Florent Demoraes

Vincent Gouëset

Marc Souris

Adrian Morfee

What can analysis of Space-Time of Action tell us about medium-term changes in adults' and children's access to place of activity? The example of Bogotá

Keywords: Medium-term urban change, joint accessibility, daily mobility, Space-Time of Action, spatiotemporal mismatch, life course stage, diachronic analysis, bivariate colocation test, Bogotá Daily mobility, Sustainable mobility practices, Public policies, Residential strategies and mobilities, Latin American metropolises Spatial Analysis, Statistics and modelling, epidemiology, health geography

Résumé

S'inspirant à la fois du prisme spatio-temporel formalisé dans la time-geography [START_REF] Hägerstrand | What about People in Regional Science? 9th European Congress of the Regional Science Association[END_REF]) et mobilisant des méthodes d'analyse spatiale, cet article a pour but d'étudier la façon dont l'accès des membres des ménages à leur lieu d'activité a évolué sur le moyen terme à l'aune des changements urbains survenus sur la même période. Pour ce faire, l'analyse repose sur le concept d'espace-temps d'action (Demoraes et al. 2020a) entendu comme l'ensemble des lieux de destination des individus pour le travail et les études, et le temps qu'ils mettent pour s'y rendre au quotidien depuis leur domicile. L'analyse s'appuie sur deux enquêtes conduites à Bogotá (Colombie) en 1993 et 2009, pour appréhender les mobilités spatiales des individus. Deux groupes à des étapes différentes du cycle de vie et qui corésident au sein des mêmes ménages sont étudiés : les écoliers et les adultes actifs. Dans un premier temps, les espaces-temps d'action sont calculés et cartographiés en gardant les limites extérieures des noyaux de concentration des lieux de destination obtenus par lissage spatial pour les deux groupes et les neuf zones d'enquête aux deux dates. Ensuite, la significativité statistique des écarts entre les espaces-temps d'action est évaluée à l'aide d'un test de colocation bivarié. Le test indique une stabilité globale dans l'accès des enfants à leur école et une situation plus contrastée pour les adultes.

Mots-clefs

Changement urbain de moyen terme, accessibilité conjointe, mobilité quotidienne, espace-temps d'action, découplage spatio-temporel, étape biographique, analyse diachronique, test de colocation bivarié, Bogotá

Resumen

Basándose en el prisma espacio-temporal formalizado en la time-geography [START_REF] Hägerstrand | What about People in Regional Science? 9th European Congress of the Regional Science Association[END_REF]) y utilizando métodos de análisis espacial, este artículo tiene por objeto examinar cómo ha evolucionado a mediano plazo el acceso de los miembros de los hogares a su lugar de actividad en acorde con los cambios urbanos durante el mismo período. Para ello, el marco analítico utiliza el concepto de espacio-tiempo de acción (Demoraes et al. 2020a) entendido como el conjunto de lugares donde las personas van a trabajar y estudiar y el tiempo que tardan en llegar allí diariamente desde su lugar de residencia. El análisis se basa en dos encuestas realizadas en Bogotá (Colombia) en 1993 y 2009 diseñadas para aprehender las movilidades espaciales de los individuos. Se estudian dos grupos en diferentes etapas del ciclo de vida y que co-residen dentro de los mismos hogares: los escolares y los adultos que trabajan. En un primer paso, se calculan y cartografían los espacios-tiempos de acción utilizando los límites exteriores de los núcleos de concentración de los lugares de destino, obtenidos mediante el alisamiento espacial para los dos grupos y las nueve áreas de estudio en ambas fechas. A continuación, se evalúa la significatividad estadística de las diferencias entre los espacio-tiempos de acción mediante una prueba de colocación bivariada. La prueba indica una estabilidad general en el acceso de los niños a su escuela y una situación más contrastada para los adultos.

Palabras clave

Cambio urbano de mediano plazo, accesibilidad conjunta, movilidad diaria, espacio-tiempo de acción, desajuste espaciotemporal, etapa biográfica, análisis diacrónico, prueba de colocación bivariada, Bogotá

Introduction: household trips, joint mobility of parents and children, and urban change

As stated in Demoraes et al. (2020a), "many studies in environmental psychology, sociology, demography, and geography have demonstrated the relevance of studying jointly the mobility of household members. Their daily trips start from the same place of residence, whose location influences the mobility practices of each member".

In terms of daily travel distance or time, some home locations may benefit certain members to the detriment of others, given that the mode of transport and travel times of each individual tend to influence those of the others [START_REF] Hägerstrand | What about People in Regional Science? 9th European Congress of the Regional Science Association[END_REF][START_REF] Pratt | On the links between home and work: family household strategies in a buoyant labour market[END_REF][START_REF] Singell | An empirical analysis of the commute to work patterns of males and females in two-earner households[END_REF][START_REF] Aguiléra | Travailler et se déplacer au quotidien dans une métropole. Contraintes, ressources et arbitrages des actifs franciliens[END_REF]. For France, mention may be made of the work by [START_REF] Berger | Mobilité résidentielle et navette. Les arbitrages des ménages d'Ile-de-France[END_REF] on trade-offs regarding residential mobility and commutes within households in the Ile-de-France, and that by [START_REF] Jouffe | Faire face aux inégalités de mobilité. Tactiques, stratégies et projets des ménages pauvres en périphérie parisienne[END_REF] on the plans and tactics of poor households on the outskirts of Paris for coping with mobility inequalities. Equally, [START_REF] Aguiléra | Travailler et se déplacer au quotidien dans une métropole. Contraintes, ressources et arbitrages des actifs franciliens[END_REF] have examined the link between working adults' lifestyle and mobility in Ile-de-France. In Latin America, Pérez [START_REF] López | Movilidad cotidiana, dinámicas familiares y roles de género: análisis del uso del automóvil en una metrópoli latinoamericana[END_REF] have studied arrangements and negotiations over car use in families in Mexico. [START_REF] Gouëset | Recorrer la Metrópoli. Prácticas de movilidad cotidiana y desigualdades socio-territoriales[END_REF] have examined how spouses in Bogotá combine their commutes as a function of their income, and at the combination of their modes of transport.

Still focusing on the family unit, other scholars adopting qualitative approaches have analyzed compromises or negotiations in families' everyday mobility, and looked at the joint daily journeys of parents and children, the latter being economically dependent on the former and reliant on where their parents reside [START_REF] Jensen | Together and Apart: Affective Ambiences and Negotiation in Families' Everyday Life and Mobility[END_REF][START_REF] Nansen | Children's interdependent mobility: compositions, collaborations and compromises[END_REF][START_REF] Rau | Shared journeys, linked lives: a relational-biographical approach to mobility practices[END_REF][START_REF] Waitt | Parenting, care and the family car[END_REF]. Depending on the age of the children studied, scholars have analyzed the spatiotemporal interdependence of trips by adults and children, or, on the contrary, the extent to which children's trips are independent of those of their parents [START_REF] Depeau | Les trajets domicile-école en milieux urbains : quelles conditions pour l'autonomie de l'enfant de 10-12 ans ?[END_REF], both for daily commutes [START_REF] Mcdonald | Household interactions and children's school travel: the effect of parental work patterns on walking and biking to school[END_REF][START_REF] Mclaren | Parent-child mobility practices: revealing 'cracks' in the automobility system[END_REF][START_REF] Fyhri | Children's active travel and independent mobility in four countries: Development, social contributing trends and measures[END_REF]) and for journeys made during free time or for leisure activities [START_REF] Depeau | Routines and informal situations in children's daily lives[END_REF]. In many countries, such as in France with its system of school zoning, primary and secondary school children tend to travel a short distance from their place of residence. To apprehend these joint mobilities and resultant family trade-offs, sophisticated data collection procedures have been developed. One instance of this is the longitudinal procedure developed in France for the ANR MOBIKIDS research program [START_REF] Depeau | MK-MOBIBACK: un dispositif hybride et intégré pour enquêter finement les mobilités quotidiennes des familles[END_REF], relating specifically to children in transition between their final year at primary school and first year at secondary school.

