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A multidirectional model for studying mobility affordance of past landscapes

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This paper presents an approach to modeling human mobility across regional landscapes that considers all possible directions of travel in order to generate a continuous surface of movement probability. The approach improves upon models of human
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  Contents lists available at ScienceDirect Journal of Archaeological Science: Reports  journal homepage: www.elsevier.com/locate/jasrep A multidirectional model for studying mobility a ff  ordance of past landscapes Lauren E. Kohut Tougaloo College, 500 West County Line Road, Tougaloo, MS 39174, USA A R T I C L E I N F O  Keywords: MobilityMovementForti fi cationGISA ff  ordanceLate Intermediate PeriodPeru A B S T R A C T This paper presents an approach to modeling human mobility across regional landscapes that considers allpossible directions of travel in order to generate a continuous surface of movement probability. The approachimproves upon models of human movement that rely on calculating travel costs between discrete points on thelandscape by providing a way to examine how landscape features shape the potential for movement. I show howthis method can be used to examine questions of mobility a ff  ordance, and the consequences for understandinghow humans experienced past landscapes. To demonstrate the usefulness of this approach, I apply the metho-dology to examine the use of hilltop forti fi cations for controlling mobility during the Late Intermediate Period(1000 – 1450CE) in the Colca Valley of the southern Peruvian highlands. 1. Introduction Studying prehistoric movement poses particular challenges for re-searchers. In some cases, roads and major passes may be historicallydocumented or still be visible on the landscape, but such formalizedroutes are rare and generally limited to long-term exchange routes oradministrative road networks (e.g. Chacaltana et al., 2017; Ur, 2003). Most paths were never formalized and their ephemeral traces are rarelypreserved in the archaeological record. Geospatial modeling has be-come an important strategy for studying mobility in contexts wherepaths are not preserved (e.g. Beaudry and Parno, 2013; Howey, 2007; Howey, 2011; Leary, 2014; Llobera et al., 2011; ten Bruggencate et al., 2016). Most approaches have focused on modeling optimal, or least-cost, paths between known points on the landscape (e.g. Contreras,2011; Gustas and Supernant, 2017; Howey, 2007; White and Barber, 2012). However, movement is a dynamic process shaped not only bythe speci fi c srcin and destination of travel, but also by changes in thephysical and political landscape; factors which are not easily capturedby least-cost paths (Howey, 2011; Howey and Brouwer Burg, 2017). Archaeologists often lack knowledge of the precise srcins or destina-tions of travelers, or may need to consider many possible points of in-terest. Environmental conditions — such as rain, snow, or drought — mayrender even well-traveled paths unusable. Changes in political alli-ances, exchange partners, or con fl ict can also shape decisions abouttravel in unpredictable ways.Even in the face of many unknown factors that in fl uence the par-ticular path an individual chooses to travel; all paths are never equallylikely. Regardless of srcin or destination, the landscape shapes possi-bilities for travel in important ways — open water, mountain slopes,marshes may provide barriers to travel, while open plains, mountainpasses, and limited ground cover may facilitate it. Thus, we can con-ceive of the landscape as providing a range of mobility a ff  ordance or adiversity of material properties that, when encountered by an agent,provide opportunities for and limitations to travel that make certainpaths more likely than others (Gillings, 2012; Llobera, 1996; Wernke et al., 2017). A focus on mobility a ff  ordance highlights the need to shifthow we approach geospatial analysis of mobility; moving away frommodeling travel between discrete points on the landscape, toward whatHowey and Bouwer Burg have termed  total landscape geospatial mod-eling  , to better re fl ect the  “ potentialities for cultural processes inheringacross the entirety of the landscape ”  (2017: 4).This paper presents an approach to modeling mobility a ff  ordanceusing Circuitscape (McRae et al., 2008), a program that integrates cir-cuit theory and graph-theory to model landscape connectedness. Theapproach outlined in this paper makes two signi fi cant contributions tothe application of Circuitscape to modeling human mobility. First, Ibuild on a method of omnidirectional circuit analysis developed byAnderson, Pelletier and colleagues (Anderson et al., 2014; Anderson et al., 2012; Pelletier et al., 2014) and advocated for by Howey and Brouwer Burg (2017) that eliminates the need for de fi ning travel srcinand destination. Second, I integrate the anisotropic costs of slope due tothe direction of travel to develop a methodology applicable to the studyof human mobility. The result is a regional raster representing theoverall probability of travel (mobility a ff  ordance) regardless of direc-tion of travel that has broad applicability to the study of mobility in thearchaeological past. https://doi.org/10.1016/j.jasrep.2018.02.031Received 21 November 2017; Received in revised form 25 February 2018; Accepted 25 February 2018  E-mail address:  lkohut@tougaloo.edu. Journal of Archaeological Science: Reports 19 (2018) 239–2472352-409X/ © 2018 Elsevier Ltd. All rights reserved.    