While, from a theoretical point of view, it is possible to present this complexity on the basis of well-described and relevant examples, it is much more difficult to envisage methods of analyzing it more globally and systematically on the basis of data sets that are, by definition, heterogeneous. How can these pathways composed of heterogeneous trace elements be identified? How to describe and organize the heterogeneous data on physical features and the information relating to movement in order to be able to analyze these pathways? How can all these pathways that structure the flow of movement in the landscape be identified? Attempting to meet this challenge, we propose the definition of a strictly abstract analytical concept based on graph theory which may be operationalized in terms of spatio-temporal analysis, the “track graph” referred to in the opening section of this paper.
5.1. Motivations and Conceptual Workflow
The identifications of the named entities and their relationships are used to define an abstract composite object called a “track graph”. This corresponds to a construct that allows us to interpret movement based on the various features observed regardless of their temporality. The interest of this abstract object lies in its ability to structure data and knowledge to describe the system of movement as a set of potentialities, rather than a juxtaposition of incompatible systems, and in the opportunity it provides for a cross-cultural analysis of movement processes, while keeping the logical link between these processes and the specific features being interpreted in each case study.
This is particularly relevant when considering how we generate knowledge through repeated observation and construction of hypotheses (Figure 10
). In the hermeneutic spiral [19
], the stage of data analysis is crucial in formulating hypotheses and conceptual models. Pattern recognition and hypothesis formulation are often strongly dependent on specific analytical techniques, such as remote sensing, GIS, network analysis, statistics or simulation modeling, which presuppose a formalized structure for the observed data. Therefore, we propose the track graph as a data structure that will allow for a relatively wide range of analytical approaches, based on graph structures. The track graph collapses all (hypothetical) evidence of movement observed, present and past, into a set of nodes and edges that can be supplied with an unlimited array of attributes. These attributes can be associated to each element of the graph through logical reconstruction via ontologies that describe and structure the body of knowledge according to various world views.
From a methodological point of view, we can subdivide our conceptual workflow into three phases (Figure 10
). The first phase is observation from one or more data sources (fieldwork records, imagery, LDTM, maps, historical documents, etc.). The observers identify archaeological features in the available set of data using a shared or individual observation protocol. While this can induce biases (see part 1), we argue that even if they appear inconsistent in the first instance, these different observations can complement each other within a given study area. In order to identify characteristics, observers also pre-interpret them in relation to a particular problem or question, a more or less defined conceptual framework, and a body of knowledge on which their expertise is based. In doing so, they develop hypotheses and an initial conceptual model to drive their observations and the way they will record and interpret them.
The second phase consists of analyzing these observed datasets, considering the way they have been recognized and interpreted from the point of view of the movement process, in order to propose a schema of the concepts used and the links established by the observers to relate various concepts. This is precisely what we attempted to do by applying an ontological approach to each of the case studies analyzed in this article. This exercise makes it possible to select all the characteristics regardless of their name or morphology and to associate them in a generic domain of “potential path”. For instance, agricultural terraces or headland ridges, which are not strictly defined as roads, are nevertheless attached to this generic domain of “potential path”. In the cases studied, the features identified all have a spatial reference that is conventionally represented by lines and points. Within the same study area, these heterogeneous layers of information, grouped under the generic domain, can then be combined. Their cartographic generalization allows them to be represented in the form of an abstract geometric model composed of nodes and edges, which constitutes the track graph.
In the third phase, we can explore the logical reconstruction of plausible paths or even movement patterns, for a given time period. This relies on the track graph together with complementary knowledge and data. In the approach developed here, the track graph is a skeleton of plausible tracks, which define the “playing ground” within which we can explore different hypothetical models of movement practices (induced models) and interpretations using, for example, rule-based or agent-based simulation models. Based on several domains of knowledge (“routes”, “networks”, “trajectories”) organized within different ontologies, we can produce various models of movement. Then, the track graph allows us to identify connections between objects that are coming from different observers and methodologies (see the discussion of bias in Section 1
) related to these models of movement.