The variables selected for these studies tend to be distance (either Euclidian or network-based), travel time, mode of travel, frequency of trip by purpose, income or social position, level of education, gender, and age. It may be noted that these works tend not to analyze or map the spatial location of daily itineraries by co-resident individuals, except that by [START_REF] Depeau | Routines and informal situations in children's daily lives[END_REF]. Furthermore, as stated in Demoraes et al. (2020a), "with only a few exceptions [START_REF] Aguiléra | Travailler et se déplacer au quotidien dans une métropole. Contraintes, ressources et arbitrages des actifs franciliens[END_REF][START_REF] Berger | Mobilité résidentielle et navette. Les arbitrages des ménages d'Ile-de-France[END_REF][START_REF] Fyhri | Children's active travel and independent mobility in four countries: Development, social contributing trends and measures[END_REF], these studies tend to examine joint mobility practices at a given point in time, thus precluding examination of how they change over the course of one or two decades. Lastly, they do not analyze how travel times or the destinations of individuals residing in the same neighborhood may evolve against the backdrop of contextual medium-term changes". One such change is alterations to demographic structure, such as the ageing of the population or alterations to household composition, with single-parent families and dual-income couples now being more numerous. Changes also stem from transformations linked for instance to urban sprawl, shifts in areas of employment or education, alterations to the transport system, deepening residential segregation, and so on and so forth.

Drawing on the space-time prism as formalized in time-geography [START_REF] Hägerstrand | What about People in Regional Science? 9th European Congress of the Regional Science Association[END_REF] and on a spatial analysis approach, this article sets out to examine medium-term changes to adults' and children's access to place of activity in the city. We also seek to understand how the mobility conditions for these two groups at different "Latin American metropolises in globalization. Territorial reconfigurations, spatial mobility, public action".

The first section introduces the relevance of the concept of STA for assessing individual's access to their place of activity. Bogotá, the city for which STAs have been calculated, is presented in section 2. Section 3 details the material used, the population studied, the method for calculating and mapping STAs, and the statistical test used to check if they have evolved over time. Results are discussed in section 4. All GIS processing was performed in SavGIS, a freeware GIS (www.savgis.org).

The concept of Space-Time of Action: a way of assessing individuals' access to places of activity

The concept of Space-Time of Action derives from the concept of Action Space, used in the human and social sciences since the 1930s (Von [START_REF] Dürckheim | Untersuchungen zum gelebten Raum[END_REF][START_REF] Lewin | Field Theory in Social Science: selected theoretical papers[END_REF]. The concept of Action Space is found in studies about migration (Wolpert, 1965), in cognitive and behavioral studies (Höllhuber 1974, Golledge and[START_REF] Golledge | Spatial Behavior: A Geographic Perspective[END_REF], and in those about daily or weekly mobilities [START_REF] Dijst | Two-earner families and their action spaces: A case study of two Dutch communities[END_REF][START_REF] Janelle | Diurnal patterns of social group distribution in Canadian cities[END_REF][START_REF] Noël | Aménagement du territoire et espaces d'action : Identification des déterminants des stratégies de déplacements de cyclistes de la région de Québec à l'aide d'un SIG[END_REF]. [START_REF] Dijst | Two-earner families and their action spaces: A case study of two Dutch communities[END_REF] provides the following definition: "the spatial unit in which the activity spaces are located and which have been visited by a person during some period of time is called the actual action space".

Action space is thus based on a set of places that an individual or group of individuals visit, primarily described using spatial metrics (mean position, dispersal, size, or distance from home). But as pointed out in Demoraes et al. (2020a), "working solely with spatial metrics is far from satisfactory if we are to apprehend individuals' access to their place of activity. Indeed, spatial metrics conceal many aspects of mobility conditions, particularly travel times. It is especially important to include the time of travel, for travel time may vary greatly for a given distance depending on the mode of transport, any connections needed (with it often easier to travel from center to periphery than from periphery to periphery), as well as the availability of a mass transit system near the place of residence".

For this reason, Demoraes et al. (2020a) suggest the concept of Space-Time of Action, referring to "all the destinations visited by individuals for work or study, together with the time they take to reach them from their home on a daily basis". The concept of STA has the advantage of broadly re-transcribing several dimensions of how individuals or groups of individuals access urban space. Indeed, following the definition put forward in [START_REF] Bavoux | Dictionnaire d'Analyse Spatiale[END_REF], "four main components of accessibility may be identified: (1) the performance of the transport networks used and services delivered, expressed in terms of time, expenditure, and/or effort, determining how easy or difficult the trip is;

(2) the nature and spatial distribution of the resource to reach; (3) time constraints relating to social functioning (working hours, the time at which the school day starts and finishes, when shops open and shut, etc.); (4) the characteristics of the individuals prone to travel (age, physical aptitude, income, education, etc.)". The concept of STA includes the first component, for travel times account not only for distance from the destination but also for the performance of the mode of transport used, and indirectly for difficulty in travelling. It also includes the second component, for it resumes the nature of the places to reach (work or study) and their spatial distribution. Travel times are also indicators of hours of work or study (the third component) in so far as, all other things being equal (the same mode of transport from the same point of departure to the same destination), the time spent travelling varies depending on whether it is rush hour or not. In the case of commutes, most take place at rush hour. Lastly, STA can also be calculated for groups sharing the same characteristics (the fourth component), and so be compared.

In Latin America, travel times are especially linked to individuals' sociodemographic characteristics, being longest for the most disadvantaged [START_REF] Antico | Onde morar e onde trabalhar: espaço e deslocamentos pendulares na região metropolitana de São Paulo[END_REF][START_REF] Cosacov | Más allá de la vivienda: los usos de la ciudad: movilidad cotidiana de residentes en Buenos Aires[END_REF][START_REF] Demoraes | Mobilités quotidiennes et inégalités socio-territoriales à Bogotá, Santiago du Chili et São Paulo. Espace, Populations[END_REF][START_REF] Jirón | Prácticas de movilidad cotidiana urbana. Un análisis para revelar desigualdades en la ciudad[END_REF][START_REF] Jirón | Exclusión y desigualdad espacial: Retrato desde la movilidad cotidiana[END_REF][START_REF] Jouffe | Las prácticas cotidianas frente a los dispositivos de la movilidad. Aproximación política a la movilidad cotidiana de las poblaciones pobres periurbanas de Santiago de Chile[END_REF], even though place-specific effects may alter this general tendency [START_REF] Demoraes | Inégalités d'accès aux ressources de la ville analysée à l'aide des mobilités quotidiennes -Approche méthodologique exploratoire à São Paulo[END_REF]. Indeed, individuals from disadvantaged households residing in central spaces may have relatively shorter travel times. This is, however, only infrequently the case.

Bogotá, a city undergoing transformation

Bogotá is the capital of Columbia (map 1). It is a city undergoing extensive transformation due to the vigorous urban and demographic dynamics at work there [START_REF] Dureau | Les inégalités d'accès aux ressources urbaines dans des quartiers périphériques en mutation nouvellement desservis par le Transmilenio à Bogotá (Colombie)[END_REF], and to its having followed since the early 1990s globalized urban models, such as that of Barcelona [START_REF] Montoya | Bogotá, urbanismo posmoderno y la transformación de la ciudad contemporánea[END_REF]. The metropolitan area of Bogotá is composed of a very extensive city center, the District Capital (DC), subdivided into 20 localidades or localities, together with 19 suburban municipalities (map 2). The city center is heavily populated, with 4.9 and 6.7 million inhabitants respectively at the time of the two censuses (1993 and 2005) closest to the two surveys used in this article, amounting respectively to 90% and 88% of the total metropolitan population. Nevertheless, demographic growth in the central localities of the DC has since slowed (map 2), with the highest growth rates now being in the outer localities, and especially in the municipalities outside the DC (Le Roux 2015). This urban sprawl was accompanied by changes in socio-residential segregation. Socio-residential segregation is a classic process in Latin America [START_REF] Carman | Segregación y diferencia en la ciudad[END_REF][START_REF] Capron | Las escalas de la segregación y de la fragmentación urbana[END_REF][START_REF] Demoraes | Vulnérabilités, mobilités et inégalités dans les métropoles d'Amérique latine. Approche socio-spatiale[END_REF], Dureau et al. 2014c[START_REF] Kilroy | Intra-urban spatial inequality: Cities as urban regions, Reshaping Economic Geography[END_REF][START_REF] Schteingart | La división social del espacio en las ciudades[END_REF]. In Bogotá, the wealthier classes (photo 1) have long been concentrated in the north-east of the District Capital, and the poorer classes (photo 1) have long been relegated