2. Resistance, current and mobility a ff  ordance This paper uses  Circuitscape  (McRae et al., 2008), an open sourcetoolbox containing a bundle of python scripts run through ESRI ArcMap10.4. The program integrates circuit theory, network theory and graphtheory to analyze regional landscape connectivity (McRae, 2006;McRae et al., 2008). The program was initially applied to landscapeecology and conservation, but has also been e ff  ective for modeling gene fl ow (McRae and Beier, 2007), disease transmission (Barton et al., 2010), and wild fi re spread (Gray and Dickson, 2015). In archaeology,Howey (2011) uses Circuitscape to model travel between monuments innorthern Michigan. In most applications, Circuitscape is used to modelmovement between known regions of interest, providing an alternativeto least-cost path analysis. Here, I provide only a brief overview of howthe program works before discussing the modi fi ed approach developedin this paper. For a thorough discussion of how Circuitscape comparesto least-cost path analysis in studying human mobility, see Howey(2011).  2.1. Overview of Circuitscape Circuitscape conceptualizes the landscape as a raster in which eachcell represents the relative resistance (travel cost) to traverse the cell(McRae et al., 2008). As with other mobility analyses, a variety of costscan be used to generate the resistance raster, including slope, vegeta-tion cover, and cultural features. Barriers can also be incorporated intothe resistance raster to prevent travel through features such as openwater or architecture. Origins and destinations of travel are representedas focal nodes, and electrical current is injected into the srcin (sourcenode) where it travels across the resistance raster to the destination(ground node). The resistance raster is transformed into a series of gridnodes connected by edges, and current travels from each grid node toall others as it moves from the source to the ground. The amount of current that passes through each grid node is determined by both theresistance of the node and the availability of other nodes.The analysis produces a current raster, where the strength of thecurrent of any given cell is interpreted as the likelihood that a travelerwill traverse the cell on its way from the srcin to the source. Areas of low resistance are more conductive, and thus have greater mobilitypotential. Similarly, areas of high resistance are less conductive andhave lower mobility potential. Additionally, large areas of similar re-sistance have greater potential for alternate paths, and this is re fl ectedin more di ff  use current. By contrast, current is concentrated into morecircumscribed corridors in areas where low resistance cells are adjacentto high resistance cells.Circuitscape does not generate the globally-optimal path betweentwo points (as produced by a least-cost path analysis); instead, it useslocally-optimal paths. Speci fi cally, as the current  fl ows through theraster, it continually seeks the path of least resistance based on the costassociated with each neighboring cell. In this way, the local landscapeexerts greater in fl uence on the possibilities of movement, which makesCircuitscape ideal for examining mobility in contexts where path opti-mization cannot be assumed — for example, in cases where individualsmay be traversing unfamiliar landscapes. Additionally, the currentraster encodes the relative potential for mobility across the entireraster, providing a means for conceptualizing the relative mobility af-fordance across the landscape.  2.2. Multidirectional circuit analysis While most applications of circuit analysis have focused on con-nectivity between speci fi c points of interest, here, the objective is tomodel overall mobility a ff  ordance without assuming srcin, destina-tion, or direction of travel. To do this, I build upon the  “ wall-to-wall ” method developed by Anderson, Pelletier, and colleagues (Andersonet al., 2014; Anderson et al., 2012; Pelletier et al., 2014; see also Howey and Brouwer Burg, 2017). In this approach, focal nodes are placedalong the edges of a square tile of the landscape. Current is injected intosource nodes along one side, and  fl ows across the tile to the oppositeside following cardinal directions. The analysis is executed four times tomodel travel in each direction — North-South, South-North, East-West,and West-East. The results of the four runs are then processed andsummed to produce a current raster re fl ecting the probability of movement from any direction, thus eliminating the need to specifysrcin and/or destination of travel.One challenge to producing a generalized model of mobility is thatthe cost associated with terrain slope is dependent upon the direction of travel. For example, a slope with a northward aspect is experienced asan uphill slope by a traveler walking south, but a downhill slope by onetraveling north. Furthermore, a person traveling east would transect theslope and experience very little e ff  ect from the slope. Slope rastersproduced in GIS software assign slope value based on the maximumelevation change between the focal cell and each of its eight neighbors.The result is a maximum slope value with no accounting for the di-rection of travel.The model described in this paper overcomes this challenge andmakes a signi fi cant contribution to wall-to-wall modeling by para-meterizing the travel costs of slope  in the direction of travel . As explainedbelow, the directional slope cost used to produce the resistance rastersis achieved by calculating the elevation change from each cell to itsadjacent cell in the direction of travel to produce separate resistancerasters for each direction of travel. The appropriate directional re-sistance raster was used in the wall-to-wall method to produce anoverall current raster for travel from any direction.In this way, the model overcomes two important challenges of modeling human movement — the need to specify srcins and destina-tions, and the di ff  erent movement costs associated with slope in thedirection of travel. 