Subsequently, the abstract object represented by the track graph can be used to reconstruct several types of significant networks. These may be recontextualized a posteriori with temporal attributes, material expressions and socio-environmental conceptions of movement, and clearly defined by a new ontology based on spatial relationships within the graph’s network and on a set of contextual knowledge. Following this approach, the same set of nodes and edges may be articulated differently depending on the model of mobility chosen. For example, we might compare the articulations produced by a regional transport road or a farmer’s trajectory in the course of his daily activities. An edge, corresponding to an archaeological feature with a specific morphology, can then simultaneously be considered as a formal road segment participating in a planned network, or as part of a trajectory defined by the practice of a farmer’s routine activity.
While these reconstructions remain hypothetical, they have the benefit of being based on all the archaeological evidence observed but being abstracted from the regionally specific frameworks implicated in their attributes. The link to these attributes is maintained by an identifier and geographical coordinates linking each segment to one or more observations with specific attributes and ontologies attached, thus making it possible to return to the initial data during the evaluation phase of the reconstruction.
The third step of this conceptual workflow is still a work in progress. In the remainder of this article, we will therefore focus in more detail on the concept of the “track graph”, its construction, and its articulation with two other concepts coming from our observational ontologies: The “pathways system” and the “path framework system” (discussed in Section 4
5.2. Track Graph Composition
We define the track graph as an abstract object, composed of a set of nodes and edges. This approach follows that of representations where geometric entities representing physical features are abstracted from their descriptive attributes, such as the approach formalized in the context of urban archaeology to explore the complexity of the urban fabric [59
]. This permits us to clearly distinguish interpreted properties such as type or class, described in the attributes, from the abstract entity, described through the geometry.
A node may represent a place, such as a city, a marketplace, a single dwelling, a marker in the landscape, or an intersection between paths. Such an intersection could be recognized as a junction or crossroad, a semantically meaningful place, or simply as a crossing of two pathways without any specific semantic meaning, for example, the intersection between an animal trail and a hiking trail. The essential characteristic of a node is that individuals and groups can move between them and through them. In other words, a node in the track graph denotes a potentially meaningful place.
Movement itself takes place on the edges, representing features understood to serve as pathways. These can be assigned various attributes, describing their material manifestations or functions. Through time, intersections and places as well as “pathways” can appear, disappear, and reappear. The track graph records and accumulates each observed feature. This geometric graph is expended as observations are made (Figure 11
). An observation allows the creation of an edge or a set of edges and nodes, and the same edge can correspond to several observations (from various observers, and/or various sources, at different observation times or according to different protocols).
Edges and nodes are given an ID and spatial coordinates that maintain a link to the initial observations which are described by a set of attributes via an ontology. While some of these attributes are purely descriptive, e.g., size, height, width, length, materials, spectral signature, topological attributes (crossing, next to, etc.), and consequently will not change between different ontological schemas, other attributes, e.g., class or type, might change between schemas. This compartmentalized approach allows nodes and edges to have different attribute sets for each ontological schema and each set of observations. For example, a researcher visually interpreting a LDTM could identify and interpret a linear topographic anomaly as a part of a Roman road. The same feature could be identified and interpreted by a Medieval archaeologist as a field boundary or as a potential pathway for farmers. This type of interpretational controversy is quite common and the source of heated debates when a research team is investigating the development of a landscape [60
]. Equally, studies combining multiple surveys for a single area highlight the complexities that arise when combining interpretations generated by multiple teams [61
]. The track graph allows us to combine these diverse sets of observations, acting as a dynamic representation of observations, evolving as new ones are made. The track graph constitutes a shared abstract canvas or skeleton that can be used to recompose meaningful systems which can be associated with different worldviews and conceptions of movement.
