An interdisciplinary bibliometric analysis of models for land-use and transport interactions
AAn interdisciplinary bibliometric analysis of models for land-use andtransport interactions
Juste Raimbault , , , ∗ Center for Advanced Spatial Analysis, University College London UPS CNRS 3611 ISC-PIF UMR CNRS 8504 G´eographie-cit´es ∗ [email protected] Abstract
Research on links between transport and land-use is by essence interdisciplinary, as a result of the multi-dimensionality and complexity of these objects. In the case of models simulating interactions between transportand land-use, the research landscape is similarly relatively broad and sparse. We propose in this paper abibliometric analysis of this literature from an interdisciplinary perspective. We first provide a survey of thevarious disciplines and approaches. We then construct an interdisciplinary corpus of around 10,000 papers, whichwe analyse in terms of citation network and semantic content. We illustrate therein the diversity of existingapproaches, their complementarity, and possible future research directions coupling some of these viewpoints.
Keywords:
Land-use Transport Interaction Modeling; Bibliometrics; Research Landscape; Interdisciplinarity
Transportation networks are well known as having a central role in shaping the evolution of land-use in urban andregional systems [Mackett, 1993]. In the context of urban planning, quantitative simulation models integrating thislink have been introduced as tools to explore future scenarios and coined as Land-use Transport Interaction (LUTI)models [Wegener, 2021]. Other disciplines such as transport geography focus on processes at other scales such assystems of cities, and have developed more stylised models [Raimbault, 2020c]. Transportation network growth isalso well understood from an economic viewpoint focusing on network investments [Levinson et al., 2012]. A varietyof disciplines and corresponding viewpoints, processes and scales, is thus focused on models linking transport andland-use.Within this highly interdisciplinary research question, some types of models and theoretical frameworks havebeen significantly less explored. For example, the construction of co-evolution models between transport andland-use, integrated across time and spatial scales, remains relatively open. Diverse hypotheses can be proposedto explain the absence of investigations on such co-evolution models: (i) following [Commenges, 2013], scientificand operational actors that would be concerned by the practical application of such models would see themselvesreplaced by the same models and have thus no incentive to develop them (sociological explanation); (ii) the differentdisciplines which develop the diverse components that are necessary to such models are compartmentalised andhave divergent motivations (epistemological explanation); (iii) the construction of such models exhibits intrinsicdifficulties making their development not encouraging and not well currently tackled. The second hypothesis canbe tested empirically using literature mapping methods.This issue on co-evolution models highlights how the research landscape, in terms of disciplines and produced lit-erature, endogenously shapes the questions tackled and processes studied. More generally, such an interdisciplinaryfield as modeling interactions between transport and land-use, involves many complementary viewpoint. Being ableto provide an interdisciplinary literature review is thus an asset for scientific reflexivity and to investigate novel andhybrid research fronts. This contribution proposes thus a broad literature survey of such models, combined with aliterature mapping approach.The application of new bibliometrics and literature mapping methods to questions related to transport geographyhas already been proposed in the literature. [Derudder et al., 2019] study from a bibliometrics perspective thescientific position of Journal of Transport Geography. [Shi et al., 2020] analyse the scientific production around the1 a r X i v : . [ c s . D L ] F e b oncept of accessibility. [Leung et al., 2019] produce citation network maps of research on the impact of fuel priceon urban transport. [Modak et al., 2019] give an overview of the dynamics of Transportation Research journalsover the last 50 years. Regarding models of interactions between transport and land-use in themselves, systematicbibliometric methods have not yet been applied.Our contribution consists in producing first a broad and cross-disciplinary survey of such models; and second apartial but also interdisciplinary map and bibliometric analysis of the literature. Our study is not exhaustive butcombines diverse viewpoints usually not combined. A companion paper [Raimbault, 2020b] provides a complemen-tary approach, with a systematic review and meta-analysis of model characteristics, and a more exhaustive corpusconstruction.The rest of this paper is organised as follows. We first review from an interdisciplinary perspective the modelsthat can be linked to interactions between transportation networks and territories, without any a priori of temporalor spatial scale, of ontologies, of structure, or of application context. This survey is done with diverse disciplinaryentries, including for example geography, transportation geography, planning. This overview suggests relativelyindependent knowledge structures and disciplines that rarely communicate. We proceed then to a literature mappingand bibliometrics analysis. Constructing a corpus of around 10,000 papers, we proceed to a multilayer networkanalysis, combining citation network and semantic network obtained through text-mining. This provides a bettergrasp of the relations between disciplines, their lexical field and their interdisciplinarity patterns. We develop now an overview of different approaches modeling interactions between networks and territories.First of all, we need to notice a high contingency of scientific constructions underlying these. Indeed, accord-ing to [Bretagnolle et al., 2002], the “ ideas of specialists in planning aimed to give definitions of city systems, since1830, are closely linked to the historical transformations of communication networks ”. The historical context (andconsequently the socio-economical and technological contexts) conditions strongly the formulated theories. Thisimplies that ontologies and corresponding models addressed by geographers and planners are closely linked to theircurrent historical preoccupations, thus necessarily limited in scope and/or operational purpose. In a perspectivistvision of science [Giere, 2010], such boundaries are the essence of the scientific entreprise, and their combinationand coupling in the case of models is generally a source of knowledge.The entry we take here to sketch an overview of models is complementary to the one taken by [Raimbault, 2018a](first chapter) and by [Raimbault, 2020b], by declining them through their main ontology of network-territoriesinteractions: the relations Network → Territory, Territory → Network and Territory ↔ Network. In this notation, adirect arrow corresponds to processes that we can relatively univocally attribute to the origin, whereas a reciprocalarrow assumes the intrinsic existence of reciprocal interactions, generally in coincidence with the emergence ofentities playing a role in these. The reference frame for scales is also the one introduced in [Raimbault, 2018a],knowing that we do not consider the microscopic scales with the choice of discarding daily mobility models. Weconsider therefore models at the mesoscopic and macroscopic temporal and spatial scales.
