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# A standardized population-based approach for food consumption analysis and socio-metabolic research: insights from its application to France

Barbara Redlingshofer, Tanguy Fardet, Caroline Petit

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Barbara Redlingshofer, Tanguy Fardet, Caroline Petit. A standardized population-based approach for food consumption analysis and socio-metabolic research: insights from its application to France. 2025. hal-05087124

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# A standardized population-based approach for food consumption analysis and socio-metabolic research: insights from its application to France

Barbara Redlingshöfer, Tanguy Fardet, Caroline Petit

## Abstract

Food consumption has a significant urban environmental impact and is progressively being considered on par with mobility and housing, all three of which involve different types of population. Despite preliminary work, there is a lack of standardized methods to quantify different populations' contribution to urban metabolism. A comprehensive framework is provided in this paper to estimate the populations present in an area and their food consumption there, over a given period of time, based on broadly available census and statistical data. Drawing on population equivalents, a standardized and consistent approach is used to integrate the different types of population and their respective time spent in the area, as well as their share of daily food intake. A case study of France shows that, in 85% of municipalities and 75% of inter-municipal cooperation areas, the present population is smaller than the resident population. The eating population is usually 5 to 20% smaller than the resident population, because children, teenagers, and commuters consume less food overall. While metropolitan areas attract populations, this is compensated by the resident population leaving for vacation, leading to close to zero or negative changes compared to the resident population. Only touristic areas attract additional populations to such an extent that the present population becomes substantially larger than the resident population over a year. Previous approaches tend to overestimate the biomass directly associated with urban food consumption. Our population-based framework can help reduce uncertainties about biomass use in cities and improve the comparison of material consumption between different areas.

250 mots

Keywords: urban metabolism, urban food flows, material flow analysis, urban sustainability, population equivalent, industrial ecology

## 1. Introduction

### 1.1. Background

At the scale of cities, food has one of the largest environmental footprints, together with mobility and housing (Goldstein et al. 2017). These three sectors and their respective impacts involve different types of population in the area, their time of presence there, and their varying use patterns of material and energy during that time. These have however not been taken into account in the impact analysis. In fact, the material and environmental footprint of food at urban scale and the associated eating population have rarely been a focus of quantitative studies (Guibrunet and Sánchez Jiménez 2023), despite their potential role in urban sustainability. Policymakers are nevertheless increasingly reengaging with food issues at the scale of cities, notably to relocalize food production, shorten supply chains, reduce food waste and, more generally, alleviate food insecurity (Doernberg et al. 2019; IPES
2017; *Milan Urban Food Policy Pact*). This turn has come after a long period of under-investment that began with the industrialization of food systems (Wiskerke 2009; Pothukuchi and Kaufman 2000).

Comprehensive quantitative assessments of urban food flows are necessary for efficient science-
based local policies. Yet, there is a lack of conceptual frameworks to integrate the different types
of population involved, how they use and inhabit different parts of a city, and how much food they
consume over time. Though this issue is not unfamiliar to some research fields, as shown in the
following review of the state-of-the-art, standardized and actionable methods to estimate the present
population and its associated food consumption over time, at the scale of urban areas, are not yet
available.

## 1.2. State-of-the-art in the estimation of population and food consumption

Concepts and methods to study the population present over time in a given area have been developed for decades in population research and statistics (Charles-Edwards et al. 2020; Charles-Edwards et al. 2021). As Panczak et al. (2020) show, estimates of the temporary population, that is, a population driven by temporary population mobility without a change of usual residence at the level of cities and regions date back to the early 20th century. With increasing mobility and access to new data sources, notably ICT-based data (e.g. mobile phone, credit card and Wifi connection data), the concepts and methods to capture the present population have proliferated. Emergency planning, tourism, transportation planning and, more recently, epidemiology are fields that benefit from information about the total population present in an area at a given time.

Swanson and Tayman (2011) refer to the *de facto* population "which involves the estimation of people where they are found rather than where they usually reside", as opposed to the *de jure* population that declared its usual residence in a given place, according to the census. Their *de facto* population includes several non-permanent populations in addition to the residents: visitors, homeless people, amenity-seeking and migrant seasonal populations, and non-resident daytime populations, present for a fraction of the time during the day. Smith (1989) addressed the challenges of defining temporary residents and the appropriate time frame for this definition, emphasizing that estimating temporary residents should be guided by the purpose of the research under consideration.

