2000). But when heterogeneous human behavior drives a system in constant flux, these

techniques are unable to capture the critical dynamics of human-environmental

interactions.

One of the advantages of using ABMs is that researchers can model processes at a variety

of different spatial and temporal scales, selecting the level of abstraction appropriate to

the question being answered. For example, models of the economic decision-making

process of farmers have been studied across a broad range of scales. Evans et al. (2001)

focused on household decision-making, wherein the agents make annual choices about

labor allocation. Berger (2001) explored how farmers adopt new technology at a regional

scale, and Gotts and Parker (2004) explore the distribution of farm sizes at the national

level. In studying acequias, however, it is not just the behavior of parciantes that interests

us. It is also the competition between different land-uses (e.g. agricultural versus urban),

which results in the development of urban land markets. This competition plays out at the

level of individual agents, necessitating an understanding of land market models from the

agent perspective (e.g. Filatova et al., 2009, Magliocca et al., 2011). In a sense, these

models build upon the classic work of von Thünen (1826) and Alonso (1964). In addition

to the importance of the economic and water network systems, the spatial environment is

critical to the long-term dynamics surrounding acequias. Within agent-based models,

space serves two purposes: it contains the agents and it defines the spatial relationships

between agents, which controls their interactions. By linking ABM and GIS in a model,

agents are situated within actual geographic locations, making their interactions more

representative of the real world (Crooks & Castle, 2012). Such integration has been

applied from the study of micro phenomena ranging from scales as small as pedestrian

movement (e.g. Haklay et al., 2001) to meso-scale issues such as residential segregation

(e.g. Benenson et al., 2002) to more macro scale issues such as urban growth and sprawl

(Xie et al., 2007). The linkage of the two is considered important because the generative

nature of agent-based modeling provides a mechanism to discover new decision making

frameworks, a capacity traditional GIS analysis lacks (Robinson et al., 2007).

By creating an integrated model, we can potentially provide new insights into the spatio-

temporal dynamics of acequias. Agent-based modeling provides us the ability to

incorporate behavior, an explicit spatial environment through GIS, and a basic

hydrological model to simulate water and sedimentation through the system. The use of

integrated models is not new in the geographical sciences (e.g. Engelen et al., 2003; Tang

et al., 2005), however, many of such models do not focus on the land-use decisions of

individual farmers, let alone the purposive impact of those farmers on regional

hydrology. For example Tang et al. (2005) integrate a cellular automata model of urban

growth and a stream flow model to explore the impact of this growth with respect to

increased levels of pollution.

3 The Model The following description is loosely based upon the Grimm et al. (2006) Overview

Design Details protocol, which is advocated in the land-use/cover change community and

the modeling community more generally to highlight the underlying mechanisms of the

designed system. We will first present a brief overview of the model, including its

purpose, its underlying technology, and its parameters with their associated ranges. The

sources of the data are discussed next, followed by a description of the overarching

structure of the objects’ internal structure, interactions, and scheduling. The model and

data are available for download at http://www.css.gmu.edu/acequia.

3.1 Purpose The purpose of the model in the short term is to study the viability of acequia-based

agriculture with regard to either fluctuations or persistent trends in patterns of population

pressure, climate, and cultural valuation. The ultimate goal in developing such a model is

to inform policy work about the sustainability of acequia-based agriculture under

different conditions. By allowing policy makers to compare side-by-side counterfactual

histories, the model can help estimate the effectiveness of different policies across a wide

range of futures.

3.2 Methodology The simulation is a spatially explicit ABM programmed in Java utilizing and extending

the MASON Simulation Toolkit (Luke et al., 2005) and its GeoMason extension

(Sullivan et al., 2010). It consists of a number of modules that capture the physical,

economic, and social processes that impact land-use patterns in the northern New Mexico

area. The model is designed to be a tool for researchers, so it includes a series of overlaid

maps showing various attributes of the spatial environment, graphs which track the

number of Parciantes and compare the number of urbanized and agricultural tiles, and an

interface which allows to user to hide layers of information or modify the parameters of

the environment mid-run. The layers of information displayed include land-use, river

location, acequia location, transportation networks, the locations of tracts of farmland,

urbanization levels, and elevation. The model includes a number of parameters which can

be adjusted to suit the underlying assumptions of the researcher, as presented in Table 1

and discussed further in Section 4.

