Simple or complicated agent-based models? A complicated issue
Environmental Modelling & Software
Agent-based models (ABMs) are increasingly recognized as valuable tools in modelling humanenvironmental systems, but challenges and critics remain. One pressing challenge in the era of "Big Data" and given the flexibility of representation afforded by ABMs, is identifying the appropriate level of complicatedness in model structure for representing and investigating complex real-world systems. In this paper, we differentiate the concepts of complexity (model behaviour) and complicatedness (model
... structure), and illustrate the non-linear relationship between them. We then systematically evaluate the trade-offs between simple (often theoretical) models and complicated (often empirically-grounded) models. We propose using pattern-oriented modelling, stepwise approaches, and modular design to guide modellers in reaching an appropriate level of model complicatedness. While ABMs should be constructed as simple as possible but as complicated as necessary to address the predefined research questions, we also warn modellers of the pitfalls and risks of building "mid-level" models mixing stylized and empirical components. Agent-based models (ABMs) have become a well-established approach for studying complex humanenvironmental systems, such as land-use systems, by explicitly modelling decision-making and dynamic interactions of individuated actors (An, 2012; Filatova et al., 2013; Matthews et al., 2007; O'Sullivan et al., 2015; Parker et al., 2003) . ABMs allow modellers to explicitly incorporate feedbacks between human and environmental systems and to investigate emergent patterns at the macro level in time and space due to interactions at lower levels of organization (Batty, 2007). As a result, ABMs continue to gain popularity among modellers. Part of the success of ABMs stems from their ability to produce emergent system dynamics from often surprisingly simple rules specified at the individual level. The most popular and highly-cited agent based models are rather simple, mainly because they aim at delivering important insights on possible explanations for general patterns (Parker et al., 2003) . A famous example is the segregation model by Schelling (1969) , based on a simple rule specifying where and under what condition individuals relocate. The model shows how highly segregated patterns of societal groups can result from surprisingly weak aversion of individuals (i.e., relatively high tolerance to another group). Most early ABMs were stylized models to represent general dynamics in, for example, economic systems (). Often simple theoretical assumptions were made to model agents, partially due to incomplete knowledge of individuals' interactions or underlying decision mechanisms, but also because of limited data availability at the individual level. According to Parker et al. (2003) , such simple models fall into the category of so-called "Picasso"models-stylized models with a high level of abstraction used to test general principles and ideally yielding generalizable results. The simplicity of rules and a lack of empirical support mean simple ABMs are often labelled "toy" models, perceived to be suitable only for "proof-of-concept" purposes (Crooks et al., 2008; Janssen and Ostrom, 2006) . In contrast, so-called "photograph" models (Parker et al. 2003 ) depend on empirical data to provide high levels of detail (Balbi et al., 2013). Such models have gained great popularity with increasing numbers of ABMs of land use/land cover change designed and implemented for particular case studies (e.g., O'Sullivan et al. (2012); Piorr et al. (2009) ). These empirical ABMs tend to be more complicated and usually demand large amounts of data, defining detailed functions rather than using heuristic rules. The success of empirical ABMs proves that ABMs are not only for "proof-of-concept", but can also be useful in addressing real-world problems. The emergence of empirical ABMs is partially driven by an increasing demand of stakeholders and decision-makers to provide support for understanding the potential implications of decisions in Published as: http://dx.