The larger goal of this study is a quantitative assessment of the total food consumption of a pop-
ulation present in an urban area over a given time period. The scientific literature provides many
examples of how food consumption can be estimated in infra-national areas like cities and regions.
Urban metabolism studies use material flow analysis (MFA) to analyze urban food flows. To esti-
mate one of these flows, food consumption, at the scale of cities, two different approaches can be
distinguished (Goldstein et al. 2017):

**balance approaches** : these apply an accounting method developed for a nation's economy-wide ma-
terial flows (European Commission. Statistical Office of the European Union. 2018), further
adjusted to evaluate flows at the scale of cities (Barles 2009); they conceptualize consumption
as the amount of material in the domestic economy that remains within a specific area and does
not leave it as export or waste, termed "domestic material consumption" (DMC)

**population-based approaches** : these combine the population located in the area with per capita food availability or consumption to assess the food consumption induced by the metabolism of humans.

These approaches however often lead to results that are difficult to reconcile (Redlingshofer 2022):
balance approaches tend to estimate larger values for food consumption than population-based ap-
proaches but rarely distinguish the processes involved. Studies using the balance approach (Bahers
et al. 2019; Barles 2009; Hoekman and Blottnitz 2017; Niza et al. 2009; Rosado et al. 2014) apply the
DMC concept to estimate the total amount of food used within an area, irrespective of who consumes
it (population, food processing companies, etc.) and what the food is used for (including when part of
it ends up as food waste). To remedy this shortcoming and provide the necessary information to align
the two indicators, Redlingshofer (2022) has proposed both to disentangle the respective contribution of food consumption and food waste to DMC, and to account for all contributions to food consumption by the population located in an area. Uncertainties in population estimates have indeed made it difficult to draw firm conclusions from the discrepancies in results obtained with the balance approach. In the case of population-based approaches, most studies simply multiply the resident population figures taken from the census, by food availability per capita (Le Noë et al. 2017; Moore et al. 2013; Codoban and Kennedy 2008; Forkes 2007). Only a few studies consider the food consumption of non-resident populations via estimates of the present population to quantify nutrient flows. These concern Brussels (Papangelou et al. 2020), the Paris metropolis or one of its peri-urban areas (Esculier et al. 2019; Tedesco et al. 2017), Amsterdam (Wielemaker et al. 2020), and Indian cities (Boyer et al. 2019). While most of them include residents and commuters or tourists, only Esculier et al. (2019) and Papangelou et al. (2020) include all three. Furthermore, the time that residents spend away from home, which does not contribute to local food consumption, is accounted for only by Esculier et al. (2019) and Tedesco et al. (2017). Finally, none of the studies provide generic formulas to reproduce or adapt these methods to other areas, nor methods to ensure that combining such results at different levels will lead to consistent results.

Besides urban metabolism studies, at least two other research fields require the quantification of food consumption in their analysis: Life Cycle Analysis (LCA) and foodshed studies. LCA, an environmental accounting tool conceptually close to material flow analysis (Finkbeiner et al. 2006), is developing a comprehensive assessment of the environmental impacts of urban sectors and activities at the level of cities, a scale hitherto rarely applied in LCA (Mirabella et al. 2019; Ghaemi and Smith 2020). Few LCA studies at that scale include food consumption (Albertí et al. 2017). Loiseau et al. (2023) developed a method to estimate food consumption at the scale of a city from individual and household consumption data, but they did not integrate the non-resident population. Mirabella and Allacker (2021) presented a bottom-up approach for calculating a population equivalent and characterizing the resident and non-resident population as users of services provided by a city. However, despite the authors' goal of performing inter-city comparisons, this study was limited to the Belgian city of Leuven, did not provide any generic method applicable to cities in general and required extensive data collection. Foodshed studies, stemming from the geography of food (Kloppenburg et al. 1996; Peters et al. 2009), also require a quantification of food consumption to achieve several goals as outlined by Schreiber et al. (2021): to identify the match between agricultural production and a region's food requirements (expressed globally or by product category, Nixon and Ramaswami 2018); to define the local foodshed size, that is the agricultural land required to cover food consumption needs (Pradhan et al. 2020); and to trace food flows, that is, food movement and concrete organization of the food basin, including food imports and exports (Miller and Mann 2020). Despite the absence of a unified methodology regarding foodshed analysis, it appears that the vast majority of studies base their calculations on the resident population, captured via the statistical system of the countries, states or cities concerned.