One important approach to the modeling of the influence of transportation networks on territories lies in the fieldof planning, at medium temporal and spatial scales (the scales of metropolitan accessibility we developed before).Models in geography at other scales, such as the Simpop models [Pumain, 2012], do not include a particularontology for transportation networks at the exception of the SimpopNet model [Schmitt, 2014], and even if theyinclude networks between cities as carriers of exchanges, they do not allow to study in particular the relationsbetween networks and territories.These approaches are generally named as models of the interaction between land-use and transportation ( LUTI ,for
Land-Use Transport Interaction ). Land-use generally means the spatial distribution of territorial activities,generally classified into more or less precise typologies (for example housing, industry, tertiary, natural space).These works can be difficult to apprehend as they relate to different scientific disciplines. We make here thechoice to gather numerous approaches having the common characteristic to principally model the evolution of land-use, on medium temporal and spatial scales. The unity and the relative positioning of these approaches coveringfrom economics to planning, remain an open question, to which [Raimbault, 2020b] introduces elements of answerthrough a systematic review and meta-analysis approach. Their general principle is to model and simulate the2volution of the spatial distribution of activities, taking transportation networks as a context and significant driversof relocations.To understand the underlying conceptual frame to most approaches, a synthesis of the general theoretical andempirical frame for land-use transport interaction models described by [Wegener and F¨urst, 2004] is as follows.The four concepts included are land-use, relocations of activities, the transportation system and the distribution ofaccessibility. A cycle of circular effects are summed up in the following loop: Activities −→ Transportation system −→ Accessibility −→ Land-use −→ Activities. The transportation system is assumed with a fixed infrastructure ,i.e. effects of the distribution of activities are effects on the use of the transportation system (and thus link to mobility in our more general frame): modal choice, frequency of trips, length of travels.The theoretically expected effects are classified according to the direction of the relation (
Land-use → Transport or Transport → Land-use , and a loop
Transport → Transport ), and according to the main factors included (residentialdensity, of employments, locations, accessibility, transportation costs) and also by the aspect which is modified bythe intervention tested (length and frequency of trips, modal choice, densities, locations). We can for example take: • Land-use → Transport : a minimal residential density is necessary for the efficiency of public transportation, aconcentration of employments implies longer trips, larger cities have a greater proportion of the modal partof public transportation. • Transport → Land-use : a high accessibility implies higher prices and an increased development of residentialhousing, companies locate for a better accessibility to transportation at a larger scale. • Transport → Transport : places with a good accessibility will produce more and longer trips, modal choice andtransportation cost are highly correlated.These theoretical effects are then compared to empirical observations, which for most of them give the wayprocesses are implemented. Some are not observed in practice, whereas most converge with theoretical expectations.A more general framework closer to the idea of co-evolution, is the one given by [Le N´echet, 2010], which situatesthe triad Transportation system/Localization system/Activities system within the relation with agents: agentscreating demand, agents building the city, external factors. From the viewpoint of urban economics, propositionsfor such models have existed for a relatively long time: [Putman, 1975] recalls the frame of urban economics in whichmain components are employments, demography and transportation, and reviews economic models of locations thatrelate to the Lowry model [Lowry, 1964].[Wegener and F¨urst, 2004] develop a state of the art of empirical studies and in modeling on this type ofapproach of interactions between land-use and transport. The theoretical positioning is closer of disciplines such astransportation socio-economics and planning (see the disciplinary landscapes described in the quantitative sectionof this paper). They compare and classify seventeen models, which however to not include an endogenous evolutionof the transportation network on relatively short time scales for simulations (of the order of the decade). We findagain indeed the correspondance with typically mesoscopic scales previously established. A complementary reviewis done by [Chang, 2006], broadening the context with the inclusion of more general classes of models, such as spatialinteractions models (which contain trafic assignment and four steps models), planing models based on operationalresearch (optimization of locations of different activities, generally homes and employments), the microscopic modelsof random utility, and models of the real estate market.