to the southern and north-western edges of the DC and to most of the suburban municipalities [START_REF] Demoraes | Análisis comparativo de la segregación social en Bogotá, Santiago y São Paulo[END_REF][START_REF] Dureau | Métropoles en mouvement : une comparaison internationale[END_REF]Dureau, Contreras et al. 2014;[START_REF] Salas | Ségrégation résidentielle et production du logement à Bogotá, entre images et réalités[END_REF]. On the cartogram, the size of the spatial units is distorted as a function of the number of households classed using the Social Condition Index (SCI). The SCI is a commonly used index in Latin America (Barbary et al., 1999;[START_REF] Dureau | Ciudades y sociedades en mutación. Lecturas cruzadas sobre Colombia[END_REF][START_REF] Salas | Ségrégation résidentielle et production du logement à Bogotá, entre images et réalités[END_REF]Le Roux, 2015;[START_REF] Demoraes | Metodología de cálculo y cartografía del Índice de Condición Social de los hogares -Aplicación al Área Metropolitana de Bogotá con base en el censo de 2018[END_REF]. It is obtained from individual census data. The index is calculated as follows: the educational climate (average years of education of people aged 15 and over in the household) is divided by the promiscuity index (number of people in the household divided by the number of rooms in the dwelling). We here retain solely classes 1 (SCI1) and 6 (SCI6), corresponding respectively to the poorest and richest 10%. The smoothed surface conveys the ratio of observed numbers to expected numbers were the distribution of households spatially uniform, a distribution which would thus correspond to that of a non-segregated city. This ratio shows what could be called the deviation from uniformity for each SCI. When the ratio is above 1, this means that there is an overrepresentation, and vice versa.

These processes of urban sprawl and segregation, together with the fragmented [START_REF] Alfonso | Bogotá segmentada: Reconstrucción histórico-social de la estructuración residencial de una metrópoli latinoamericana[END_REF] or polycentric pattern of Bogotá [START_REF] Beuf | Les centralités à Bogotá, entre compétitivité urbaine et équité territoriale[END_REF], Le Roux 2015), mean that resources are unequally distributed across the metropolitan areas. Work opportunities are spatially concentrated (map 5), with job density tending to disadvantage the poorer localities and municipalities. This urban model, which is very common in Latin America, places major constraints on people's daily mobility. Commutes are much longer, take more time, and are much more expensive for households living far away from the inner city of Bogotá. The level of public transport service is much lower and more informal in the outskirts. Moreover, in 2009 suburban municipalities still did not have an integrated transport system with the DC [START_REF] Moreno | Segregación en el espacio urbano de Soacha. ¿Transmilenio como herramienta integradora?[END_REF]. Concerning education, a broad distinction may be made between two different rationales, one pertaining to primary and secondary schools, the other to higher education. In the first case, public schools are uniformly distributed in space, while the best reputed private schools are concentrated in the upmarket districts or suburban municipalities (particularly in Chía, see map 1). The universities are mainly concentrated in the city center and on the northern outskirts of Bogotá, with certain specific improvements between the two dates:

while mid-quality technological and higher education courses became available in the poorer outskirts, more upmarket university courses developed in the wealthy localities of the capital and in the municipality of Chía.

Lastly respective purposes and methodologies are detailed in [START_REF] Dureau | La movilidad de las poblaciones y su impacto sobre la dinámica del área metropolitana de Bogotá. Documento de trabajo nº 2 : metodología de la encuesta cuantitativa[END_REF] and [START_REF] Dureau | Encuestas movilidad espacial Bogotá METAL 2009: metodología de las encuestas[END_REF][START_REF] Dureau | Una metodología de producción y análisis de la información común a las tres metrópolis[END_REF]. In these surveys, spatial mobility was studied in a global approach including all mobilities irrespective of distance (intra-urban travel or to the rest of the national territory or abroad) and travel time (ranging from daily trips to migrations). Nine survey zones were common to the two dates (map 1).

Material and method of analysis

These zones constitute an illustrative mosaic of the range of socio-economic profiles, housing conditions, and urbanization stages (map 3) in the Bogotá metropolitan area. This diversity derives directly from the sampling method implemented in the 1993 and 2009 projects [START_REF] Dureau | La movilidad de las poblaciones y su impacto sobre la dinámica del área metropolitana de Bogotá. Documento de trabajo nº 2 : metodología de la encuesta cuantitativa[END_REF][START_REF] Dureau | Encuestas movilidad espacial Bogotá METAL 2009: metodología de las encuestas[END_REF], whose objective was to confirm the influence of these parameters on households' mobility. These zones thus bring out the wide variety of daily mobility strategies households use, and also show highly contrasting levels of access to activity places as analyzed in Demoraes et al. (2020a;2020b), [START_REF] Dureau | Cambios urbanos, transporte masivo y desigualdades socioterritoriales en unos barrios del occidente de Bogotá[END_REF] and [START_REF] Dureau | Les inégalités d'accès aux ressources urbaines dans des quartiers périphériques en mutation nouvellement desservis par le Transmilenio à Bogotá (Colombie)[END_REF]. It should be noted that the households surveyed at the two dates were statistically representative of their zone of residence. It should also be noted that it was not a longitudinal survey, for the households surveyed in 1993

were not the same as those surveyed in 2009.

This article uses only one component of these two surveys, namely commutes from home to place of activity (place of work and place of study), collected in similar fashion at both dates. Given the purpose of the surveys (an overall understanding of all forms of mobility throughout the life cycle), and the quantity of information which may be gathered in a reasonable length of time using a questionnaire, sequences within daily journeys were not recorded. We therefore do not have details about the routes through the city, only about one destination per day per individual recorded at the level of sectors, which is a fairly fine-grained spatial level (there being 630 sectors in all in the Bogotá metropolitan area, map 2). In addition to destination, we also have data for both dates concerning mode of transport and travel time.

The fact that there is only one destination per day and per person (the place of work or study) implies that the accessibility we characterize is only one facet in individuals' overall accessibility to the city's resources. In Bogotá, this overall accessibility is in fact not so different from that measured based solely on places of work and study.

Indeed, the last three major origin-destination surveys in 2005, 2011, and 2019 respectively show that in Bogotá, 59%, 57%, and 55% of trips were made to work or study (excluding the return home). Most trips are therefore essential, non-delegable, and non-deferrable (except in the context of a pandemic), and clearly mark the pulse of the city. Furthermore, polygonal mobility in Bogotá is rare, i.e., on days when a person is working or studying, they make very few trips on the same day for other purposes. This is due both to the high cost of transport in relation to household income and to the length of the journeys, which involve leaving home very early in the morning and returning very late at night with no time for other activities. In addition, the working week is 48 hours, also leaving little time for other activities.

As already pointed out in Demoraes et al. (2020a), "both CEDE-ORSTOM and ANR-METAL surveys are precious sources of data without equivalent for Bogotá for the period under consideration. One of the limits to detailed study of daily mobility in Colombia, as in many Latin American countries, relates to the paucity of secondary sources, mainly origin-destination surveys and, to a lesser extent, population censuses". Origin-destination surveys provide overall knowledge about daily trips (their frequency and intensity) depending on age, gender, mode of transport, purpose, and income. They also provide information about household car ownership rates.