The model includes a graphical user interface, one configuration of which is displayed in

Figure 2. Clockwise from the top left, the graphical user interface (GUI) features a map

with the option to activate or deactivate any layer of data, the model controller, a panel of

adjustable parameters, and a series of graphs. The graphs summarize the dynamics of

important system statistics over time. Such an interface allows for ease of use in

understanding and debugging the model (Grimm, 2002).

3.3 Data Data utilized within the model comes from the work of Cox (2010) and is supplemented

with GIS information from the United States Geological Survey’s EarthExplorer (2011).

The data represent the county of Taos and its surrounding area. The shapefiles were

processed with ArcGIS into 30m2 raster grid cells because this was the finest grain

resolution at which data was available for all of the necessary layers. The land-use

classification utilized here is that which is described in the work of Homer et al. (2007).

3.4 Objects Acequias are a complex system, and changes in the low-level dynamics associated with

that system make it difficult to understand the macro-trends in local development. In this

simulation, there are four major spatial, temporal, and behavioral processes represented:

the cultivation and sale of crops, the hydrological system, the functioning of a real estate

market, and acequia participation. Water, land, parciantes, and real estate agents are all

simulated to try to understand the interplay of these processes and to capture the turnover

of agricultural land into urbanized, residential space as that turnover is impacted by the

ever-critical access to water. An overview of the relationships between the types of

objects and the attributes of the objects is given in Figure 3, and a flowchart of the

process by which the different objects are scheduled is given in Figure 4. Every iteration

through the flowchart, or “tick”, represents a year in simulation time. A year was selected

because it provided an appropriate granularity of time during which the agents could

interact and make decisions. Simulations are typically run for a period of 50 years, a

number that reflects a reasonable time horizon for the utility of our results.

Water: Climate is abstractly simulated in this context by controlling rainfall and

therefore the amount of water available in the system for use in agriculture. Rainfall is

modeled on an annual scale, so the distribution of rain throughout the year is not

considered. The propagation of water throughout the environment is accomplished by a

network of rivers and acequias. This distinction between rivers and acequias is important

because acequias experience sedimentation at a rapid rate, while rivers typically do not

experience significant sedimentation over a 50 year period. The network represents the

waterways as directed links between the raster cells of the environment. At the beginning

of every year, a user-defined amount of rain is added across the network; the water moves

down the elevation gradient until no further movement is possible. Figure 5A shows the

elevation gradient overlaid with the water network, with the acequias in red. A closer

view of acequias and rivers is shown in Figure 5B. Acequias build up sedimentation –

that is, experience a decay in water system link weight - every year unless they are

maintained. A fraction of the water that flows through the decayed link is lost, in inverse

proportion to the link’s weight. An unmaintained section of acequia can eventually cut

off all ”downstream” nodes from access to hydration (discussed further in Section 4.1).

Land: Within the model land is a passive object, in that it is irrigated by the water

network and cultivated by Parciantes. Parciantes can choose to grow various kinds of

crops on their tracts of land tiles. The income (I) from a tract of land of size (P) on which

is planted a crop that brings in (C) units of money per unit of planted land is given by:

I = C ∗ P (1) The income derived from various crops is user-determined, and a range of crops can be

made available to the Parciantes in any given simulation. In fact, because Parciantes hold

multiple units of land as part of their land tract, it is possible for a Parciante to plant a

different crop on each of his units of land. This functionality would not be possible in a

cellular automata. Figure 1 shows a subset of the tracts of land included in the simulation,

and demonstrates the range in tract size and shape. Land becomes urbanized and unfit for

farming after it is sold. Figure 5C shows the initial pattern of urbanization relative to

acequias and roads, while Figure 5D contextualizes the land-use patterns relative to the

surrounding area.