A single observation, for example a line identified on an aerial image, can also be represented as a set of edges connected by nodes. In this case, the nodes do not have the role of origin or destination but will only link edges to geometrically represent an entity, while some may contribute by representing other observations. This highly abstract structure has several advantages. One is that it allows nodes and edges to be treated as active or inactive. For example, in a set of edges and nodes that represent a Roman road, one of the nodes may also correspond to a junction that allows a farmer to join the road from a terrace edge passageway. In the first case, the node cannot be related to any semantic data, it is a simple graphical convention and is therefore inactive in the graph when it is analyzed as a network. In the second case, the same node is active since it corresponds to an element that has a semantic role, representing a junction of two or more edges.
In the track graph, the network of active places and pathways is only a subset of the total set of realized places and pathways. This graph structure provides a mechanism through which edges and nodes can be activated for modeling movement at specific points in time. A second interest of the track graph which arises from its abstract nature is the possibility to use it as an analytical framework that can be transposed to several transcultural case studies. This allows for the comparison of patterns of paths based on the same structure, while interpreting each of them using the ontology specific to the community under study.
5.3. Summing Up and Making Connections: Track Graphs, Pathway Systems, and Path Framework Systems
In this paper, we illustrated our approach to developing formal models of two types of logic which underpin processes related to movement: The “path framework system” and the “pathway system”, by analyzing a body of literature about a landscape. Then, we explored how these formal models of movement can be leveraged in the interpretation of data from sources such as aerial imagery, LDTMs, field surveys, and historic maps, and how these observations can be integrated through a “track graph”.
To summarize, the “path framework system” and “pathway system” provide complementary models of movement and are intended to be used together. The “path framework system” (Figure 12
) is used to describe a path network designed by a society, or at least recognized as such by a group. This includes formal paths which can be used for transport or travel from an origin to a destination. In this conceptual framework, movement is essentially destination-oriented [62
]. In developing territorial models, the “path framework system” could be used to model how formal systems of movement contribute to the social, political, or cultural integration of the population.
The “pathway system” is used to describe the trajectory produced by one or more actors through the performance of their activities. This trajectory is essentially informal, although it may include components of the formal road system. In the “pathway system”, the movement is activity oriented rather than destination oriented. The movement logic of the “pathway system” could be approached analogously to the wayfaring process, as developed by Ingold [31
], but associated with the idea of habitus [47
], which over the long term produces a collectively created imprint in the landscape.
The “track graph” is a network graph in which each entity (node or edge) represents a physical feature in the landscape, and their physical and spatial connections are represented as connections in the graph. The “track graph” links the two models of movement in a single analytical framework provided by its abstract representation of features in the physical landscape. Unlike the “path framework system” and the “pathway system”, the “track graph” does not contain any interpretations of what the features represented are used for or when they were in use. It only acts as an abstract support for both conceptual frameworks. Its structure, composed of edges and nodes, is simply a convention to facilitate analysis.
In the articulation of the three concepts, the handling of time deserves careful attention. As explained, the “track graph” is a set of nodes and edges that covers the total of all observed and inferred potential paths and places, regardless of their chronological range. In this sense, the “track graph” itself historically and archaeologically atemporal
, conflating features from all periods. At a given moment of observation (O1
), the “track graph” structure records the totality of the realized or potential paths and can be used for exploring plausible paths, using a specific ontology describing movement behaviors and associated knowledge about a given space-time (Figure 11
). New observations may be added to the “track graph”, tagged with their observational moment (O2
), capturing the development of the understanding of the landscape and movement in it through an iterative process of modeling, observation, and interpretation. The temporality of the “track graph” is related to the time at which the observations are made, at which we have arrived at a particular state of knowledge.
Unlike the “track graph”, the “pathway system” and the “path framework system” are historically and archaeologically temporal. They are chronologically bounded and their dynamics reflect a dynamic that is historically meaningful. In archaeology, we are interested in analyzing patterns and dynamics within a time frame (T) with defined durations (from t0 to tn). Therefore, we can refer to different reconstructions of movement patterns (induced models) as being valid for a particular time frame, defining the nodes and edges that were present at t0, and defining which ones become active or inactive until the end date tn. Thus, within our time frame T, we can have reconstructions R1,…,Rn.