These surveys have the advantage of being representative of the entire city and being conducted regularly, following a largely standardized methodology enabling diachronic analysis. However, in the case of Bogotá, the

Selection of the study population

To meet our objective of understanding medium-term changes in how co-residing children and adults access their activity places, we selected households with at least one working individual (with a main or secondary paid activity, including at home) and at least one child in primary or secondary education (table 1). We thus retained 49% of households surveyed in 1993, and 44% of those surveyed in 2009. We excluded students from our study, because there were too few of them among the households surveyed, especially in 1993, and so analyzing them would have led to insignificant results.

Principle and method of calculating Space-Time of Action for groups of individuals

The principle for calculating Space-Time of Action we adopted in this article is inspired by that detailed in Demoraes et al. (2020aDemoraes et al. ( , 2020b)). STAs were calculated at an aggregated level, that is, by category of individual (working adults, schoolchildren) and for each survey zone for the two dates (1993 and 2009) so as to detect changes in how these categories access their activity place on a daily basis. Each category for each survey zone and for each date is hereafter referred to as a group.

To calculate the STAs, we used location of place of residence (at the city block scale), location of place of activity (at the sector scale), and travel time. These three variables were processed using a series of GIS operations. This The locations of PTAs form a simple point pattern that can be summarized to shape a STA for each category of individual (working adults, schoolchildren) and for each survey zone for the two dates (1993 and 2009). Several methods (standard deviational ellipses, travel probability fields, kernel density estimations, convex-hull polygons, Cassini ovals, bean curves, etc.) exist for summarizing and visualizing point patterns. For an extensive review of these mapping techniques, see [START_REF] Schönfelder | Activity spaces: Measures of social exclusion?[END_REF], [START_REF] Rai | Capturing Human Activity Spaces[END_REF], Lord et al. 2009, Patterson and[START_REF] Patterson | Potential Path Areas and Activity Spaces in Application: A Review[END_REF], and [START_REF] Vich | Suburban commuting and activity spaces: using smartphone tracking data to understand the spatial extent of travel behavior[END_REF].

We experimented with three of these methods, namely standard deviational ellipses, convex-hull polygons, and kernel density estimations, which seemed well suited to our data and for mapping STAs at an aggregated level, by group of individuals in our case. In the end, we opted for kernel density estimations, also called smoothed surfaces or heat maps (map 7). We used these surfaces mainly because they schematize very accurately the spatial distribution of the point patterns, unlike standard deviational ellipses which are far too sketchy. We also discarded convex-hull polygons which connect the furthest removed points without taking the distribution of the other points into account, thus tending to exaggerate the extent of STAs. More specifically, after several trials, we used the following parameters to compute the smoothed surfaces: a 1000-meter-bandwith, 2 a triangular smoothing function, 3 and a sum function to calculate local concentrations. 3 The triangular function relies on a linear decreasing function of the weight of the neighbours to be considered in the calculation. It thus gives an aesthetic result with a regular colour scaling.

To display the STA of two groups on a single map (and so detect any changes between 1993 and 2009) and to better delineate the STAs, we vectorized the heat map (initially a raster layer). For each group, this produced a kernel density outer ring which is a polygon encompassing all the PTAs of a group (map 8 and map 9). We applied the same method for the two categories of individuals (working adults, schoolchildren) in the 9 survey zones for the two dates. We therefore computed STAs portrayed in 18 facetted maps (map 10). Visual examination of these maps indicates apparent discrepancies between STAs in many cases, but may we really detect changes between 1993 and 2009 in how groups of individuals access their place of activity?

H 0 H f n i A H 0 H 0 H f n i A H p u s A H f n i A H p u s A H p u s A H f n i A H f n i A H d i r d a M - 0 1 9 0 0 2 n i n o i t c a f o e m i t - e c a p s s ' n e r d l i h C 3 9 9 1 n i n o i t c a f o e m i t - e c a p s s ' n e r d l i h C a í h C - 8 0 9 0 0 2 n i n o i t c a f o e m i t - e c a p s ' s t l u d A 3 9 9 1 n i n o i t c a f o e m i t - e c a p s ' s t l u d A a í h C - 8 0 d i r d a M - 0 1 9 0 0 2 n i n o i t c a f o e m i t - e c a p s s ' n e r d l i h C 3 9 9 1 n i n o i t c a f o e m i t - e c a p s s ' n e r d l i h C 9 0 0 2 n i n o i t c a f o e m i t - e c a p s ' s t l u d A 3 9 9 1 n i n o i t c a f o e m i t - e c a p s ' s t l u d A a h c a o S - 1 1 9 0 0 2 n i n o i t c a f o e m i t - e c a p s s ' n e r d l i h C 3 9 9 1 n i n o i t c a f o e m i t - e c a p s s ' n e r d l i h C a h c a o S - 1 1 9 0 0 2 n i n o i t c a f o e m i t - e c a p s ' s t l u d A 3 9 9 1 n i n o i t c a f o e m i t
- á t o g o B - s y e v r u s 9 0 0 2 L A T E M R N A d n a 3 9 9 1 M O T S R O - E D E C : s e c

Assessing the significance of the differences between Space-Times of Action using a bivariate colocation test

Space-Times of Action can be modeled as two-dimensional objects. We therefore used a spatial statistical test to assess the significance of the spatial differences between these objects. More specifically, we selected a bivariate colocation test primarily used in spatial epidemiology [START_REF] Souris | Statistical methods for bivariate spatial analysis in marked points. Examples in spatial epidemiology[END_REF]. This test ascertains whether, overall, the points of one spatial distribution are significantly close to points of a second spatial distribution. Souris and Bichaud applied this colocation test to check if cases of two diseases were spatially congruent. We selected this test for our study because it seemed well suited to checking any discrepancies between the STAs associated with the groups described earlier. A first attempt at applying the bivariate colocation on action spaces in Santiago de Chile may be found in [START_REF] Demoraes | Live nearby, be different, work apart? Some learnings from action spaces discrepancies in Santiago de Chile[END_REF]. A formal description of this test, detailed in Souris (2019: 135-136), is summarized below.

The bivariate colocation test works on the following principles. Let S1 represent a set of N1 locations, S2 a set of N2 locations. Each location is characterized by a Boolean mark (0 or 1). P1 is the set of positive locations in S1, and P2 the set of positive locations in S2. In our case, P1 represents the PTAs of the individuals belonging to group 1 (for instance, schoolchildren living in Gustavo Restrepo in 1993), and P2 the PTAs of the individuals belonging to group 2 (to keep the same example, schoolchildren living in the same survey zone in 2009). First, the Euclidian distance between each PTA from group 1 and its closest PTA from group 2 is calculated. Second, the mean of these distances is computed. This mean is hereafter referred to as the index.

Two hypotheses can be stated:

• a null hypothesis H0: the observed index cannot be differentiated from the indices obtained by a random spatial distribution of the positive marks. If the test returns H0, no spatial relation between the two point patterns can be detected. In this case, it cannot be said that there was any stability or, on the contrary, any significant change in how groups of individuals access their place of activity;

• an alternative hypothesis HA: the probability of obtaining the observed index by chance is lower than a determined α value (0.05 for instance). If the test returns HA, a spatial relation between the two point patterns does exist. In this case, the relation can either be a significant similarity (no change) or a significant dissimilarity (significant change) as we shall see below.

The statistical distribution of the index under the H0 hypothesis is estimated using a Monte Carlo simulation (4,000 iterations): at each iteration and for each zone, the P2 PTAs are randomly permuted among S2, which refers to all PTAs of individuals living in the zone in 2009, and the index is calculated using the P1 PTAs. The probability of the observed index can be inferred from this estimated statistical distribution. The null hypothesis (H0) is rejected if the probability of the observed index is lower than the α value, which equates to a risk of wrongly rejecting H0 (Type I Risk).