## 1.3. Scientific gap and research question

Overall, few studies integrate non-resident populations in quantitative assessments of a city's food consumption. The contribution of visitors and tourists to food consumption (and nutrient intake) is thus largely overlooked. Some authors have suggested that the food metabolism remains under-estimated when only “households” (residents) are considered (Barles 2009; Goldstein et al. 2017) and that using a population-based approach integrating the additional, non-resident population should yield a larger eating population. This would accordingly show a larger annual urban food consumption, compared to simplified approaches based on the resident population. However, the time that residents spend away, on vacation or elsewhere, should also be considered, which makes it unclear whether the net population balance should be positive or negative. Depending on the urban profile, residents' time spent away (vacation, commuting) may counterbalance the effect of the additional non-resident population on a city's total eating population and its related annual food consumption. A comprehensive
method to assess the present and eating population is therefore necessary to estimate the total food consumption in a city.

This paper aims to develop a conceptual framework to assess the present and eating populations in a given area, drawing on a population-based approach. We present the method and its results, using France as a case study. Analyzed at different spatial scales, according to French administrative units, the results reveal: i) the difference between the present and the eating population approach compared to the resident population approach; and ii) the characteristics of cities and urban areas in terms of an eating population profile. We then discuss the usefulness of the approach as well at its limitations and some perspectives for research and policy.

## 2. Methods

The following section describes the model, data, and the underlying hypotheses used to compute the present and the eating populations (with data specific to the case of France). The model provides two alternative metrics: the present population equivalent, which considers population types and their respective time spent in a given area; and the eating population equivalent, which introduces a normalization step to account for the difference in the amounts of food consumed by different populations.

All code and data used are available on the following git repository: https://codeberg.org/tfardet/article Present population Redlingshoefer-Fardet-Petit 2025.

### 2.1. Present population and present population equivalents

The present population in a given area at a given time can be split into three exclusive categories:

* residential contribution: by residents (r), as given by the national census, during their time spent at their usual residence,

* commuting contribution: by people who commute (c) to their place of work or study in the area (these include residents during their time away from home, if they work within their area of residence),

* touristic contribution: by tourists (t), either residents on vacation or people from abroad, who spend at least one night in the area.

Over a given time period T, the present population (PP) in the area will be a combination of the populations associated to three categories, indexed by $i \in \{r, c, t\}$, such that $P_r$ gives the residents, $P_c$, the commuters, and $P_t$, the tourists. During the week-end, the present population may be mostly composed of the residents and tourists, whereas during business hours on weekdays, the present population may be mostly commuters, senior residents, and tourists. As the time and duration over which these populations are present in the territory vary widely depending on the age-group (indexed j for each age-group – AG), we further divide these three categories by age such that $P_{ij}$ gives the population for category i in the age-group j. To account for these variations in time and space, each sub-population group ij is associated with an amount of time spent ($t_{ij}^{(s)}$) in the area over the full time period T.

From the population and the time spent in the area, we define the present population equivalent in the area, $PPE_{ij}$, such that

$$PPE_{ij} = \frac{t_{ij}^{(s)}}{T} P_{ij} \quad \text{or} \quad PPE_{ij} = \sum_{sg_i} \frac{t_{sg_i,j}^{(s)}}{T} P_{sg_i,j} \quad (1)$$

depending on whether group i is a single homogeneous group or is divided into subgroups {$sg_i$}.
The population P<sub>ij</sub>, present for t<sub>ij</sub><sup>(s)</sup> is thus equivalent to a smaller population equivalent PPE<sub>ij</sub> that would be present during the whole time T. Overall, the total present population (PP) in the area over the time period T is given by

$$PP = \sum_{i \in \{r,c,t\}} \sum_{j \in \{AG\}} PPE_{ij} \qquad (2)$$

## 2.2. Detailed definitions for the population equivalents

In many countries, the national statistics bureau provides data that can help estimate the various populations and the time they spend in an area. We propose the following definitions for each of the population equivalents, with the parameters and sources for France detailed in Table 4.