Parciantes: The Parciante agents represent the individual acequia owners who make

land-use and acequia maintenance choices in the real world. In the context of the

simulation, Parciantes choose whether to maintain their acequias, plant crops, or sell their

land. A flowchart summarizing the choices of Parciantes and the order in which those

choices are made is shown in Figure 6. They have a number of attributes, including a set

of tiles of land (collectively, the tract), a reserve of money, and a “strategy” (discussed at

length below). Different tiles of land can be planted with different crops or even sold off

based on economic need, a capability not often present in land-use or land cover change

models. In the simulation described here, the reserve of money represents agent

resources, and if its value dips below zero the Parciante is forced to sell his land to any

bidder. Money is expended when the agent helps maintain his acequia, a cost burden (B)

which is determined by the length of the acequia (A), the number of Parciantes associated

with a given acequia (N), the number of rights (R) the agent has, and a weighting factor

(W) such that:

B = A ∗ R ∗ W/N (2) In this model, the parameter W is used to capture the cost of acequia-maintenance labor,

and can be lessened to simulate the reception of aid or raised to emulate labor becoming

more expensive. To reflect the importance of cultural heterogeneity and personal

preference in these decisions, Parciante agents are further endowed with a “strategy” that

defines their approach to land-use decisions. One example of such a strategy is the

Traditionalist, who values his land above all else and will hold onto it for as long as his

money holds out. A different strategy, the Follower, leads the Parciante to observe what

his neighbors are doing, and emulate the behavior of the majority. A third implemented

strategy is that of the Prodigal Son, who detests farming and will sell his land as soon as

some minimal price is offered to him. These simple policies represent only a fraction of

the behavioral complexity that Parciante agents could display. Parciante interaction and

influence happen either through the emulation of other Parciante choices, as in the

Follower strategy, or as Parciantes retire from farming and stop maintaining their

acequias, placing greater maintenance burdens on their fellow Parciantes.

Real Estate Agents: The Real Estate Agents represent the rising demand for housing in

the area, and their goal is to buy and develop as much land as possible. These agents are

endowed with a certain budget and randomly contact Parciantes to offer them a sum of

money in exchange for their particular tract of land. The offer prices follow the model

proposed by Filatova et al. (2009) and consist of a budget constraint (Y), a utility

constraint (U), and a final offer price (O) that is based on both the budget and utility. An

agent with budget (B) bidding on a tract with transport cost (T, proportional to the

distance of the tract from the road) has a constraint that he cannot bid more money than

he has, so his budget constraint is his budget less the transport costs. The utility (U) is a

function of the amenity (A - here, the utility of the land is assumed to be equivalent to the

tract size) and the normalized distance of the tract from the economic center (P). The

offer price (O) is calculated relative to the agent’s budget, the utility of the tract, and a

weighting factor (b). This weighting factor is based on the work of Filatova et al. (2009)

and reflects the affordability of housing relative to other goods, for example the cost of

crops. These can be summarized as follows:

Y = B−T (3) U = Aα Pβ (4) O = Y U2 (5)

(b2 + U2) If the Parciante agent accepts the Real Estate Agent’s offering price, the tract of land is

urbanized and the Parciante removed from the simulation. The distribution of Real Estate

Agent budgets is determined by the user and can be modified mid-run. The scheduling of

Real Estate Agents in the simulation is shown in Figure 7.

4 Results Given the richness of this model, only a sample of our results will be presented here. We

have selected a series of case studies that are representative of the capabilities of the

model. For interested readers, an executable of the model along with the source code and

data are available at the project website (http://www.css.gmu.edu/acequia). We do this

for the sake of replication and docking, because if a model cannot be meaningfully

compared to other work its credibility is unverifiable and its ramifications necessarily

proscribed (Axtell et al., 1996). Before we can present the results, however, we turn to

verification and validation of the model.

4.1 Verification and Validation Within this paper we refer to “verification” as the process of ensuring that the

implemented model matches the designed model (North & Macal, 2007). This process

involved checking that the components of the model behave as expected, a feature which

is often taken for granted. Performing this type of verification is sometimes referred to as

testing the “inner validity” of the model (Brown, 2006). The model was built in an

iterative fashion, and we ensured that each of the submodules demonstrates the

appropriate behavior over the space of acceptable inputs, stepping through the code as

advocated by Gilbert and Troitzsch (2005). To test that the water network functioned

correctly, for example, we deactivated all of the Parciantes and allowed the acequias to

go unmaintained for several decades. We then compared this unmaintained environment

with one filled with eternally vigilant Parciantes, and found that the decaying and

maintenance functionalities produced the logical and expected results. Figure 8 compares

the result of these two tests side-by-side, with Figure 8A showing the acequias flowing

freely after 100 years of regular maintenance and Figure 8B showing the unmaintained

tracts carrying substantially less flow after the same amount of time.