For our analysis, we used bilateral tests to search for both similarity and dissimilarity. We compared the STAs of pairwise groups for each of the survey zones. If the observed index is lower than the lowest simulated indices (Iobs < Imin-sim), the null hypothesis is rejected and HAinf is accepted, meaning that the two point patterns are significantly characterized by global similarity. If the observed index is greater than the greatest simulated indices (Iobs > Imax-sim), the null hypothesis is rejected and HAsup is accepted, meaning that the two point patterns

Results and discussion

The results of the statistical colocation tests indicate an overall stability in children's access to place of schooling in 6 out of the 9 survey zones, and a more contrasting situation for adults. More specifically, the results bring out four types of change between 1993 and 2009 if we conjointly consider how schoolchildren and working adults access their place of activity (table 2).

The first type of combined change is observed in four survey zones (Gustavo Restrepo, San Cristobal Norte, Bosa, and Soacha). In these zones, there was a significant stability in children's access to place of school, but the situation for working adults changed significantly. The second type encompasses Candelaria and Chía. In these zones, children's access to place of school was also significantly stable, but there is no evidence of any significant trend concerning working adults' access to place of work. The third type corresponds to Normandía, where we may observe the opposite situation. The fourth type is characterized by Perseverancia and Madrid. In these zones, we may observe neither any significant stability nor any significant change for either children or adults. In short, in Bosa, Gustavo Restrepo, and Soacha (type 1), children's access to place of schooling remained stable, with a rather low spatiotemporal mismatch between home and school (the maximum Distance-Time being 3.19km), but the situation for working adults worsened between the two dates (larger STAs and longer Distance-Times). In other words, home location became less favorable for working adults than for children in these three survey zones over the period under study.

Conversely, in San Cristobal Norte (also type 1), a zone which urbanized mainly in the 2000s (map 3), Distance-Times for working adults decreased from 5.98km to 4.72km between 1993 and 2009, whereas children's access to place of schooling remained stable. This improvement for working adults is also consistent with the information derived from map 12. The 2009 STA is much smaller (27.6km²) than the 1993 STA (48.3km²) and is less offset from the survey zone. This can be explained both by the increase in the use of public transport, whose modal share rose from 45.8% to 61.4%, and by the decrease in travel time in public transport, which dropped from 52 to 38 minutes over the same period. This reduction in travel time is mainly due to the commissioning of the Transmilenio in 2001, providing a fast service whose route passes not far from the study area.

As we saw, the case of Normandía (type 3) is unusual because it is the only survey zone with a significant stability in the SPAs of working adults between 1993 and 2009. Unfortunately, no significant conclusion can be drawn for schoolchildren residing there. The Distance-Time between home and work remained stable, at around 4.3km, corresponding to a comparatively low spatiotemporal mismatch in the context of metropolitan Bogotá. The drop in the proportion working at home, from 35% to 22%, which could have led to longer travel times, was compensated by the emergence of new business zones near this neighborhood, in Ciudad Salitre, along the El Dorado avenue connecting downtown to the airport, and around the airport, among other areas (map 5).

Conclusion

Using the concept of STA, this article has analyzed changes over a sixteen-year interval in how two groups of individuals-at different stages in their life course and residing in nine illustrative neighborhoods-access their place of activity in the metropolitan area of Bogotá. With the city expanding and undergoing profound transformation between 1993 and 2009, our findings bring out two main rationales: an overall stability in children's access to place of schooling wherever they reside, and a worsening situation for working adults with a growing spatiotemporal mismatch in most significant cases. Still, two exceptions emerged from this overall trend. First, the case of Normandía, illustrating how deteriorating access to place of activity is not inevitable in a large metropolis, thanks notably to the emergence of secondary centralities. Second, the zone of San Cristobal Norte which benefited fully from the BRT service introduced nearby during the study period.

STAs therefore constitute an appropriate way of gauging the medium-term impacts of commissioning new transport infrastructure and of urban transformations, whether the latter are organized (such as planning operations) or spontaneous and not fully controlled (such as urban sprawl). Nonetheless, more empirical studies are needed. First, in Bogotá, to verify if the dual trend of stability for schoolchildren and enlarging STAs for working adults has continued over the past two decades. Second, to check if such a trend also arises in other Latin American cities. Indeed, improving access to the city for all population categories is a challenge for urban stakeholders striving to develop more inclusive and sustainable metropolises. Our next step will therefore be to apply the same methodology to process data we will be collecting in 2022 as part of the ANR-funded Modural program in Bogotá (https://modural.hypotheses.org/le-projet). The objective is to implement a similar processing method, at least for the two survey zones analyzed in this article, namely Bosa and Soacha.

Furthermore, from a methodological point of view, calculating STAs is simple using a GIS, requiring only three input variables (origin, destination, and travel time). It may thus be applied to numerous surveys for which individual destinations is available, and to places of activity other than work and school. Above and beyond the use made of STAs and bivariate colocation tests in this article, assessing the significance of discrepancies between STAs could be applied in many other domains, either for a given date or else in a diachronic perspective. For a given date, one of the first applications which comes to mind is linked to segregation or discrimination. Following a gender-based or racial approach, or focusing on handicapped people, for instance, the test could be used to identify social groups experiencing noteworthy inequalities in access to work, education, or leisure amenities. In a diachronic perspective, STAs could be used for instance for a longitudinal study of changes in accessibility to healthcare facilities for patients with a chronic illness, with a view to reorganizing healthcare provision within a territory. The approach also seems suitable for monitoring mediumterm transformations in center-periphery relations. A significant retraction in STAs between two dates would either indicate improved connectivity between the inner-city and the outskirts, or a maturing of the latter due to a growing number of local jobs, making the need to go downtown less compelling.

  stages in their life course have changed depending on where they reside in the city. The article works primarily with the concept of Space-Time of Action (STA) which provides a way of gauging one aspect of individuals' access to urban space. The analysis is based on data about commutes by working adults and their co-resident children gathered during two surveys at a sixteen-year interval in Bogotá (Colombia). The first survey was conducted in 1993 as part of a joint program headed by F. Dureau (ORSTOM) and C.E. Flórez (CEDE: Centro de Estudios sobre Desarrollo Económico de la Universidad de los Andes). The second was carried out in 2009 as part of the METAL research program headed by F. Dureau and funded by the French National Research Agency, under the title:

Map 1 :

 1 The location of Bogotá, main roads, transport network, and location of the nine survey zones at both dates(1993 and 2009) in the metropolitan area //gadm.org/download_country_v3.html) Right insert: author: G. LeRoux (2015: 129). Source: ANR METAL GIS database. Map 2: Changes to population distribution between 1993 and 2009 in the District Capital of Bogotá and Soacha Authors: F. Demoraes. Sources: DANE 1993, 2005. Data processing: A. Salas, ANR METAL The process of urban sprawl in Bogotá (map 3) has been well documented by various researchers (Garavito and De Urbina 2019, Montoya 2012, Salazar et al. 2014). Between 1990 and 2010, the area of the District Capital increased from 241km² to 327km². Over these two decades, urban sprawl filled in the interstitial gaps between built-up areas in the first outer-ring, and also reached the outskirts.

Map 3 :

 3 Photo 1 -Example of deprived housing in the southern outskirt versus upmarket building in the north-east of the District Capital of Bogotá

Map 4 :

 4 Evolution of socio-residential segregation between 1993 and 2005 based on the household's Social Condition Index (SCI) in the District Capital of Bogotá and Soacha Author: F. Demoraes. Adapted from Demoraes, Bouquet, and Mericskay 2021. Sources: DANE 1993 and 2005 -Initial data processing: A. Salas, M. Piron, and F. Dureau -Base map: A. Lepetit and F. Bahoken.

Map 5 :

 5 Changes to the distribution of jobs in the District Capital of Bogotá between 1992 and 2005 Author: F. Demoraes, taken from G. Le Roux (2015: 129). Sources: for 1992, taken from F. Dureau (2000: 249); for 2005, taken from DANE 2005. Data processing: G. Le Roux

3. 1 .