The commuter population equivalent is computed as follows:

$$PPE_{c,j} = \frac{t_{c,j}^{(s)}}{T} P_{c,j} = \frac{d_{c,j} f_c^{(t)}}{T} P_{c,j} = \frac{t_{c,j}^{(s)}}{T} \left( P_{c,j}^{(\text{in})} + P_{c,j}^{(\text{local})} \right) \qquad (3)$$

where P<sub>c,j</sub> is the population that leave its residential space to work or study in the area. It can be split into P<sub>c,j</sub><sup>(in)</sup>, the non-resident commuters, and P<sub>c,j</sub><sup>(local)</sup>, the population that both resides and works/studies in the area. The time spent on the trip and daily activities over the total duration T is t<sub>c,j</sub><sup>(s)</sup>, which is the number of days where commuting happens, d<sub>c,j</sub>, multiplied by the fraction of the day spent at the commute destination, f<sub>c</sub><sup>(t)</sup>.

The tourist population is estimated based on data about the nights spent in different accommodations (one "night" is considered as 24h spent locally by one person):

$$PPE_{t,j} = \frac{1}{T} \left( N_{t,nr,j}^{(m)} + N_{t,r,j}^{(m)} + N_{t,r,j}^{(nm)} \right) \qquad (4)$$

with N<sub>t,nr,j</sub><sup>(m)</sup> the nights spent by people not living in the country (non-residents) in market accommodation, N<sub>t,r,j</sub><sup>(m)</sup> the nights spent by residents of the country in market accommodation, and N<sub>t,r</sub><sup>(nm)</sup> the nights spent by residents of the country in non-market accommodation.

Finally, the resident population equivalent is computed as follows:

$$PPE_{r,j} = \frac{t_{r,j}^{(s)}}{T} P_{r,j} + \frac{t_{c,j}^{(s)}}{T} P_{r,j}^{(\text{sedentary})} \qquad (5)$$

with the resident population divided into two distinct contributions. The first is common to all residents of age-group j and represents the "standard resident time", t<sub>r,j</sub><sup>(s)</sup>, which is the time spent at home on business days (outside working or studying hours) and during days off (excluding holiday trips that are counted in the tourist population equivalent, as N<sub>t,r,j</sub><sup>(m)</sup> and N<sub>t,r</sub><sup>(nm)</sup>). The second contribution is residents who do not commute to a place of work or study on business days. This notably includes retirees and unemployed people. The associated duration t<sub>c,j</sub><sup>(s)</sup> is the same as for commuters.

In the Supplementary Material we provide alternative formulas to compute population equivalents for countries where commuter data is not available, or where more precise or granular data about employment and students is available, as well as details on the constraints between time spent by residents in different activities, to ensure that all their time is consistently accounted for.

## 2.3. Eating population, eating population equivalents, and associated food consumption

For the population that is present in the area over a period of time, one can define another population equivalent associated with the fraction of a daily ration consumed by that population.

