Settlement Dynamics and Hierarchy from Agent Decision-Making: a Method Derived from Entropy Maximization

Mark Altaweel 0 ) Institute of Archaeology, University College London , 31-34 Gordon Square, London WC1H 0PY, UK This paper presents an agent-based complex system simulation of settlement structure change using methods derived from entropy maximization modeling. The approach is applied to model the movement of people and goods in urban settings to study how settlement size hierarchy develops. While entropy maximization is well known for assessing settlement structure change over different spatiotemporal settings, approaches have rarely attempted to develop and apply this methodology to understand how individual and household decisions may affect settlement size distributions. A new method developed in this paper allows individual decision-makers to chose where to settle based on social-environmental factors, evaluate settlements based on geography and relative benefits, while retaining concepts derived from entropy maximization with settlement size affected by movement ability and site attractiveness feedbacks. To demonstrate the applicability of the theoretical and methodological approach, case study settlement patterns from the Middle Bronze (MBA) and Iron Ages (IA) in the Iraqi North Jazirah Survey (NJS) are used. Results indicate clear differences in settlement factors and household choices in simulations that lead to settlement size hierarchies comparable to the two evaluated periods. Conflict and socio-political cohesion, both their presence and absence, are suggested to have major roles in affecting the observed settlement hierarchy. More broadly, the model is made applicable for different empirically based settings, while being generalized to incorporate data uncertainty, making the model useful for understanding urbanism from top-down and bottom-up perspectives. - Spatial modeling of settlement rank-size hierarchies has once again become a major topic of discussion in archaeology (e.g., see Bevan and Wilson 2013; Crema 2013; Davies et al. 2014), with equation- and agent-based models (ABMs) being the most common types of approaches. This paper proposes to combine methodological contributions from ABMs and entropy maximization as a way to create a simple and a transferable model that can potentially address a variety of empirical cases derived from archaeological survey. While simulation models have enabled the actualization of processes that underline key theoretical assumptions about urbanization and settlement dynamics, relatively few case studies have integrated comprehensive and relatively intensive archaeological survey that can inform us how well model and theoretical design fit observations from the field. Such models should provide a theoretical framework to evaluate case studies and enable a quantitative-based comparison between periods to allow one to determine what underlying reasons could lead to observed rank-size hierarchies. Various publications have applied forms of spatial interaction in assessing settlement hierarchy or site interactions (Evans 1982; Knappett et al. 2008). Spatial entropy maximizing models (Harris and Wilson 1978; Wilson 2012) have been developed to address how settlement interaction affects urban expansion or contraction. While these models have been largely applied to modern and economic settings, recent work has also applied them to past settlement systems (Bevan and Wilson 2013; Davies et al. 2014). The advantage of these methods is that they are general and accommodate a variety of case studies, including archaeological survey data at different spatial scales, and do not have complex data requirements, making them useful for cases where uncertainty prevents the understanding of specific processes that lead to observed settlement patterns. In summary, such entropy models allow the incorporation of spatial factors and feedback effects of geography, transport, and site attractiveness over a given time that enable settlement patterns to develop across a study region. Nevertheless, classical entropy maximization models do not employ individual or agent decisionmaking, a key factor if we are to know how theoretical complexity and complex systems from basic social units affect urban development (Adams 2001; Bentley and Maschner 2003). This paper explores the integration of individual or agent-based methods with entropy maximization methods in understanding settlement change and settlement size hierarchy within a given region whereby households are utilized as agents. The goal of this paper is to present a simulation model that explores how the spatial setting and factors that affect individual choice result in settlement transformations and rank-size hierarchies observed in the archaeological record, while also accounting for sitespecific and other regional factors that could affect settlement dynamics. Initially, background information focused on the case study is given. Then the applied methodology is introduced and discussed. Several scenarios demonstrating the models applicability are conducted in order to demonstrate how the model addresses the goal presented. The scenarios focus on how well model results fit the settlement size distribution, rank-size hierarchy, and account for uncertainty in settlement occupation while addressing these scenarios. Results from these scenarios are discussed, particularly how they provide insight for the research goal. The conclusion discusses broader benefits and future applications of the advanced method. The North Jazirah Survey (NJS; Fig. 1; Wilkinson and Tucker 1995) provides the test 2 case in which the applied model will be demonstrated. Because this region (~530 km ) has been well surveyed and a large portion of sites from various periods recovered, it serves as a useful test case. Furthermore, the area provides very different types of settlement patterns in periods studied, which could then be explored further to see what factors could have contributed to these observations. The first set of sites, 43 sites with a total area of nearly 226 ha and dominated by the site of Tell al-Hawa (29 % of the total area; site 1 in Fig. 1), derive from the Middle Bronze Age (MBA; 20001600 BC). At this time, societies across northern Mesopotamia began to develop large urban spaces and smaller settlements more intensively, while politically there was fragmentation with small states across northern Mesopotamia for much of the period (Guichard 2009). Many sites are likely to have been settled for most of this period, with excavations having indicated long-term occupation (Wilkinson and Tucker 1995; Altaweel 2006, 2007). The settlement rank-size distribution for the MBA can be given in a natural log graph (Fig. 2a), with Table 1 providing an indication of the top 10 sites for each period. While the MBA represents a period of political fragmentation whereby there was a range of major and minor settlements, the Iron Age (IA; 1200600 BC) was a time of intensive and evenly dispersed small settleme (...truncated)