3. Methods 3.1. Analysis and focus regions This simulation is subject to edge e ff  ects around the perimeter of theanalysis region because the current is concentrated as it leaves thesource and as it approaches the ground. To avoid these edge e ff  ects, thetotal analysis region used to produce the current raster needed to be atleast four times the size of the research focus region (Anderson et al.,2014; Anderson et al., 2012; Koen et al., 2014; Pelletier et al., 2014). The focus region was delimited to encompass a roughly 25km bu ff  erfrom the forti fi cations identi fi ed during survey, resulting in a total areaof 2346×2346 cells (~76km 2 , Fig. 1A). The total analysis regioncomprised 5428×5428 cells (~176km 2 , Fig. 1A). The results werelater clipped to the focus region for interpreting the results of theanalysis. 3.2. Resistance raster  The model requires four resistance rasters — each one representingthe relative cost in traveling one cardinal direction. Ground cover in thecase study region consists mainly of scrub and the region lies above thetree line. Additionally, given the mountainous terrain, slope is theprimary cost for pedestrian travel. Therefore, only slope was modeled inthis analysis. Other mobility analyses have incorporated additionalvariables (Gustas and Supernant, 2017; Howey, 2011), which should be considered for other contexts and applications. Elevation data was de-rived from SRTM DEM data with 1-arc  sec  (32.45m resolution). Theprocess for developing each resistance raster is elaborated for north-ward travel.Slope cost was calculated for each direction of travel. For each rastercell, focal statistics were used to calculate the elevation of the cellimmediately to the north. Slope was then calculated as a ratio of   L.E. Kohut   Journal of Archaeological Science: Reports 19 (2018) 239–247  240  elevation change and horizontal distance by subtracting the cell ele-vation from the elevation of the cell to the north and dividing the dif-ference by the cell size (32.45m). The resulting slope raster was re-calculated to remove any outliers, here deemed to be values greaterthan 2 (60°). Outliers could be attributed isolated anomalies in the DEMdata or extremely steep slopes considered to be not traversable. Allslope values greater than two were reclassi fi ed as No Data (in fi niteresistance) and thus excluded from the circuit analysis. The result was aslope raster with values ranging from 0 ( fl at terrain) to 2.Two methods for calculating the anisotropic travel cost of slopewere used in separate analyses and their results compared: Bell andLock's (2000) logarithmic slope cost, and Tobler's (1993) hiking func- tion. The primary di ff  erence between the two is that Tobler's hikingfunction is asymmetrical, where the lowest cost is a slight downslope,rather than  fl at terrain. Visual comparisons of both results found thateach method had particular strengths and weaknesses. Tobler's methodfor calculating slope cost provided more marked decline in current  fl owalong steep slopes, while Bell and Lock's method captured more subtlevariation in cost, especially with respect to uphill travel. In comparingthe results of each, I found that Bell and Lock's method better ap-proximated slope costs and provided greater di ff  erentiation in the re-sults.Following Bell and Lock (2000), slope values were rescaled loga-rithmically to account for non-linear e ff  ect of slope on travel cost, anddivided by the arctangent of 1 (0.01745, Fig. 2). Because Circuitscapedoes not recognize zero values (zero mobility cost) in resistance rasters,a value of one was added to each raster cell, so that zero slope values( fl at terrain) were assigned a cost of one.Next, open water areas were assigned  “ No Data ”  values so that onlypedestrian travel was considered in the analysis. Hydrological data wasderived from SRTM hydrology shape fi les to ensure congruence with theelevation data. Fig. 1.  Process for producing the current raster. A) DEM of the south-central Andes showing the analysis and focus regions. B) DEM of the focus region. C) Resistance raster for northwardtravel. D) Current raster for northward travel.  L.E. Kohut   Journal of Archaeological Science: Reports 19 (2018) 239–247  241  Finally, the resistance raster was scaled from 0.01 to 100 by mul-tiplying the raster by 100 and dividing by the maximum cost to producea resistance raster that re fl ected the relative cost of northward travelacross each cell. The process was repeated for southward, easterly, andwesterly travel to produce a total of four resistance rasters. 3.3. Wall-to-Wall conductivity analysis For the wall-to-wall conductivity analysis, each vertex (wall) of theanalysis area polygon was used as a focal node and served as either asource or ground depending on the direction of travel. For example, fornorthward travel, current was injected into the southern focal node(source) and traveled across the northward resistance raster to thenorthern focal node (ground). The analysis was run a total of four times,once for each direction of travel (Fig. 3). The results of each run wereclipped to the focus area and normalized, and then all four rasters weresummed to produce a composite current raster re fl ecting the overallconnectivity of each cell considering all directions of travel.The resulting current raster displays the overall current values fortravel across each cell from any direction. These values can be inter-preted as representing the overall permeability of each cell across thelandscape.I tested whether using eight directions of travel, rather than four,signi fi cantly impacted the results of the analysis. Comparisons of theresults of four directions versus eight directions found that less than0.001% of raster cells had a di ff  erence of greater than 1 standard de-viation. I concluded that the results from four directions of travel weresu ffi cient for capturing landscape permeability. 