To validate the assumption that the included parameters had reasonable impacts on the

model outcome, a parameter sweep was carried out. Each input parameter was varied to

explore its effect on the simulation outcome, and especially on final land-use patterns.

Varying each of the parameters did produce a statistically significant and reasonable

impact on the number of surviving Parciantes at the end of a 50-year period. As an

example, we present here two such comparisons, varying either the amount of rainfall or

the number of real estate agents in the system. The results of the simulation are presented

here in terms of the number of agricultural tiles that were ultimately urbanized, the total

number of Parciantes who sold their land, and the total number of acequias which were

no longer being cared for by the end of the simulation. Each of the scenarios described

was run 30 times, and the reported statistics represent the averages of the measured

variables over all of the runs. In each of these verification efforts, 80% of the Parciantes

were assigned to be “Followers” while the remaining population was evenly divided

between Prodigal Sons and Traditionalists.

4.1.1 Rainfall In the case of variation of amount of rainfall, the “Drought” scenario corresponds to a

rainfall of 1 unit annually while the “Flood” scenario indicates rainfall of 50. The base

case used as a point of comparison here is the “Default” scenario, which has a rainfall of

15 units. As seen in Table 2, the effects of varying the rainfall are noticeable. In the

default scenario, 506.1 tiles of agricultural land were lost by Parciantes over the course of

the simulation, a number massively less that that associated with the drought scenario and

noticeably greater than that associated with flooding. The variation in the number of

Parciantes lost is informative in light of this fact, as we see roughly equivalent numbers

of farmers lost in the Default and Drought scenarios while the Flood scenario produces

much higher rates of retention. Because the number and budgets of Real Estate Agents

are constant, the loss of Parciantes is capped by the limited demand for land. However,

the Real Estate Agents can afford to buy bigger tracts of land as Parciantes are squeezed

out by low crop yields. We can compare these with the Flood scenario, in which

Parciantes can grow crops without being thwarted by the weather and fewer farmers

either choose or are forced to leave.

4.1.2 Real Estate Agents The results of varying the number of Real Estate Agents are summarized in Table 3. The

Default scenario with 10 Real Estate Agents is compared to simulations with either 0 or

100 Real Estate Agents. Again, the impact of the variation is noticeable and reasonable:

when demand increases, more Parciantes’ land is “consumed”. Likewise, when demand

decreases to the point of not existing, no land is consumed. We can use these results to

further verify the correct functioning of the model. Even when demand is completely

absent and no land is being urbanized, some acequias are lost. This is due to the fact that

some acequias were not associated with any Parciantes at the beginning of the simulation

because either the land had been urbanized before the simulation began or the acequias

are not near any land currently being used for agricultural work. However, as the number

of Real Estate Agents increases, more Parciantes who are willing to sell their land

randomly encounter the Real Estate Agents and sell their property, resulting in the loss of

many more acequias.

4.1.3 Further Analysis More detailed analysis of a full parameter sweep is available on the project website,

including information about varying Real Estate Agents’ budgets, the hydration cutoff,

and the crop prices, which we omit here for reasons of space. While the end goal of this

model is that it be used in a predictive capacity, information about historical acequia

channel locations and land-use within the study and detailed empirical data on land

transitions was largely absent. As a result, the model was not validated in the traditional

manner against real-world data (see Balci, 1996; Crooks et al., 2008), and is better suited

for exploratory purposes at present.

4.2 Scenarios

A panel of scenarios is presented here for comparison. Because the end goal of the model

is to support policy work, the physical parameters of the world such as rainfall and the

sediment buildup rate are held constant while the social parameters are varied. The

economic conditions of the world are also held constant, but two critical parameters of

the simulation are varied: the attitudes of the agents and the cost of acequia maintenance.