Then, modeling techniques can be used to simulate movement and establish routes within the track graph structure. This is, for example, what happens in an application such as ORBIS (http://orbis.stanford.edu/
), where a network of Roman roads and cities is used to explore different travel routes within the Roman Empire. Within this static network, which forms a typical example of a path framework system, routes can be defined as subsets of nodes and edges that are connected for the purpose of a single, individual journey. These routes can be short or long, straight or circuitous, and can be connected to and nested in other routes. Simulations similar to these can explore various manifestations of one or more movement behaviors at a single point in time, for example focusing on understanding the consequences of uncertainties in data attributes [63
] to assess the plausibility of routes.
Next, we consider the role of nodes in the “track graph”, and how they are used in modeling the trajectories of journeys made within the framework defined by the “pathway system”. The concept of the “pathway system” is rooted in the paradigm of the meshwork, a theoretical framework radically different from that of a network, and consequently any modeling within this meshwork-based paradigm requires a fundamentally different approach [31
]. In a meshwork, we focus on the people who move through the landscape and how their practices of movement cause “knots” to emerge. These “knots” are defined as places where their journey’s trajectories intertwine (an interweaving of lines in Ingold’s language). Visually, these are places where the physical features associated with movement intersect, but which have no semantic meaning for the actors involved in their journeys as they move along these pathways. An example of this kind of knot is the intersection between a paved road and the route taken by a roe or a wild boar moving across the landscape (Figure 13
In contrast to the situation in the network paradigm where each node is a point of connection, the knot of the meshwork paradigm is not, a priori, making a meaningful connection between routes. In order to articulate these two conceptions, the network and the meshwork, in a formal and operational model which can be used in graph-based analyses and calculations, we have chosen to treat these knots as nodes within the “track graph”. This is a pragmatic decision taken because when constructing a graph in most current software systems it is a technical necessity that the nodes are present as fixed features, rather than being dynamically generated during the running of an analysis. To reconstruct the plausible paths or the circulation patterns which might have been used by actors moving around the “track graph” at a given moment or period of time, we use attributes to assign a node, acting as an entirely abstract element on the graph, the function of a “connector” (active nodes) or a “knot” (inactive nodes). This approach semantically separates the presence of a node in the graph from its usual function as a connector.
To explore this idea, consider a research exercise in which a team models movement through the landscape at two different moments in time. In the first moment, the junction between a farmers’ path crossing a road has a specific meaning for farmers and is recognized and marked by a group of farmers as a crossroads. Therefore, it is an active node having the function of a connector in the track graph when running a model simulating movement through the system. In the second moment, the formal road exists, but there is no place marked by a group as an official crossroads. In this second moment, although the direction of the farmer’s travel may change, turning from the farm path onto the road, and this may be represented in the simulation as a change of direction between two edges geometrically separated by a node in the “track graph”, this node will have an inactive status because it is not acting as a connector because it is not a “crossroads”—a recognized destination or otherwise meaningful feature in the landscape. The assignment of “active connector” or “inactive knot” attributes to nodes on a graph provides a mechanism through which we can attempt to implement network analysis and modeling approaches dependent on graphs within the conceptual model of a meshwork.
Through dynamic simulation, using an agent-based modeling (ABM) for example, a large set of reconstructed individual trajectories can emerge, using various combinations of the track graph elements, which change at each iteration. The trajectories emerging at ti, based on the modeled behavior of the agents, and related to the pathway system, will lead to the creation of a specific set of “pathways” encapsulated in a set of edges and nodes within the track graph. These sets will have an effect on modeled trajectories in the next iteration at ti+1, because the existence of pathways influences the beliefs and knowledge of subsequent groups of agents. This provides a mechanism for the simulation to drive changes in the attributes of nodes and edges in the “track graph” (e.g., “crossroads”, “path”) from iteration to iteration. Models such as these can be used to validate specific hypotheses, for example if observed formal “path framework systems” could have served other purposes, or if certain movement practices imply or preclude the combined use of path framework and pathway systems.