This is the eating population (EP), which is defined based on the same principles as the present population (PP). One eating population equivalent is an adult that eats their entire food ration over
<table><caption>Table 1: Parameters used to compute the present population and population equivalents in an area.</caption><thead><tr><th>Name</th><th>Description</th><th>Source or value</th></tr></thead><tbody><tr><td>P<sup>(in)</sup><sub>c,j</sub></td><td>People working locally but living outside the area<br>People studying locally but living outside the area</td><td>Work commute survey<br>Study commute survey</td></tr><tr><td>P<sup>(out)</sup><sub>c,j</sub></td><td>Residents who work outside the area<br>Residents who study outside the area</td><td>Work commute survey<br>Study commute survey</td></tr><tr><td>P<sup>(local)</sup><sub>c,j</sub></td><td>Residents who also work in the area<br>Residents who also study in the area</td><td>Work commute survey<br>Study commute survey</td></tr><tr><td>P<sub>r,j</sub></td><td>Resident population for age-group j from the local census</td><td>French national census</td></tr><tr><td>P<sup>(sedentary)</sup><sub>r,j</sub></td><td>Residents of age-group j who do not commute to a place of work or study</td><td>P<sub>r,j</sub> = (P<sup>(out)</sup><sub>c,j</sub> + P<sup>(local)</sup><sub>c,j</sub>)</td></tr><tr><td>N<sup>(m)</sup><sub>t,nr,j</sub></td><td>Nights spent in market tourism accommodation by non-resident tourists of age-group j</td><td>Non-resident overnight stays</td></tr><tr><td>N<sup>(m)</sup><sub>t,r,j</sub></td><td>Nights spent in market tourism accommodation by resident tourists of age-group j</td><td>Resident overnight stays</td></tr><tr><td>N<sup>(nm)</sup><sub>t,r,j</sub></td><td>Nights spent in non-market tourism accommodation by resident tourists of age-group j</td><td>See Supplementary Material</td></tr><tr><td>t<sup>(s)</sup><sub>i,j</sub>, d<sub>X,j</sub></td><td>Time and days spent on the different activities</td><td>See Supplementary Material</td></tr></tbody></table>

duration *T*; each eating population equivalent (EPE) is therefore similar to the associated PPE but uses a food consumed ratio instead of the time spent ratio, and the daily food consumptions of the age-group, *C*<sub>j</sub>, comparing it to that of an adult, *C*<sub>adult</sub>. In the case of France, this data is based on the INCA 3 study (Anses 2017) which analyzed the food consumption and eating habits of a large panel of inhabitants across multiple regions and food groups.

This leads to the following definitions:

$$EPE_{t,j} = \frac{C_j}{C_{\text{adult}}} PPE_{t,j} \qquad (6)$$

as tourists consume their entire daily ration in the course of this activity, the eating population equivalent is obtained by multiplying the tourist PPE by the ratio of the age-group food consumption over the adult food consumption.

$$EPE_{c,j} = \frac{d_{c,j} f_c^{(c)} C_j}{T C_{\text{adult}}} P_{c,j} \qquad (7)$$

as commuters consume a fraction *f*<sub>c</sub><sup>(c)</sup> of their daily ration during lunch and snacking on commute days (*d*<sub>c,j</sub>).
$$ EPE_{r,j} = \frac{C_j}{C_{\text{adult}}} \left[ \underbrace{\frac{d_{nc,j}}{T} P_{r,j}}_{\substack{\text{full daily consumption} \\ \text{during no-commute days}}} + \frac{d_{c,j}}{T} \left( \underbrace{(1 - f_c^{(c)}) (P_{r,j} - P_{r,j}^{\text{(sedentary)}})}_{\substack{\text{fraction consumed} \\ \text{on commute days}}} + \underbrace{P_{r,j}^{\text{(sedentary)}}}_{\substack{\text{full consumption} \\ \text{for sedentary residents}}} \right) \right] \quad (8) $$

$$ = \frac{C_j}{C_{\text{adult}}} \left( \frac{(1 - f_c^{(c)}) d_{c,j} + d_{nc,j}}{T} P_{r,j} + \frac{f_c^{(c)} d_{c,j}}{T} P_{r,j}^{\text{(sedentary)}} \right) \quad (9) $$

as residents consume their whole ration on no-commute days ($d_{nc,j}$), and only $1 - f_c^{(c)}$ on commute days ($d_{c,j}$), except for the “sedentary” residents who work and study and hence eat their whole daily ration in the area of their residence.

As for the present population equivalent, the total eating population equivalent is given by EP = $\sum_i \sum_j EPE_{ij}$. The food consumption can then be computed directly from the EP as:

$$ FC = C_{\text{adult}} \cdot EP. \quad (10) $$

Detailed values for these parameters in France are given in the Supplementary Material.

The main results of this study show the relative change between the present or the eating population respectively and the resident population, for selected administrative units in France. Relative change refers to the change between the newly calculated populations and the resident population expressed as a percentage of the original resident population. It is calculated via the following formulas:

$$ RC_{\text{PP}} = \frac{PP - \sum_j P_{r,j}}{\sum_j P_{r,j}} \quad (11) $$

for the relative change between the present population and the resident population, and

$$ RC_{\text{EP}} = \frac{EP - \sum_j P_{r,j}}{\sum_j P_{r,j}} \quad (12) $$

for the relative change between the eating population and the resident population.