The variety of existing models lead to operational comparisons: [Paulley and Webster, 1991] synthesise a projectcomparing different model applied to different cities. Their result allow on the one hand to classify interventionsdepending on their impact on the level of interaction between transportation and land-use, and on the other hand toshow that the effects of interventions strongly depend on the size of the city and on its socio-economic characteristics.Ontologies of processes, and more particularly on the question of equilibrium, are also varied. The respectiveadvantages of a static approach (computation of a static equilibrium of households localisation for a given specifica-tion of their utility functions) and of a dynamical approach (out-of-equilibrium simulation of residential dynamics)has been studied by [ ? ], within a metropolitan frame on time scales of the order of the decade. The authors showthat results are roughly comparable and that each model has its utility depending on the question asked.Different aspects of the same system can be included within diverse models, as show for example [Wegener et al., 1991],and traffic, residential and employments dynamics, the evolution of land-use as a consequence, also influenced by astatic transportation network, are generally taken into account. [Iacono et al., 2008] covers a similar horizon withan additional development on cellular automata models for the evolution of land-use and agent-based models. The3emporal range of application of these models, around the decade, and their operational nature, make them usefulfor planning, what is rather far of our focus to obtain explicative models of geographical processes. Indeed, it is oftenmore relevant for a model used in planning to be understandable as an anticipation tool, or even a communicationtool, than to be faithful to territorial processes, at the cost of an abstraction. [Timmermans, 2003] formulates doubts regarding the possibility of interaction models that would be really inte-grated, i.e. producing endogenous transportation patterns and being detached from artefacts such as accessibilityfor which the influence of its artificial nature remains to be established, in particular because of the lack of dataand a difficulty to model governance and planning processes. It is interesting to note that current priorities forthe development of LUTI models seem to be centred on a better integration of new technologies and a betterintegration with planning and decision-making processes, for example through visualization interfaces as proposedby [Wee, 2015]. They do not aim at being extended on problematics of territorial dynamics including the networkon longer time scales for example, what confirms the range and the logic of use and development of this type ofmodels.A generalisation of this type of approach at a smaller scale, such as the one proposed by [Russo and Musolino, 2012],consists in the coupling between a LUTI at the mesoscopic scale to macroeconomic models at the macroscopic scale.They indeed generalise the framework of LUTI models to propose a framework of interaction between spatial econ-omy and transportation ( Spatial Economics and Transport Interactions ). This framework includes LUTI models atthe urban scale, and at the national level macroeconomic models simulating production and consumption, competi-tion between activities, production of the stock of the offer of transportation. Transportation models still assume afixed network and establish equilibria within it, what implies a small spatial scale and a short time scale. These donot consider the evolution of the transportation network in an explicit manner but are interested only in abstractpatterns of demand and offer. Urban economics have developed specific approaches that are similar in their context:[Masson, 2000] for example describes an integrated model coupling urban development, relocations and equilibriumof transportation flows. [Wilson, 1998] highlights several possible theoretical developments for LUTI models, butalso in terms of their operational application.Thus, we can synthesise this type of LUTI approach, by the fundamental following characteristics: (i) modelsaiming at understanding an evolution of the territory, within the context of a given transportation network; (ii)models in a logic of planning and applicability, being themselves often implied in decision-making; and (iii) modelsat medium scales, in space (metropolitan scale) and in time (decade).
An “opposite” modeling paradigm is focused on the evolution of the network. It may seem strange to consider avariable network while neglecting the evolution of the territory, when considering some potential network evolutionmechanisms (potential breakdown, self-reinforcements, network planning) which occur at mainly longer time scalesthan territorial evolutions. We will see that there is no paradox, since (i) either the modeling focuses on theevolution of network properties , at a short scale (micro) for congestion, capacity, tarification processes, mainly froman economic point of view; (ii) or territorial components playing indeed a role on the network are stable on the longscales considered.Modeling approaches which aim at explaining the growth of transportation networks generally take a bottom-up and endogenous point of view. They thus try to unveil local rules that would allow to reproduce the growth of thenetwork on long time scales (often the road network). As we will see, it can be a topological growth (creation ofnew links) or the growth of link capacities in relation with their use, depending on scales and ontologies considered.To simplify, we distinguish broad disciplinary streams having studied the modeling of the growth of transportationnetworks: these are respectively linked to transportation economics, physics, transportation geography, and biology.We thus converge with the classification by [Xie and Levinson, 2009b], which propose an extended review ofmodeling the growth of transportation networks, in a perspective of transportation economics but broadened to otherfields. [Xie and Levinson, 2009b] distinguish broad disciplinary streams having studied the growth of transportationnetworks: transportation geography has developed very early models based on empirical facts but which have focusedon reproducing topology rather than mechanisms (the contribution of geography would however consist in limitedefforts at the time of [Chorley and Haggett, 1970], which we do not develop further below); statistical models oncase studies produce very limited conclusions on causal relations between network growth and demand (growthbeing in that case conditioned to demand data); economists have studied the production of infrastructure bothfrom a microscopic and macroscopic point of view, generally not spatialized; network science has produced stylised4odels of network growth which are based on topological and structural rules rather than rules built on processescorresponding to empirical facts.
Economists have proposed models of this type: [Zhang and Levinson, 2007] review transportation economics liter-ature on network growth, recalling the three main features studied by economists on that subject, that are roadpricing, infrastructure investment and ownership regime, and finally describes an analytical model combining thethree. These three classes of processes are related to an interaction between microscopic economic agents (usersof the network) and governance agents. Models can include a detailed description of planning processes, suchas [Levinson et al., 2012] which combine qualitative surveys with statistics to parametrise a network growth model.[Xie and Levinson, 2009a] compares the relative influence of centralised (planning by a governance structure) anddecentralised growth processes (local growth which does not enters the frame of a global planning).[Yerra and Levinson, 2005] show with an economic model based on self-reinforcement processes (i.e. that in-clude a positive feedback of flows on capacity) and which includes an investment rule based on traffic assign-ment, that local rules are sufficient to make a hierarchy of the road network emerge with a fixed land-use.[Levinson and Karamalaputi, 2003] proceed to an empirical study of drivers of road network growth for
TwinCities in the United States (Minneapolis-Saint-Paul), establishing that basic variables (length, accessibility change)have the expected behavior, and that there exists a difference between the levels of investment, implying that localgrowth is not affected by costs, what could correspond to an equity of territories in terms of accessibility. The samedata are used by [Zhang and Levinson, 2017] to calibrate a network growth model which superimposes investmentdecisions with network use patterns. A synthesis of such approaches is done in [Xie and Levinson, 2011].