 1 Material used: two surveys for apprehending changes to spatial mobility in Bogotá between 1993 and 2009 Our analysis is based on two surveys conducted in Bogotá, devised in the wake of work by the GRAB research initiative (steered by INED-the French National Institute for Demographic Studies) to apprehend individuals' spatial mobilities from a biographical perspective. The first of these was the 1993 CEDE-ORSTOM survey headed by Dureau and Flórez, in which 922 households and 3,973 individuals were questioned; the second was the 2009 ANR-METAL survey, headed by Dureau, in which 881 households and 3,256 individuals were questioned. Their

  first major standardized OD survey dates from 2005. An earlier survey exists for 1996, financed by Japan, but it was devised using a specific methodology and sectorization, precluding comparison with the 2005 survey. Furthermore, it is not possible to access individual data for the 1996 survey. The only available results are aggregated by sector, making it impossible to study jointly the mobilities of various household members. The CEDE-ORSTOM and METAL surveys are thus the only sources for analyzing the changing conditions in which commutes were conducted by Bogotá households during the 1990s and 2000s, a pivotal period characterized, as seen earlier, by the mass expansion in the number of private cars and the commissioning of the Transmilenio.

  comprised three main stages. The first two stages are individual-based, and the same as those inDemoraes et al. (2020b). We refer the reader to this work for further explanation about these first two stages. The third stage is group-based and derived from that inDemoraes et al. (2020a). The three stages are the following: 1. Calculating distances and speeds 2. A series of translations 3. A series of calculations of smoothed surfaces and kernel outer rings.3.3.1. First stage: calculating distances and speeds (individual level)In the surveys we used, different travel times may be assigned to a single destination, either because individuals go there from different places, or because individuals departing from the same place of residence do not use the same mode of transport. It was thus a matter of retaining the times of individual trips for each destination to bring out any variations in how individuals access their activity place. In this first stage, calculations were therefore made at an individual level.The first step consisted in calculating the Euclidean distance for each origin-destination pair in 1993 and in 2009, and in calculating average speed of travel for each pair.1 The second step consisted in calculating overall average speed of travel for all the origin-destination pairs in 1993 and 2009. Since the objective was to define a synthetic measure of access to place of activity, we did not break this down into speed by mode of transport. It should be noted that for our reference population, overall average speed did not change between 1993 and 2009 (10.8km/h). In the third step, this average overall speed was used to calculate a Distance-Time, corresponding to the distance an individual would have travelled in the length of time recorded for their actual journey had they been travelling at the overall average speed. This distance-time was calculated using the following formula: Distance Time= OD Euclidean distance m * Overall average speed m/min Speed m/min 3.3.2. Second stage: translation operations (individual level) In this second stage, calculations were once again made at an individual level. Distance-Time was used to calculate the location of what we called Place-Times of Activity (PTAs). These lay at different distances aligned with the initial origin-destination segment (maps 5). PTAs are shifted as follows: = nearer to home when the individual reaches the place more quickly, i.e. at greater speed than overall average speed, = further from home when the individual reaches the place less quickly, i.e. at less than overall average speed. The PTA coordinates were calculated by applying trigonometric principles (more detail in Demoraes et al. 2020a). The location of PTAs is not solely geographic, since they include a time dimension (derived from travel time). PTAs were thus positioned in a new, spatiotemporal reference system. Map 6 shows the results of the operation for the group of working adults residing in the Gustavo Restrepo survey zone in 1993. Map 6: Comparison for working adults residing in 1993 in Gustavo Restrepo (Bogotá) of Activity Places (in blue) and Place-Times of Activity (in red), positioned respectively in planimetric and spatiotemporal reference systems Author: F. Demoraes. Source: 1993-CEDE-ORSTOM survey. 3.3.3. Third stage: smoothed surfaces and kernel outer rings (aggregate level, group-based)

Map 7 :

 7 Kernel density estimation (heat map) symbolizing the Space-Time of Action of working adults residing in Gustavo Restrepo in 1993 (Bogotá) Author: F. Demoraes. Source: 1993-CEDE-ORSTOM survey. 2 This bandwidth is a compromise to ensure a minimum number of PTAs are considered for the smoothing calculation given the nearest neighbour distance among PTAs. It also avoids excessively enlarging the STA around the furthest removed points.

Map 8 :

 8 Kernel density outer ring delineating the Space-Time of Action of working adults residing in Gustavo Restrepo in 1993 (Bogotá) Author: F. Demoraes. Source: 1993-CEDE-ORSTOM survey. Map 9: Kernel density outer rings delineating the Space-Times of Action of working adults residing in Gustavo Restrepo in 1993 and in 2009 (Bogotá) Author: F. Demoraes. Sources: 1993-CEDE-ORSTOM and 2009-METAL surveys.

  are significantly characterized by global dissimilarity. All in all, 18 tests were carried out (two tests for each one of the nine zones). Map 11 illustrates the principle of the test using the example of STAs associated with schoolchildren living in Gustavo Restrepo in 1993 and in 2009. The top map corresponds to the observed situation. The observed index equates to 768 meters. The other two maps below are the first 2 of the 4,000 iterations of the Monte Carlo simulation, given as examples. The first simulated index equates to 797 meters. The second equates to 808 meters. The related statistical distribution of the index under the H0 hypothesis based on the 4,000 simulations is plotted in graph 1. The observed index (768 m) lies outside the 95% confidence interval [785 m; 1353 m] and is lower than the lowest simulated indices (Iobs < Imin-sim). Hence the null hypothesis is rejected and HAinf is accepted, meaning that the two point patterns are significantly characterized by global similarity. In other words, the STA of schoolchildren living in Gustavo Restrepo in 1993 is significantly the same as the STA of schoolchildren living there in 2009. This result exhibits a significant stability in how children access their school from this survey zone between 1993 and 2009.

Graph 1 :

 1 Result of the bivariate colocation test for schoolchildren in Gustavo Restrepo Author: F. Demoraes. Sources: 1993-CEDE-ORSTOM and 2009-METAL surveys.

Table 2 :

 2 Test results of the significance of the differences between Space-Times of Action, by place of residence and by category of individual (working adults, schoolchildren) in 1993 and 2009 Author: F. Demoraes. Sources: 1993-CEDE-ORSTOM and 2009-METAL surveys. HAsup observed in type 1 is thus associated with a significant change. But what exactly does a significant change mean? Does it imply an improvement or, on the contrary, a worsening in access to place of activity between the two dates? To answer this question, we took as our indicator the mean of the Distance-Time between home and PTA. In three cases (Bosa, Gustavo Restrepo and Soacha), Distance-Times have increased, implying longer distances and/or travel times for working adults in 2009 as compared to 1993 (graph 2). All differences are significant based on the Kolmogorov-Smirnov non-parametric statistical test. Graph 2: Mean of Distance-Times between home and Place-Time of Activity for working adults living in the four zones of type 1 where a significant change in STAs between 1993 and 2009 was detected Author: F. Demoraes. Sources: 1993-CEDE-ORSTOM and 2009-METAL surveys. If we take the example of Soacha, a disadvantaged suburb with a high proportion of SCI1-households (map 4), the Distance-Times for working adults increased from 6.49km to 8.3km. This result is consistent with what may be inferred from visual examination of the STAs at both dates on the map (map 12). The 2009 STA is much larger (44.1km²) than the 1993 STA (34.4km²), and is more offset from the survey zone. Map 12: Space-Times of Action of working adults residing in 1993 and in 2009 in the survey zone located in Soacha (left) and in San Cristobal Norte (right) Author: F. Demoraes. Sources: 1993-CEDE-ORSTOM and 2009-METAL surveys. The enlargement of STAs for working adults in Soacha between 1993 and 2009 may be explained by three factors. First, the decrease in working at home, which dropped from 30% to 20% of the total number of working adults surveyed in this zone at the two dates. More adults left home for work each day in 2009 than in 1993, implying more travel time overall. Second, the modal share of public transport rose from 58.8% to 64.8%. Third, the increase in travel time on public transport, which rose from 58 to 64 minutes over the same period. Soacha's dependence on Bogotá for work was still very strong in 2009, as stated in Gouëset et al. 2016, while travel between the two municipalities remained difficult (due to road congestion) and the Transmilenio did not yet reach Soacha.