4. Case study: Colca Valley hillforts This case study uses the results of survey of forti fi cations in theColca Valley to demonstrate the regional mobility analysis described inthe paper, and a potential use in the study of defensive landscapes. Theforti fi cations date to the Late Intermediate Period (1000 – 1450CE), atime of increased warfare across much of the highland Andes (Arkush,2006; Arkush, 2010; Arkush and Tung, 2013; Covey, 2008). Survey was conducted in the Colca Valley, a prominent highland river valley in thewestern cordillera of the southern Peruvian Andes. The study area 01020304050607080901000510152025303540455055606570758085    R   e    l   a      v   e   c   o   s   t Slope angle Relave effort by slope Fig. 2.  Relative travel e ff  ort by slope following Bell and Lock (2000:88 – 89). E ff  ort cal-culated as ° TAN SlopeTAN  ( )(1 ) . Relative cost values re-scaled to 100. Fig. 3.  Current rasters for each direction of travel. Normalized current rasters were clipped to the focus area and summed to produce the overall current raster.  L.E. Kohut   Journal of Archaeological Science: Reports 19 (2018) 239–247  242  encompasses a 1200km 2 region of the central and upper reaches of theColca Valley. The 33 forti fi cations recorded during survey represent anear-complete record of defensive architecture in the central and upperstretches of the valley during this period (Fig. 4).Forti fi cations here range from small single-walled enclosed outpoststo large forti fi ed settlements comprising upwards of 200 structuresenclosed by multiple concentric walls. Two broad classes of forti fi ca-tions can be distinguished: forti fi cations with domestic structures ( re- sidential forti  fi cations ), and those without ( non-residential forti  fi cations ).Variation in defenses suggests that these sites had distinct defensiveuses. Residential forti fi cations (9/33) were clearly designed to o ff  erprotection to the residents who lived in or adjacent to the defensivewalls. The largest of these settlements had extensive and densely settledresidential areas with as many as 161 house structures, and their sizeand elaboration is comparable to the largest settlements in the regionduring this time. Approximately two thirds (24 of 33) are non-re-sidential forti fi cations that were constructed and used by communitieswhose permanent residence lay elsewhere. Half of the non-residentialforti fi cations were located within one kilometer of a non-defensivesettlement and likely served as the primary defenses for these settle-ments, which are located near the valley bottom and along the lowerhillslopes closer to prime agricultural areas. The remaining redoubtswere located along the higher valley slopes or high elevation grasslandson either side of the valley, and generally much further from knownsettlements in the area.The mobility analysis described above was used to examine theextent to which forti fi cations were strategically placed to control areaswhere travel — and thus threats from possible attackers — were mostlikely. Prior spatial cluster analysis (Ripley's K) found signi fi cant clus-tering of forti fi cations, and I was interested in whether forti fi cationsclusters corresponded to areas of high mobility a ff  ordance. In parti-cular, mobility a ff  ordance was used to address two questions. The  fi rstwas whether forti fi cations were clustered in areas with high mobilitya ff  ordance, suggesting the presence of particularly vulnerable travelareas. The second was whether forti fi cations were located in areas withhigher mobility a ff  ordance, which would suggest they were used stra-tegically to monitor areas where travel was most likely. 4.1. Regional mobility a  ff  ordance To produce the regional mobility a ff  ordance raster, each directionalrun was normalized so that values scaled from 0 to 100, and the fournormalized rasters were summed and clipped to the research focus area.The  fi nal regional a ff  ordance raster had values ranging from 0 to 300,with 0 representing complete barriers to mobility, and 300 representingthe highest mobility a ff  ordance (Fig. 5).The regional mobility a ff  ordance raster provides insights into howthe topography of the valley shapes possibilities to pedestrian traveland how forti fi cations may have been used to control the movement of people. Overall, the more extreme topography of the western part of thevalley results in highly constrained opportunities for mobility. Mobilityis most limited along the valley slopes where access is canalized alongnarrow ridgelines, a few more gradual mountainsides, and throughravines (Fig. 5A). Mobility a ff  ordance is higher in the valley-bottomareas nearer to the Colca River, where the terrain is  fl atter and moreopen (Fig. 5B). Overall, access to the western reaches of the valley from Fig. 4.  Overview of the survey area and documented forti fi cations.  L.E. Kohut   Journal of Archaeological Science: Reports 19 (2018) 239–247  243

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