Physics has more recently introduced infrastructure network growth models, largely inspired by this economicliterature: a model which is very similar to the last we described is given by [Louf et al., 2013] with simpler cost-benefit functions by obtaining a similar conclusion. Given a distribution of nodes (cities) which population followsa power law, two cities will be connected by a road link if a cost-benefit utility function, which linearly combinespotential gravity flow and construction cost (what gives a cost function of the form C = β/d αij − d ij , where α and β are parameters), has a positive value. In this approach, the assumption of non-evolving city populations whereasthe networks is iteratively established finds little empirical or thematic support, since we showed that network andcities had comparable evolution time scales. This models is thus closer to produce in the proper sense a potentialnetwork given a distribution of cities, and must be interpreted with caution. These simple local assumptions aresufficient to make a complex network emerge with phase transitions as a function of the relative weight parameterin the cost function, leading to the emergence of hierarchy. [Zhao et al., 2016] apply this model in an iterativeway to connect intra-urban areas, and shows that taking into account populations in the cost function significantlychanges the topologies obtained.An other class of models, close to procedural models in their ideas, are based on local geometric optimizationprocesses, and aim at resembling real networks in their topology. [Bottinelli et al., 2017] thus study a tree growthmodel applied to ant tracks, in which maintenance cost and construction cost both influence the choice of newlinks. The morphogenesis model by [Courtat et al., 2011] which uses a compromise between realisation of interac-tion potentials and construction cost, and also connectivity rules, reproduces in a stylised way real patterns of streetnetworks. A very close model is described in [Rui et al., 2013], but including supplementary rules for local optimiza-tion (taking into account degree for the connection of new links). Optimal network design, belonging more to thefield of engineering, uses similar paradigms: [Vitins and Axhausen, 2010] explore the influence of different rules ofa shape grammar (in particular connection patterns between links of different hierarchical levels) on performancesof networks generated by a genetic algorithm.We can detail the mechanisms of one of these geometrical growth models. [Barth´elemy and Flammini, 2008]describe a model based on a local optimization of energy which generates road networks with a globally reasonableshape. The model assumes “centres”, which correspond to nodes of a road network, and road segments in spacelinking these centres. The model starts with initial connected centres, and proceeds by iterations to simulate networkgrowth the following way: (i) new centres are randomly added following an exogenous probability distribution, atfixed duration time steps; (ii) the network grows following a cost minimisation rule: centres are grouped by projectionon the network; each group makes a fixed length segment grow in the average direction towards the group startingfrom the projection (except if it vanishes in length, a segment then grows in the direction of each point). This modelis adjusted in order that areas of parcels delimited by the network follow a power law with an exponent similar5o the one observed for the city of Dresden, Germany. It has the advantage to be simple, to have few parameters(probability distribution for centres, length of segments built), to rely on reasonable local rules. This last point haspitfalls, since we can then expect the model to only capture a reduced complexity, by neglecting various processessuch as governance. An other approach to network growth are biological networks. This approach belongs to the field of morphogeneticengineering, which aims at conceiving artificial complex systems inspired from natural complex systems and onwhich a control of emerging properties is possible [Doursat et al., 2012].
Physarum machines , which are modelsof a self-organised mould ( slime mould ) have been proved to solve in an efficient way difficult problems (in thesense of their computational complexity) such as routing problems [Tero et al., 2006] or NP-complete navigationproblems such as the Traveling Salesman Problem [Zhu et al., 2013]. These properties allow these systems toproduce networks with Pareto-efficient properties for cost and robustness [Tero et al., 2010] which are typical ofempirical properties of real networks, and furthermore relatively close to these in terms of shape (under certainconditions, see [Adamatzky and Jones, 2010]).This type of models are relevant since self-reinforcement processes based on flows are analogous to link rein-forcement mechanisms in transportation economics. This type of heuristic has been tested to generate the Frenchrailway network by [Mimeur, 2016], making an interesting bridge with investment models by Levinson we previ-ously described. For this last study, validation criteria that were applied remain however limited, either at a levelinappropriate to the stylised facts studied (number of intersection or of branches) or too general and that can bereproduced by any model (total length and percentage of population deserved), and belong to criteria of form thatare typical to procedural modeling which can only difficultly account of internal dynamics of a system as previ-ously developed. Furthermore, taking for an external validation the production of a hierarchical network reveals anincomplete exploration of the structure and the behavior of the model, since through its preferential attachmentmechanisms it must mechanically produce a hierarchy. Thus, a particular caution will have to be given to the choiceof validation criteria.
