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Agent-Based Modeling

Agent-based modeling is distinct from statistical analysis and interpretation of data, equation-based analytical approaches to discovery, and numerical modeling of system dynamics. In analytical approaches, formulas are used that represent changes in system states. An example is Mathusian population change through time: Pt = P0ert, where P0 is an initial population size, r is a growth rate, t is time, and Pt is the population at that time (see Turchin 2001 for a more complete treatment). An evident feature of such an approach is that the entity being modeled is the entire population. The same is true for numerical modeling of systems (e.g., Stella is a popular example of software used in such work; IEEE systems, Lebanon, New Hampshire, US), although they adopt a simulation approach. Populations known as stocks are modified at rates set by model designers, and during simulations portions of populations flow into other stocks. Analytical approaches take a top-down approach to discovery, with the structure of the population represented by hypotheses the analyst has incorporated into equations (Grimm 1999).

Agent-based modeling uses a bottom-up approach to discovery (Grimm 1999) that recognizes that individuals are the basic units of decision making, and determine (at least in part) population responses when aggregated. Simulations are composed of autonomous agents that interact with other agents and the environment according to rules (e.g., Billari et al. 2006). Simulations are made, allowing agents to interact, and emergent responses are sought (i.e., formally, an aggregate response not obvious from the constituent parts; less formally, something that is unforeseen, unpredictable, and interesting). Rather than employing deductive or inductive approaches, an abductive approach is used to explore reasonable hypotheses that may explain a suite of observations (e.g., Griffin 2006; Lorenz 2009). These ideas give context to Epstein's quote describing generative social science and the usefulness of agent-based simulation, “if you didn't grow it, you didn't explain its emergence” (Epstein 1999:43). Being able to grow a pattern of interest and visualize the interactions of agents on a computer screen provides supporting evidence that the rules of interaction embedded in the model are good candidates to represent real interactions.

The rules describing interactions are hypotheses, and analysts use methods such as scenario analyses, a structured form of in silico experimentation (Peck 2004) in discovery. Different rules may be enabled or disabled in simulations representing different hypotheses of interaction, and the emergent patterns compared to observed patterns to judge the suitability of the competing hypotheses (Grimm and Railback 2006). Alternatively, scenarios may be used to address “what if” questions, where rules on assessed simulation models are varied to represent future conditions, different responses, or changes in policy or management (e.g., Boone et al. 2011).

The bottom-up approach of ABM that focuses on simulations of individuals has several benefits and costs when compared to top-down analytical approaches. (The following dichotomies refer to typical methods, and advanced methods can blur distinctions between the approaches.) Mathematical models such as the Mathusian population equation given yield precise solutions very quickly, and can be efficiently implemented, often with little data. In contrast, ABM models include stochastic components and the simulation of time passing that may slow the generation of results, and coding the models may be rapid or take significant time. Some ABMs use a great deal of data, but it is a misconception that the method requires more data than analytical approaches; some well-known and influential models require just one or a few parameters, such as Schelling's (1971) model of dynamic segregation, Axelrod's (1984) competitions using Prisoner's Dilemma, and Reynolds (1987) modeling of flocking using Boids, and all that it has spawned (see Macy and Willer 2002 for a review). Analytical models are highly stylized, to prevent problems from becoming mathematically intractable, whereas ABMs may be highly stylized or realistic. In contrast to the single scale of population models, results from ABM analyses are inherently multi-scale, in that analyses may be reported at the scale of agents, or any aggregate of interest. For example, some grand simulation of individuals across a broad region may report results for those individuals, summaries of households composed of those individuals, summarized by village, or for the entire population included in the simulation. The realistic approach used in many ABMs allows for a variety of scenarios to be addressed.

The top-down, population-based analytical approach implies that population members are identical and static. Treating each individual as identical can be a severe limitation in analytical approaches. Consider the simple biological example of forest stand growth from seedlings. Treating each seedling the same as the rest implies that through time the seedlings will mature at the same pace and a uniform forest will grow. In practice this is not the case. Variations between individuals cause some trees to shade others, and to grow more rapidly, yielding a more realistic result of a forest with diverse size classes. In ABM, variation between individuals is easily incorporated, and interactions between individuals with different initial attributes, such as body masses or livestock holdings, can yield more realistic results (Huston et al. 1988). This is why some social scientists have embraced the ABM approach, as some of the variability seen in the real world can be captured in these types of models. Examples where variation between individuals may be important are numerous in social settings, such as in economics, land use and tenure, altruism, and risk analyses. Here we have focused upon variation intrinsic to individuals as they are initialized, but in an ABM, agents that may be initialized identically each has its own experiences that yields differences in individuals, making results path dependent.