By investigating how these features of the world impact the final outcome of the model,

we can better understand how educational programs that increase cultural valuation of

acequias or tax cuts which lessen the financial burden on individual farmers might

influence the long-term development of the acequia system. Here, we consider the results

of nine scenarios in which the price ranges from 1 to 5 to 15 units of money per acequia

right and the distribution of strategies varies such that 80% of Parciantes are

Traditionalists, Followers, or Prodigal Sons with the remainder being equally split

between the other two strategies. As in the case of the verification studies, each of the

scenarios was run 30 times and the statistics presented represent the average of the

outcomes. Other than the parameters explicitly being varied, the variables are set to

default values as presented in Table 1.

The results of the scenarios are presented in Table 4. Considering the results in terms of

price, a clear (and expected) trend exists. As the price increases, more agricultural land is

lost to urbanization, more Parciantes sell their farms, and more acequias go defunct. The

difference between prices of 1 and 5 is greater than the difference between 5 and 15 in

every category regardless of Parciante attitude, reflecting nonlinearity in the relationship

between the price and the agent’s decisions.

Within a given price, the different distributions of attitudes vary in some interesting

ways. When the price was at its highest, the only distinction was in the amount of land

urbanized under the scenario when Traditionalists dominated the landscape. Apparently,

Traditionalist big landowners were less willing to sell their land and lessened the overall

amount of land that was ultimately urbanized. Interestingly, when prices were lower,

Follower-heavy environments saw higher rates of land loss than even Prodigal-heavy

scenarios. Overall, however, the results are much more strongly influenced by price than

by Parciante attitude. This is an important conclusion from the standpoint of

policymakers and community members, as it suggests that it may be less effective to

educate than it is to contribute.

The examples presented here show that the acequia system is sensitive to variations in the

cultural valuations of its members, and that changing the cost of acequia maintenance has

a significant impact on how viable this traditional form of farming is as a lifestyle. The

spatial externalities associated with one Parciante’s decision to sell his land are captured

and transmitted by the acequia organizations, a system feedback that has implications for

farmers downstream. These examples reflect the importance of incorporating not only the

physical or market forces of the acequia system but also the social influences. The

sensitivity studies presented in Section 4.1 indicate how important environmental factors

are to the development of the system over time, and yet in otherwise identical worlds,

agent attitude and financial assistance produce strikingly different outcomes. The

interdependencies and feedbacks of this system would be difficult to achieve with purely

statistical or geospatial models.

5 Conclusion The model presented here uses empirical GIS data to build a realistic model of a complex

socio-physical system. By representing the interacting modules of physical, economic,

and social processes, the interconnected nature of the acequia system is more precisely

represented. The results highlight the importance of this unified approach; the scenarios

presented above show that largely similar environments can result in very different trends

of land-use and development in terms of the number of urbanized tiles or functioning

acequias at the end of 50 years. The use of an agent-based model to understand the

interaction of the different stakeholders and the environment from the bottom up was

crucially important for representing interaction among the agents, social influence, and

the way individual choices can impact the environment and thus propagate forward to

impact others.

As with all models, the purpose of this simulation is to consider a selection of the

different ways the system might evolve. We study the ways in which these different

futures may come about, in order to better understand the interplay of dynamics which

might make certain efforts on the part of individuals, communities, or government

anywhere from highly effective to completely meaningless. We would argue that this is

the function of models, to inform debate by formalizing ideas (Batty, 2012). Moreover,

Epstein (2008) discusses various reasons for building models independent of prediction.

These include explanation, the illumination of core uncertainties, and education. We

believe our model is useful in these varying capacities, as it forces researchers to consider

the systems being modeled in formal, explicit terms.