Finally, we can mention other tentatives such as [De Leon et al., 2007, Yamins et al., 2003], which are closer toprocedural modeling [Lechner et al., 2004, Watson et al., 2008] and therefore have only little interest in our casesince they can difficultly be used as explicative models (following [Varenne, 2017], an explicative model allows toproduce an explanation to observed regularities or laws, for example by suggesting processes which can be at theirorigin; if model processes are explicitly detached from a reasonable ontology, they can not be potential explanations).Procedural modeling consists in generating structures in a way similar to shape grammars, but it also concentratesgenerally on the faithful reproduction of local form, without considering macroscopic emerging properties. A shapegrammar is a formal system (i.e a set of initial symbols, axioms, and a set of transformation rules) which actson geometrical objects. Starting from initial patterns, they allow generating classes of objects. Classifying themas morphogenesis models is however imprecise and corresponds to a misunderstanding of mechanisms of
PatternOriented Modeling [Grimm et al., 2005], which consists in seeking to explain observed patterns, generally at multiplescales, in a bottom-up way. Procedural modeling does not correspond to such procedural approaches, since it aimsat reproducing and not at explaining. Such type of models (exponential mixture to produce a population densityfor example) can be used to generate initial synthetic data uniquely to parametrise other complex models (see forexample [Raimbault, 2019b]).
An last approach to modelling mentioned in the introduction the link between transportation networks and ter-ritories is to consider them as co-evolving , in the sense of intricate relations implying a dynamical modeling andstrong coupling in time between the corresponding components. Such models are rather sparse in the literature andcorrespond to many disciplines without an unified background.[Achibet et al., 2014] model the co-evolution of buildings and road networks with an agent-based model. [Barth´elemy and Flammini, 2009]generalise the model of [Barth´elemy and Flammini, 2008] into a co-evolution model by allowing the density of net-work nodes to dynamically evolve and adapt to centrality. [Ding et al., 2017] describe a co-evolution model couplingmultiple layers of the transportation network. 6able 1:
Synthesis of modeling approaches.
The type gives the sense of the relation; the class is the scientificfield in which the model is inserted; scales correspond to our simplified scales; functions are given in the senseof [Varenne, 2017]; we finally give the type of results they provide and the paradigms used.Type Class Temporal Scale Spatial scale Function Results ParadigmsNetworks → Territories LUTI Medium Mesoscopic Planning,Prediction Land-use sim-ulation Urban eco-nomicsTerritories → NetworksEconomics Medium Mesoscopic Explanation Role ofeconomicprocesses Economics,GovernanceNetworks Geometricalgrowth Long Meso or Macro Explanation Reproductionof stylizedshapes Simulationmodels,Local opti-mizationBiologicalnetworks Long Mesoscopic Optimization Productionof optimalnetworks Self-organizednetworkTerritories ↔ NetworksEconomics Medium Mesoscopic Explanation Reinforcementeffects EconomicsNetworks Geometricalgrowth Long or NA Micro, Meso orMacro Explanation Reproductionof stylizedshapes Simulationmodels,Local opti-mizationUrban Sys-tems Medium, Long Macroscopic Explanation,prospection Stylized facts Complex ge-ographyNetwork growth models described above from the perspective of economics can also be generalised into co-evolution models by making land-use component evolve. [Levinson et al., 2007] integrate into the network invest-ment model an evolving population and unveil self-reinforcing hierarchies. [Li et al., 2016] extend this model byincluding the dynamics of real-estate prices. [Levinson and Chen, 2005] proposes a prediction model for the coupleddynamics of land-use and transport.[Raimbault et al., 2014] generalise the model of [Moreno et al., 2012] based on a cellular automaton coupled withan evolving road network, and show that a variety of urban forms can be produced therein. [Raimbault, 2019c]integrates into this model multiple heuristics for network growth and shows their complementarity to also producevarious urban forms. [Wu et al., 2017] introduce a model linking population diffusion with an evolving networkunder local optimisation rules.Systems of cities are also an appropriate scale to model interactions between territories and transportation net-works, and more particularly their co-evolution. [Baptiste, 1999] models inter-urban migrations coupled with theevolution of capacities in the inter-urban road network. [Blumenfeld-Lieberthal and Portugali, 2010] simulate net-work breakdown as a growth mechanism and integrates population exchanges between cities. [Schmitt, 2014] buildson this model to introduce the SimpopNet model for the co-evolution of cities and transportation networks, whichwas shown to effectively capture circular causation regimes by [Raimbault, 2020c]. [Raimbault, 2018b] integratesself-reinforcing abstract networks into an urban dynamics model to provide a co-evolution model. This model isgeneralised to physical transportation networks by [Raimbault, 2020a].
We synthesise this survey by recalling the broad types of models that we reviewed, organising them by type (relationbetween networks and territories), by class (broad classes corresponding to the stratification of the review), andby giving the temporal and spatial scales concerned, the functions, the type of result obtained, the paradigmsused. This synthesis is given in Table 1. We notice an unbalance between the last section accounting for modelsintegrating effectively a strongly coupled dynamic (and possibly a co-evolution) and the preceding approaches,confirming a sparsity of such approaches suggested before. We will in the next section investigate more generally,from a quantitative viewpoint, the research landscape of the models we surveyed here.7able 2:
Composition of the initial corpus for the construction of the citation network.
Discipline Title ReferencePolitical science
Les effets structurants du transport:mythe politique, mystification scien-tifique [Offner, 1993]Interdisciplinary
R´eseaux et territoires-significationscrois´ees [Offner and Pumain, 1996]Geography
Villes et r´eseaux de transport: desinteractions dans la longue dur´ee(France, Europe, Etats-Unis) [Bretagnolle, 2009]Transportation Land-use transport interaction: state ofthe art [Wegener and F¨urst, 2004]Economics The co-evolution of land use and roadnetworks [Levinson et al., 2007]Economics Modeling the growth of transportationnetworks: a comprehensive review [Xie and Levinson, 2009b]Physics Co-evolution of density and topology ina simple model of city formation [Barth´elemy and Flammini, 2009]
In this section, we propose a bibliometric analysis complementary to the survey above. The idea is not to propose anexhaustive analysis or map of the literature, but to give an interdisciplinary perspective, focusing on the diversity ofdisciplines and approaches and their complementarity. The method and open source tools applied here are describedby [Raimbault, 2019a]. We proceed in particular to (i) a citation network analysis, unveiling endogenous disciplinesby clustering the network; (ii) a semantic network analysis, extracting relevant keywords from paper abstracts andretrieving semantic communities in the co-occurence network; (iii) an analysis of interdisciplinarity patterns bycrossing the two semantic and citation network layers.