In contrast to static members of populations in analytical approaches, ABM can represent adaptation, learning, and evolution in agents. This makes ABM well suited to represent the complex and adaptive coupled systems that are a focus of current sustainability research. The rules used to control decision making may reflect adaptation. For example, in our work livestock owners may move their animals to more distant areas in drought conditions. Local interactions between agents make learning from neighbors straightforward, and imparting agents with different forms of memory is possible. Given a group of neighbors contacted by a given agent, that agent may ask if any member of the group is doing better in some objective way than the agent, and if so, adopt the practices of the neighbor. For example, a farmer in a valley may observe harvests by her neighbors, and if one of their harvests exceeds her own, adopt those cropping practices (see the example below of Lansing and Kremer 1993). Genetic algorithms, evolutionary programming, and other evolutionary computation techniques evolve adaptations using a framework adopted from biology. Agents with a given set of attributes perform better on some objective function than others in the group, and produce offspring that have related but mutated sets of attributes. Through selection, agents evolve to be well adapted to local conditions. Biological examples include Boone et al. (2006) and Boone (2010). Human evolutionary examples are given in Barton et al. (2011) and Barton and Riel-Salvatore (2012).

An important use of ABMs is in communication with audiences. Imagine a traffic modeler explaining to a lay audience about the number of vehicles that may be supported on a given road. The presenter may show a formula that describes maximum traffic flow, q* (from Malone et al. 2001) : q* =(β+ 2γ1/2 L1/2)-1, where β is the reaction time of drivers, γ is the reciprocal of twice the maximum average deceleration of a following vehicle, and L is vehicle length, although the details are not relevant here.

Alternatively, the presenter may show output from an ABM, where vehicles are moving along the road in reasonable ways, jams develop and clear, and vehicle densities may be reported directly (Fig. 9.1). Efforts have different purposes, of course, but in general, audiences identify with the visual nature of ABM output. People identify with agents in models and readily anthropomorphize; they themselves are individuals experienced in interactions with other individuals and environments. Perhaps most important is the ability of agent-based modeling to integrate disciplines (Axelrod 2006). Almost by its nature, simulating complex system attributes involves interdisciplinary teams. Such a team may include a hydrologist, ecologists specializing in primary and secondary production, anthropologists and an economist, plus programmers and other specialists in technology. As the team creates rules that define interactions between the agents and the ways they interact with the environment, team members must break down their high level understanding of the causes of behaviors into something that may be represented logically. The rules must be conveyed to the technical team members with sufficient mutual understanding to allow them to be represented in computer code. The team must develop a common language and understanding. But beyond that, “[t]he creation of a model forces the articulation of any number of individual design decisions, and thoughtfully done, each can be a starting point for new understanding.” (Johnston et al. 2007:82). Identifying commonalities between disciplines is particularly rewarding (Axelrod 2006). Some bodies of theory are applicable to diverse fields, such as theories that touch upon acquiring resources (e.g., with ties to economics, anthropology, animal foraging), altruism and cooperation (e.g., ethology, interpersonal relationships), issues of carrying capacity (e.g., grazers, hunters, members in markets), Tragedy of the Commons (Hardin 1968) or lack thereof (e.g., grazing dynamics, ocean fisheries management, group dynamics). Discussing these commonalities can strengthen a team. In summary, agent-based modeling is a useful approach when: interactions between individuals and the environment are a focus; a model is complex with many interactions; non-linear relationships are important; variability between individuals

Fig. 9.1 Microsimulation of traffic flow, an instance of an online applet simulation tool by M. Treiber (2011). The work is introduced in Treiber and Kesting (2010)

is of interest; randomness and path dependency are relevant; restrictive assumptions are to be minimized; and visualization and understanding by stakeholders is an objective. We have provided a high-level overview of the utility of agent-based modeling. Some aspects of constructing agent-based models have been cited, but more detailed reviews of techniques (e.g., Kraus 1997; Gilbert and Terna 2000; Berry et al. 2002; Bonabeau 2002; Ramanath and Gilbert 2004; Goldstone and Janssen 2005; Grimm et al. 2005; Janssen and Ostrom 2006; Aumann 2007; Railsback and Grimm 2011), tools (Wilensky 2001; Gilbert and Bankes 2002; Railsback et al. 2006; Nikolai and Gregory 2009; Railsback and Grimm 2011), assessment pathways, a critically important aspect of simulation (Grimm et al. 2005; Wilensky and Rand 2007; Gilbert 2008), and comments (Bankes 2002; Richiardi et al. 2006) are available to those constructing models. Example models and other resources are available from the Network for Computational Modeling for SocioEcological Science (CoMSES Net, at openabm.org/).

 
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