  , transport service provision is another important variable in changes to daily mobility in Bogotá. This is characterized by recent growth in household car ownership rates. According to the 2005 and the 2011 origindestination surveys conducted in the Bogotá Metropolitan area (SDM, 2005 and SDM, 2011), these rates rose from 30% to 41% between the two dates. Another key process over this period was the modernization of public transport with the commissioning of a Bus Rapid Transit (BRT) system as of 2001, known as the Transmilenio

(map 1). Broadly speaking, and as shown in

[START_REF] Dureau | Les inégalités d'accès aux ressources urbaines dans des quartiers périphériques en mutation nouvellement desservis par le Transmilenio à Bogotá (Colombie)[END_REF]

, cars still tend to be the preserve of the wealthy, while poor people walk, travel by bus, bike, or motorbike. The only mode of transport used by all social classes in Bogotá in 2009 was the Transmilenio.

Table 1 :

 1 Distribution of households in Bogotá with at least one working adult and one child in education, by survey zone in 1993 and 2009 and by category of individual (working adults, schoolchildren) Reference population: individuals co-residing in households where at least one adult is in paid work (either at home or outside place of residence) and where at least one child is in education (primary or secondary school). NB: the numbers are of individuals with a known destination in the Bogotá metropolitan area.

		Number of	Number of	Number of	Number of
		households	individuals	schoolchildren	working adults
	Survey zone (Id)	1993	2009	1993	2009	1993	2009	1993	2009
	Bosa (07)	50	57	165	190	86	90	79	100
	Chía (08)	29	27	101	81	44	32	57	49
	Gustavo Restrepo (05)	51	52	185	156	89	65	96	91
	La Candelaria (02)	53	47	181	146	98	69	83	77
	Madrid (10)	49	47	182	162	96	88	86	74
	Normandía (04)	46	26	158	70	61	19	97	51
	Perseverancia (01)	44	19	144	58	73	26	71	32
	San Cristobal Norte (06)	66	35	233	108	126	50	107	58
	Soacha (11)	46	50	155	165	75	69	80	96
	Overall total	434	360	1504	1136	748	508	756	628
	Sources: CEDE-ORSTOM 1993 and ANR METAL 2009 surveys, Bogotá. Data processing:
	F. Demoraes.

  Map 11: The principle of the bivariate colocation test: observed situation versus simulated situations based on the example of STAs associated with schoolchildren living in Gustavo Author: F.Demoraes. Sources: 1993-CEDE-ORSTOM and 2009-METAL surveys.

	Restrepo in 1993 and in 2009 (Bogotá)
																								r e s b O	d e v	n o i t a u t i s
																								5 0 (	-	o v a t s u G	R	r t s e	) o p e
																								p u o r G	1
																								l	t -e c a	m i	e	f o	s	l o o h c	i	n	3 9 9 1	) 9 8 = N (
																								p u o r G	2
																								l p	t -e c a	i	e m	f o	s	l o o h c	i	n	9 0 0 2	) 5 6 = N (
																								x e d n I	=	8 6 7	. m
																								Link between each Place-Time of Activity of group 1 (schoolchildren in 1993)
																								to the closest Place-Time of Activity of group 2 (schoolchildren in 2009). The length of these links is
																								averaged to compute the index.
	i F	s r	t	s	n o i t a l u m i													d n o c e S	i s	l u m	i t a	n o
	Points from group 2 are randomly permuted among S1	Points from group 2 are randomly permuted among S1
	s t n i o P	m o r f	p u o r g	1	o d	t o n	e v o m	s t n i o P	r f	m o	p u o r g	1	o d	t o n	e v o m
																								1 m e i t p u -e c o r G a l p	f o	h c s	l o o	i	n	3 9 9 1	) 9 8 = N (	p u o r G t -e c a l p	1 m i	e	f o	c s	l o o h	i	n	3 9 9 1	) 9 8 = N (
																								o r G	p u	2	p u o r G	2
																								i s	l u m	e t a	d	l p	t -e c a	i	e m	) 5 6 = N (	i s	l u m	t a	d e	l p	c a	-e	i t	e m	) 5 6 = N (
																			x e d n I	=	7 9 7	. m	x e d n I	=	8 0 8	. m
				S1: all possible Place-Times of Action of the individuals living in the survey zone in 2009 (N = 149)	N
				h C	l i	s ' n e r d	S	T -e c a p	i	e m	f o	A	t c	o i	n	i	n	9 9 1	3	u S	y e v r	Z	e n o	0	3	km

Expressed in meters per minute (m/min).

funded Modural research program. He works in

Authors' short biographies

Florent Demoraes 1,2 Florent Demoraes, who holds a PhD and HDR in Geography, is a full professor at Université Rennes 2 and a member of the CNRS 6590 Research Unit (Espaces et Sociétés) which he directed from 2016 to 2019 (Rennes site). He is currently on a two-year secondment to the French Institute of Andean Studies (IFEA) in Bogotá to conjointly steer with Vincent Gouëset the ANR-funded Modural research program. He works in Latin American metropolises on 1) the relationship individuals have with the city depending on their place of residence, their position in the social hierarchy, and their biographical stage; 2) sustainable mobility practices and social inequalities; 3) transformations to social divisions of space. https://orcid.org/0000-0001-6113-9960 / https://perso.univ-rennes2.fr/florent.demoraes Key words: Daily mobility, Segregation, Spatial Analysis, Space-time of action, Latin American metropolises


Événement : communication au colloque The Diasporic Plate: Food in the Contemporary Diasporic World in Times of

First of all, let me warmly thank the organizers for putting this conference together and for inviting me. This is an extremely interesting event which proves -if it need be -that food is a prism through which scores of other topics can be creatively envisaged.

I am a French lecturer in English, and I have lately focused my research on the food motif in English political theatre, notably in Edward Bond's work where it is prevalent. But starting from there I felt like checking what was also going on at home with maybe the idea of comparing food presence on both English and French stages, at a later stage. This conference gave me some direction for exploring theatre in my own country, and for this also, thank you very much. What I am going to present now is the beginning of this project that I am looking forward to developing in the coming years.

As surprising as it may seem, food is not that present on the French contemporary diasporic stage. Perhaps playwrights split between France and another terroir feel inhibited by the enormity of the French food culture? Nevertheless, the fact is that precisely where one would expect to find scores of these prime cultural tags that food items and cuisine are, one is left a bit hungry.

Of course, there are some examples. But I found them in pieces of relatively inferior artistic quality. I am thinking of plays like Farid Omri's Bacon Couscous, staging a mixed North-African and French couple. In this charming comedy the triumph of love over cultural differences is symbolised by the fusion of the 2 food items in the oxymoronic (but no doubt delicious) dish mentioned in the title. However, we are talking about a quite traditionally written mainstream comedy, here.

True, some more elaborate pieces also use the food motif as a direct symbol of a particular diasporic identity. Fellag in How to Prepare a Good Little Couscous turns it into the emblem of his original Maghreb: "… couscous represents our deepest identity, since, as common saying goes, Maghrebi are couscous, in the same way that English people are rosbifs and Italians macaroni". But In his play, the food motif is not just a cultural signpost. It also serves other, more central functions, that enrich the dramatic text. In this way, Fellag and the other playwrights I am going to mention are heirs to the great ancestors of French diasporic contemporary theatre, Samuel Beckett (Irish) and Eugène Ionesco (Rumanian and French).

In Beckett and Ionesco's works, the food motif is never used as an ethnic label, a vehicle for nostalgia about a lost country or as the emblem of a particular cultural mix, but rather -and right from the start -as a properly dramatic constituent, that is to say as an element which helps them develop their original thought through the medium of theatre. And their thought is a structural one, focused on a (the?) general frame within which individual stories take place. What I mean by that is that both playwrights use the food motif to express their conception of humanity as a whole.