We construct an interdisciplinary corpus by reverse exploration of citation networks. Starting from a seed of initialpapers, we collect citing papers up to level two. Our initial corpus is constructed starting from the state-of-the-art established above. Its complete composition is given in Table 2. It includes seven “key” references identifiedfor each of the disciplines previously described. The aim here is not to be exhaustive (it is in the companionpaper [Raimbault, 2020b]), but to construct a description of the neighbourhood of domains we deal with, and givea glimpse of their articulation. It is tailored here to have a reasonable size (leading to a final network that can beprocessed without a specific method regarding the size of data), but the methods used here have been developed onmassive datasets, for example with patent data [Bergeaud et al., 2017], the full bibliography of [Raimbault, 2018a](appendix F).The Table 2 gives the composition of the initial corpus for the construction of the citation network. We includevarious disciplines, from planning/transportation to economics and geography, including physics. Publication yearsare comparable for the paper considered (at the exception of [Offner, 1993] and [Offner and Pumain, 1996] whichhowever belong to disciplines with lower citation rates), to cover comparable research coverages.Following the methodology of [Raimbault, 2019a], we retrieve from Google scholar all papers citing the seedcorpus, and all papers citing these citing papers (constructing a citation network at depth two, consisting in thescientific “heritage” of the seed corpus. The network obtained contains V = 9462 references corresponding to E = 12004 citation links. In terms of languages, English covers 87% of the corpus, French 6%, Spanish 3%, German1%, completed by other languages such as Mandarin.We collect also therefore abstracts for the previous network, in order to do a semantic analysis. As done by[Raimbault, 2019a], abstracts are collected using the Mendeley API. These are available for around one third ofreferences, giving V = 3510 nodes with a textual description.8able 3: Description and size of citation communities.
Domain Size (% of nodes)LUTI 18%Urban and Transport Geography 16%Infrastructure planning 12%Integrated planning - TOD 6%Spatial Networks 17%Accessibility studies 18%
Basic statistics for the citation network already give interesting informations. The network has an average degreeof ¯ d = 2 .
53 and a density of γ = 0 . .
26, what is relatively high for social sciences. It is important to note that it has a single weakconnected component, what means that initial domains are not in total isolation: initial references are shared ata minimal degree by the different domains. We work in the following on the sub-network of nodes having at leasttwo links, to extract the core of network structure. Furthermore, the network is necessarily complete between thesenodes since we went up to the second level.We proceed for the citation network to a community detection with the Louvain algorithm, on the correspondingnon-directed network. The algorithm gives 13 communities, with a directed modularity of 0.66, extremely significantin comparison to a bootstrap estimation of the same measure on the randomly rewired network with gives amodularity of 0 . ± . N = 100 repetitions. Communities make sense in a thematic way, since we recoverfor the largest the domains presented in Table 3.Naming of communities are done a posteriori by inspecting their contents, according to the broad fields unveiledin the literature review done previously. We note that this naming is indeed exogenous and necessarily subjective.As further developed for the semantic network, there does not exist any simple technique for an endogenous naming.We must keep this aspect in mind for the positioning of interpretations and conclusions.The Fig. 1 shows the citation network and allows us to visualise the relations between these domains. It isinteresting to observe that works by economists and physicists in this field fall within the same category of thestudy of Spatial Networks . Indeed, the literature cited by physicists contains often a larger number of references ineconomics than in geography, whereas economists use network analysis techniques. Moreover, planning, accessibility,LUTI models and Transit Oriented Development (TOD) are very close but can be distinguished in their specificities:the fact that they appear as separated communities witnesses of a certain level of compartmentalisation. Thesemake the bridge between spatial network approaches and geographical approaches, which contain an important partof political science for example. Links between physics and geography remain rather low. This overview naturallydepends on the initial corpus, but allows us to better understand its context in its disciplinary environment.
The extraction of keywords is done following an heuristic based on [Chavalarias and Cointet, 2013], further devel-oped by [Bergeaud et al., 2017]. A complete description of the method and its implementation for multi-lingualscientific corpuses is detailed by [Raimbault, 2019a]. It is based on second-order relations between semantic enti-ties, which are n-grams , i.e. multiple keywords which can have a length up to three. These are extracted based ontheir co-occurence matrix, which statistical properties yield a measure of deviation from uniform co-occurrences.This measure is used to evaluate the relevance of keywords. By selecting a fixed number of relevant keywords K W = 10000, we can then construct a network weighted by co-occurrences.The topology of the raw network does not allow the extraction of clear communities, in particular because of thepresence of hubs that correspond to frequent terms common to many sub-disciplines included here. These words areused in a comparable way in all the studied fields, and do not carry information to separate them (but they wouldcarry some if we were comparing a corpus in quantitative geography and a corpus in qualitative anthropology forexample). We focus on terms making the specificity of each sub-field and filter keywords according to a maximaldegree k max . Similarly, edges with small weights are considered as noise and filtered according to a minimal edgeweight threshold θ w .The sensitivity analysis of the characteristics of the filtered network, in particular its size, modularity and9igure 1: Citation Network.