In the future we hope to validate the model further by comparing the land-use patterns

projected by the model with the real land-use patterns of the area derived from land cover

data collected in 2008. It is the authors’ hope that this model will be used by researchers

seeking to answer questions about the rigorousness of this community resource

management system, its specific strengths and critical weaknesses, and how to protect

this traditional way of life. The work also potentially lays the foundation for further

investigations into the relationship between climate change and acequias, and could build

upon previous studies looking at addressing everything from seepage and groundwater

(e.g. Fernald et al., 2007) to the interactions of acequias and aquifers (e.g. Fernald et al.,

2010) to water flow as a result of rising temperatures in the mountain ranges surrounding

the area (Harding, 2010). While the model at this time does not allow farmers to sell or

rent portions of their land, it would be easy to add this capability, giving researchers an

even more detailed understanding of the dynamics of micro-scale land-use change. These

changes occur at a lower level than most forms of modeling can represent, yet their

impact on the unit of analysis is crucial. The nuance of an individual farmer’s bankruptcy

influencing his neighbors and perhaps touching off a local exodus is a subtlety that

cannot be captured by microsimulation or system dynamics models (Gilbert & Troitzsch,

2005). Even neighboring farmers are influenced by an individual parciante’s choice to

rent land for residential use, making the importance of capturing this interaction even

more critical. Through a nuanced understanding of the system and the ways it might

evolve over time, it may yet be possible to prevent a tragedy of the commons.

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Figure 1: A map portraying a sample of individual tracts of land held by acequia parciantes in

part of Taos, New Mexico, overlaid with rivers and acequias.

Figure 2: A sample screenshot of the graphical user interface.

Figure 3: The structured hierarchy of modeled entities in the simulation, including methods and the parameters which influence their execution.

Figure 4: A flowchart of the model steps.

Figure 5: GIS data for the study area including A) elevation, rivers, and acequias, B) a closer view of part of A), with box highlighting area of interest, C) the relationship between acequias, roads, and urban areas, and D) land use patterns.

Figure 6: A flowchart of the Parciante subroutine.

Figure 7: A flowchart of the Real Estate Agent subroutine.

Figure 8: The water network, after 100 years of regular maintenance (A) and after 100 years of no maintenance (B). The darker the line, the more clear the segment is of sedimentation;

only unmaintained acequias are impacted by sedimentation in this model, and appear in lighter shades.

Type Parameter Description Range Default Parciante Costs

acequiaCostWeight the cost of maintaining an acequia right over the unit of time

[0, 100] units of money per right

5

cropPrices the amount of income generated by a unit of a given kind of crop

[0,1000] units of money

10

Acequia Processes rainfallThisYear annual rainfall [0,100] 15

acequiaDecayRate rate at which unmaintained acequia capacity degrades annually

[0,1.0] 0.99

hydrationCutoff minimum amount of waterflow for land to be ”irrigated”

[0, 100] units of water per tick

20

Real Estate Costs weightUtility importance of utility [0,1.0] 0.5

weightProximity importance of proximity to offering price

[0,1.0] 0.5

budgetStdDev std dev in real estate

agent budgets [0, 25] 10

budgetThisYear mean of real estate budgets

[0,1000] units of money

100

numRealEstateAgents number of real

estate agents [0,1000] 10

Table 1: Parameters of the model.

Loss of

Land (tiles) Loss of

Parciantes Loss in

Acequias Default - 15 506.1 467.8 903.4 Drought - 1 15965.6 467.4 903.5 Flood - 50 89.0 150.0 869.1

Table 2: A comparison of average results of simulation run with varying levels of rainfall.

Loss of

Land (tiles) Loss of

Parciantes Loss in

Acequias Default - 10 506.1 467.8 903.4 0 Realtors 0.0 0.0 849.0 100 Realtors 2517.0 2342.0 1507.0

Table 3: A comparison of average results of simulation run with varying numbers of Real Estate

Agents.

Scenario Price = 1

Loss of Land (tiles)

Loss of Parciantes

Loss in Acequias

Traditionalists 403.1 327.3 889.0 Followers 411. 7 327.8 888.7 Prodigal 406.3 324.3 888.1 Price = 5 Traditionalists 490.8 467.6 901.8 Followers 515.3 468.0 903.1 Prodigal 493.0 468.7 902.1 Price = 15 Traditionalists 516.5 491.6 905.9 Followers 544.1 491.8 905.6 Prodigal 544.5 491.3 904.4

Table 4: A comparison of the results of the nine scenarios with varying acequia maintenance costs and

Parciante attitude distributions. Here, the label “Traditionalist” entails that 80% of the Parciantes were Traditionalists, 10% were Followers, and 10% were Prodigals, and so forth.