Of course, writing in a second language and in a country whose secular and democratic tradition protected them from the stranglehold of politics or religion unfettered their writing, freed it from verisimilitude and stretched dramatic expressivity as far as it could go. Without the food motif taking a more prevalent place than others in their plays, Beckett and Ionesco's unbridled expressivity allowed its evocative qualities to start blossoming on the French stage.

Thus, for example, to render his flawed vision of humanity, Beckett uses the food motif inversely. The nothingness which frames, and thereby invalidates Mankind's existential experience is at work inside his characters. It devours them from within, making them thinner and thinner one play after the other, until they remain like voice or even just breath presences. It may be paradoxical in a country that sees itself as the birthplace of gastronomy, but the first apparition of the food motif on the French (diasporic) stage is an "anti-motif": the force which, in Beckett's plays, drives humanity towards death rather than towards life. However, this "antimotif" proved very fruitful. It revolutionized dramatic writing as, for the first time, it gave material stage expression to a void, a shortage. The freedom from plausible reference allowed Beckett to have the lack of food bear the metaphysical concept of a fundamental satiety forever escaping humankind. Man is forever hungry for transcendence, but he can never reach it.

Ionesco too uses food items to deplore the transcendence-free human condition. But he rather points to the all-pervasiveness of materiality through the proliferation of objects on stage. Thus, in Victims of Duty he has the stage filled with cups of coffee by Madeleine, a conservative bourgeois, when she carries out a hundredfold the demand of the authoritarian Policeman to bring him a cup of coffee. For Ionesco, matter (and so, also edible matter) is an evil force which thrives when spirituality is absent, like the eggs that Roberte lays in hundreds in The Future is in Eggs, and that are destined to become "de la chair à saucisson" ("sausage-meat / cannon fodder").

Beckett and Ionesco's propensity to use the food motif to contextualize human behaviour, to depict the framework which conditions Mankind's existence, is still to be found among diasporic playwrights to this day. Even if not all of them are as metaphysical as their illustrious predecessors, and if, for each of them, this context is different (political, or sociological, or historical, etc.), it is almost always foremost in their plays. In Europe Connexion for example, the background is political. In it, Alexandra Badea depicts the effects, but also the causes of the psychological collapse of a parliamentary assistant working at the European commission. His burn-out does not result so much from the work pace there, than from the moral contortions he has to go through in order to keep his self-respect when pushing laws half-proposed half-imposed by the industrial lobbies which run the world. It is no chance that Badea has him work at the "environment, public health and food security" sub-commission, where he actively pushes regulations limiting food labelling to "basic information only", or outlawing seeds that are not owned by industrial groups, or legalizing carcinogenic pesticides. This character falls physically and morally apart when accepting to be a cog in a machine designed to exploit his fellowman to death. At the hands of industry, food serves the opposite of its original nourishing function. It "fattens" some happy few but devours most people who live by it. Europe's multicultural ideal is seen as an ideological gadget of very little weight compared to the structural reality of things, and the main character's collapse mirrors that of his corrupt world which is no longer designed to feed him.

Interestingly, even when it is not overtly posited, the general framework is present in some plays as a watermark, a nearly invisible but nonetheless essential bone-structure. It is notably the case with playwrights of French West Indian or of African origin, a number of whom stage their stories in terms of power relationships modelled upon the colonial motif of cannibalism. Thus, José Pliya in Cannibales explores the journey which leads to the eventual acceptance of a child's death in terms of incorporation, including the incorporation of grief itself. "Like the cannibal warriors who used to eat their enemy's heart so as to incorporate his strength, [the character called Nicole] decides to eat the object of her grief together with all the clichés, the preconceived ideas, the idols of social representation which go along with it." Even more explicitly, Gaël Octavia, in Conger Eel and Lobster, likens the relationship of a man and his wife's lover to that of these two animals, both linked by "a happy and straightforward" association since they are respectively predator and prey to the same creature, the octopus. "The octopus gobbles up the lobster and the conger eel gobbles up the octopus." Eat or be eaten is also how Papa sees life in Marie N'Diaye's Papa must eat, where Papa, accusing white society of having sucked, digested and left him powerless, decides to get his own back by returning to his French family to bleed them dry.

But the food motif does not only serve to capture the overall picture. It also serves diasporic playwrights to think up all these various frames, as well as what is at play inside them. Many of them use it as a dramatic constituent for its expressive properties which help them formalize their conception of the world. Just as Beckett had used its anemizing effect, or Ionesco its subjugating effect to shape their vision of humanity, contemporary playwrights also use the food motif to make the stage speak their own language.

Quite evidently, very often, food will be a major actancial force. In Europe Connexion, for example, it is the moral charge borne by the food motif which holds up the main character's dream career plan, and therefore moves the play forward.

But the agency of food objects is also used to shape playwrights' ideas. Quite a few diasporic plays involve the audience in some culinary action that is part of the play. For example, in Sicilia, Clyde Chabot, welcomes the audience with great care. They are first seated around a table partially set with glasses, small plates, and napkins, and strewn with objects, some of them visible (wine bottles, bread baskets, numerous photographs), and some hidden under cloths. They are then drawn into the tale of Chabot's trip in search of her lost Sicilian origins thanks to the photographs they are invited to pick up, examine, and circulate. The involvement in a common experience will deepen when Chabot finally unveils the hidden peppered pecorino cheese, "the only cultural element to have been passed on to her", she says. The revelation-like unveiling of the cheese, followed by its sharing among the audience along with Sicilian wine, turn it into the centre of a communion which unites the table-companions together, as well as with the playwright. Each person's individuality is at the same time erased, since the tasting is experienced by everybody, but also celebrated, since it also calls upon each and everybody's personal memories. Dramatized in that way, the cheese manifests a particular conception of humanity, as made up of entities distinct from one-another but also stock-related.

So, one has to admit that the food motif in contemporary French diasporic theatre is quite intellectual in nature, since it serves to draw a context before telling a story within it, as well as to formalise general concepts. What I would like to suggest as an open conclusion, is that maybe the food motif also serves another function: that of protecting diasporic playwrights' pride. Indeed, the complexity of mixed identities as well as that of inter-and trans-cultural relationships is such that it is challenging for someone split between terroirs to claim full legitimacy to one of them without feeling awkward or even ashamed. One of the strategies to bypass those, a subtle, modest yet efficient strategy, is precisely to use the food motif to celebrate the taste of human diversity. All the playwrights I mentioned here, and many more, use it, but I want to finish on the Compagnie du maladroit and their play Brothers, which shows it well.

In the play, the larger context is historical. It is about two French-born brothers who reconstruct the story of their recently deceased grandfather, a refugee Spanish anarchist. On his kitchen table, with the foodstuff they find in his cupboard, they replay his involvement in the Spanish Civil War, and his eventual settlement in France. Food is the material with which/by which/ through which this epic is told, where moral and political choices are a question of life or death. Food quite naturally takes upon itself these absolute values: life and death. The grandfather's ethnicity is but alluded to and comes much after his existential choices, which constitute the true foundation of his identity -of any Man's identity, the play suggests. In Brothers, the conceptual contents of the play are also informed by the materiality of food objects. Brown sugar cubes stand for the Republicans ("the reds"), white caster sugar for the Francoists. This materiality gives a palpable dimension to the story telling. Notably, it vividly evokes the wear, the crushing, the fragmentation of bodies in the battles or during the exodus. It also allows for a degree of personalisation, sugar cubes representing individuals as defined by their existential choices, caster sugar representing anonymous, conformist crowds. Finally, coffee, whose texture and colour evoke a virgin soil capable of accommodating new roots, will come to materialise the land of exile and of new beginnings. The French-born brothers will subtly pass on the succulence of their mixed identity at the end of the play, when they make a coffee whose aroma spreads in the auditorium, sweeten it with a brown sugar cube, drink it together and conclude: "Indeed. That does change the taste".

The power of food is such that it facilitates the mental projection of the audience in a play, and diasporic playwrights find there a delicate means to transmit their histories and what these taste like.