We visualise references having at least two links, using a force-atlas algorithm.Colors give communities described in text. In orange, blue, turquoise: urban geography, transport geography,political sciences; in pink, black, green: planning, accessibility, LUTI; in purple: spatial networks (physics andeconomics).community structure, is given in Fig. 2. It is used to set the optimal parameters for the semantic network.We choose parameter values allowing a multi-objective optimization between modularity and network size, θ w =10 , k max = 500, by the choice of a compromise point on a Pareto front, what gives a semantic network of size( V = 7063 , E = 48952). A visualization of the corresponding semantic network is given in Fig 3.We then retrieve communities in the network using a standard Louvain clustering on the optimal filtered network.We obtain 20 communities for a modularity of 0.58. These are examined manually to be named, the automaticnaming techniques [Yang et al., 2000] being not elaborated enough to make the implicit distinction between thematicand methodological fields for example (and in fact between knowledge domains, see [Raimbault, 2017]) whichis a supplementary dimension that we do not tackle here, but necessary to have meaningful descriptions. Thecommunities are described in Table 4. We directly see the complementarity with the citation approach, since emergehere together subjects of study (High Speed Rail, Maritime Networks), domains and methods (Networks, RemoteSensing, Mobility Data Mining), thematic domains (Policy), pure methods (Agent-based Modeling, Measuring).Thus, a reference may use several of these communities. We furthermore have a finer granularity of information.The effect of language is strong since French geography is distinguished as a separated category (advanced analysescould be considered to better understand this phenomenon and benefit from it: sub-communities, reconstruction ofa specific network, studies by translation; but these are out of the scope of this exploratory study). We note theimportance of networks, and of issues related to political sciences and socio-economic geography.10igure 2: Sensitivity analysis of modular properties of the semantic network as a function of filteringparameters. (Top Left)
Pareto front of the number of communities and the number of vertices (two objectivesto be maximised), the colour giving the value of θ w ; (Top Right) Pareto front of the modularity as a function ofnumber of vertices, for varying θ w ; ( Bottom ) Values of possible objectives (modularity, number of communities,number of connected components, number of vertices, density, size balance between communities), each objectivebeing normalised in [0; 1], as a function of parameters θ w and k max .11igure 3: Semantic network of domains.
The colour of links gives the community and the size of keywords isfixed by their degree. 12able 4:
Description of semantic communities.
We give their size, their proportion in quantity of keywords(under the form of multi-stems ) cumulated on the full corpus, and representative keywords selected by maximaldegree. Name Size Weight KeywordsNetworks 820 13.57% social network, spatial network, resili
Policy 700 11.8% actor, decision-mak, societi
Socio-economic 793 11.6% neighborhood, incom, live
High Speed Rail 476 7.14% high-spe, corridor, hsr
French Geography 210 6.08% syst`eme, d´eveloppement, territoire
Education 374 5.43% school, student, collabor
Climate Change 411 5.42% mitig, carbon, consumpt
Remote Sensing 405 4.65% classif, detect, cover
Sustainable Transport 370 4.38% sustain urban, travel demand, activity-bas
Traffic 368 4.23% traffic congest, cbd, capit
Maritime Networks 402 4.2% govern model, seaport, port author
Environment 289 3.79% ecosystem servic, regul, settlement
Accessibility 260 3.23% access measur, transport access, urban growth
Agent-based Modeling 192 3.18% agent-bas, spread, heterogen
Transportation planning 192 3.18% transport project, option, cba
Mobility Data Mining 168 2.49% human mobil, movement, mobil phone
Health Geography 196 2.49% healthcar, inequ, exclus
Freight and Logistics 239 2.06% freight transport, citi logist, modal
Spanish Geography 106 1.26% movilidad urbana, criteria, para
Measuring 166 1.0% score, sampl, metric
Distribution of keywords within communities provides an article-level interdisciplinarity measure. The combinationof citation and semantic layers in the hyper-network provide second-order interdisciplinarity measures (seman-tic patterns of citing or cited), that we don’t use here because of the modest size of the citation network (see[Raimbault, 2019a] and [Bergeaud et al., 2017]). More precisely, a reference i can be viewed as a probability vectoron semantic classes j , that we write in a matrix form P = ( p ij ). These are simply estimated by the proportions ofkeywords classified in each class for the reference. A classical measure of interdisciplinarity [Bergeaud et al., 2017]is then I i = 1 − (cid:80) j p ij . Let A be the adjacency matrix of the citation network, and let I k matrices selecting rowscorresponding to class k of the citation classification: Id · c ( i )= k , such that I k · A · I k (cid:48) gives exactly the citations from k to k (cid:48) . The citation proximity between citation communities is then defined by c kk (cid:48) = (cid:80) I k · A · I k (cid:48) / (cid:80) I k · A . Wedefine the semantic proximity by defining a distance matrix between references by D = d ii (cid:48) = (cid:113) (cid:80) ( p ij − pi (cid:48) j ) and the semantic proximity by s kk (cid:48) = I k · D · I k (cid:48) / (cid:80) I k (cid:80) I k (cid:48) .We show in Fig. 4 the values of these different measures, and also the semantic composition of citation communi-ties, for the main semantic classes. The distribution of I i shows that articles orbiting in the LUTI field are the mostinterdisciplinary in the terms used, what could be due to their applied character. Other disciplines show similarpatterns, except geography and infrastructure planning which exhibit quasi-uniform distributions, witnessing theexistence of very specialised references in these classes. This was an expected result given the targeted sub-fieldsexhibited (political sciences for example, and similarly prospective studies of type cost-benefit are restricted inscope). This first link between network layers confirms the specificities of each field. Regarding semantic composi-tions (Fig. 4, top right panel), most provide an external validation of both classification given the dominant classeswhich are in relative agreement. The field which is the less concerned by socio-economical issues is infrastructureplanning, what could give reason to critics of technocracy. Issues on climate change and sustainability are relativelywell dispatched. Finally, geographical works are mostly related to governance issues.Proximity matrices (Fig. 4, bottom) confirm the conclusion obtained previously in terms of citation. Indeed, theintersection between citation classes is low, the highest values being up to one fourth of planning towards geographyand of LUTI towards TOD (but not the contrary, since the relations can be in one direction only). However,13igure 4: Patterns of interdisciplinarity. (Top Left)
Statistical distribution of I i by citation classes, in otherwords distribution of interdisciplinarity levels within citation classes; (Top Right) Semantic composition of citationclasses: for each citation class (in abscissa), the proportion of each semantic class (in color) is given; (Bottom Left)
Citation proximity matrix for c kk (cid:48) between citation classes; (Bottom Right) Semantic proximity matrix s kk (cid:48) betweencitation classes.semantic proximities show for example that LUTI, TOD, Accessibility and Networks are close in their semanticcontents, what is logical for the first three, and confirms for the last that physicists mainly rely on methods ofthis fields linked to planning to legitimate their works. Geography is more isolated, its closest neighbour beinginfrastructure planning. This last result is directly linked to the choice of the seed corpus, with a strong influenceof French geography which in practice remains far from urban economics and physics. To what extent transportgeography more generally is close to planning and economics remain as an open question for a possible extensionof this work. These results globally show that domains sharing terms remain in isolation, despite sharing somecommon problematics and subjects.We conclude this analysis with a quantification of proximities between the layers of the hypernetwork. It isstraightforward to construct a correlation matrix between two classifications, through the correlations of theircolumns. We define the probabilities P C all equal to 1 for the citation classification. The correlation matrixbetween it and P extends from -0.17 to 0.54 and has an average with an absolute value of 0.08, what is significantin comparison to random classifications since a bootstrap with b = 100 repetitions with shuffled matrices gives aminimum at − . ± . . ± .
02 and an absolute average at 0 . ± . b = 100 gives a value of 0 . ± . We have in this paper sketched an overview of disciplines and approaches in relation to the modeling of interactionsbetween transport and land-use, and also their relations. We provide an interdisciplinary bibliometric study, fromcitation and semantic viewpoint, confirming the diversity and complementarity of approaches. The companionpaper of this work [Raimbault, 2020b] aims at understanding with more details and more exhaustively the contentof each field and corresponding models.A possible direction to extend this quantitative epistemological analysis would be to work on full textes relatedto the modeling of interaction between networks and territories, with the aim to automatically extract thematicswithin articles. Methods more suited for full texts than the one used here for example include Latent DirichletAllocation [Blei et al., 2003]. The idea would be to perform some kind of automatised modelography, extending themodelography methodology developed by [Schmitt and Pumain, 2013], to extract characteristics such as ontologies,model architecture or structures, scales, or even typical parameter values, as done manually in [Raimbault, 2020b].It is not clear to what extent the structure of models can be extracted from their description in papers and itsurely depends on the discipline considered. For example in a framed field such as transportation planning, usinga pre-defined ontology (in the sense of a dictionary) could be efficient to extract information as the disciplinehas relatively strict conventions. In theoretical and quantitative geography, beyond the barrier of diversity ofpossible formalisations for a same ontology, the organisation of information is surely more difficult to grasp throughunsupervised data-mining because of the less framed and literary nature of the discipline: synonyms and figures ofspeech are more frequent in social sciences and humanities, making it more difficult to extract a possible genericstructure of knowledge description.The methodology developed here is efficient to provide reflexivity instruments, i.e. it can be used to studyour approach itself. One of its application is to the scientific journal Cybergeo in a perspective of Open Scienceand reflexivity in [Raimbault, 2019a]. Combined with complementary bibliometrics methods into an interactiveweb application as described by [Raimbault et al., 2021], this allows journal authors and editors to better situatetheir work in the literature and thus enhance reflexivity. One other application to scientific reflexivity is done by[Raimbault, 2018a] on its own corpus of references, with the aim to reveal possible neglected research directions ornovel issues. A possible way to extend this approach would be to produce scientific maps in a dynamical way, usingthe git history which allows to recover any version of the bibliography at a given date during the duration of theproject.Such approaches also provide a better understanding of knowledge production patterns, what can be linked toquantitative epistemology in general [Chavalarias and Cointet, 2013], and more specifically to the theoretical andempirical construction of knowledge frameworks to grasp complexity, such as the one described by [Raimbault, 2017].To conclude, we proposed in this paper to survey and map through bibliometric methods a landscape of dis-ciplines dealing with the modelling of land-use and transport, and of relations between these disciplines, in termsof citations but also of level of interdisciplinarity. We showed a high diversity and complementarity, and a strongpotential for novel approaches bridging these viewpoints.
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