## 2.4. French administrative units in 2019 as a case study

Located at the westernmost edge of Europe, France, in its metropolitan part, covers 551,695 km². Metropolitan France has a population of 66.1 million (as of January 2024). Its complex and structured territorial organization encompasses several levels of local authorities: 12 regions, 96 provinces (départements), nearly 35,000 municipalities (communes) and 1,254 inter-municipal cooperation areas, abbreviated EPCIs. EPCIs are legal entities formed by multiple municipalities that collaborate to deliver public services. Local authorities have been able to draw up territorial food projects since the 2014 national law for the future of agriculture, food, and forestry established a legal framework for territorial food projects to foster food sovereignty and support local producers and short supply chains. These projects are mainly implemented on an inter-municipal scale, hence the choice of EPCIs as the main level of analysis.

The reference year is 2019, for which a complete data set was available for this study and which was not affected by the impacts of the COVID-19 pandemic on tourism and employment.
### 3. Results

At the municipal scale, the findings show a negative or close to zero relative change between present (PP) and resident populations ($RC_{PP}$, as defined in equation 11) for most of the municipalities, shown by grey to blue areas on the map (Figure 1A). In 70% of French municipalities, the PP is more than 6% lower than the resident population, 6% being the loss expected from the resident population leaving on vacation. An $RC_{PP}$ lower than -6% points to the negative contribution of commuters leaving the city to travel to neighboring municipalities for work or study. In 85% of the municipalities, the PP is

<figure><img src="image_3.png" /></figure>

**Figure 1:** Variation of the population equivalent compared to the resident population, depending on the area. **Top:** Relative change between the present and resident populations ($RC_{PP}$, as shown in equation 11) at the municipal level over one year. **A.** Map showing the variation from municipalities that lose population, in blue, to municipalities that gain population, in red. **B.** Distribution of the relative change. The y-scale is logarithmic below -6% and above 6% and linear in-between. A relative change of -6% refers to the loss expected from the resident population leaving on vacation. **Bottom:** Relative change at the level of French inter-municipal cooperation areas (EPCIs) over one year, either between the present (PP) and the resident populations ($RC_{PP}$, in **C**) or between the eating (EP) and resident populations ($RC_{EP}$, as given by equation 12, in **D**). A relative change between -5 and 5% is shown in light grey, while negative changes between -5 and -20% or more go from light to dark blue. Areas where the PP or EP are significantly larger than the resident population are shown in colors going from salmon to dark red. The Greater Paris metropolitan area is marked by a black contour and the inset shows the smaller EPCIs of the Île-de-France region. Black circles designate the centers of the 50 largest urban areas.
lower than the resident population ($RC_{PP} < 0$ on Figure 1B). Municipalities with the highest $RC_{PP}$ (in salmon to red shades) broadly belong to two main categories: touristic areas (mountain regions like the Alps or Pyrenees, the Mediterranean, Atlantic, and Channel coasts, Corsica, and specific recreational destinations such as theme parks) and centers of activity such as large cities that see a large number of incoming commuters.

At the scale of EPCIs (Figure 1C), only around 30% of the areas have an $RC_{PP}$ lower than -6%, and the majority ranges between -5 and 5%, which is a relatively small variation, shown by a large share of EPCIs in light grey. EPCIs, and especially urban ones, encompass a territory that sustains most of the activities of its population, meaning that fluxes of people in and out of the area represent a smaller fraction of the contribution to the PP compared to individual cities. The 50 largest urban areas in France, shown by a black circle, do not record very high relative changes but instead lie in the majority range, between -5 and 5%. At the temporal scale of a year, incoming population flows (commuters, tourists) are counterbalanced by outgoing flows linked to residents' departures, notably for vacation. EPCIs surrounding large cities usually display a negative $RC_{PP}$, as the cities drain commuters towards them on working days. In rural areas, far from urban centers, EPCIs display a relative change close to zero, indicating balanced population flows with other areas, driven by employment and education opportunities within these EPCIs. As for the municipal level, the EPCIs with the highest $RC_{PP}$ are touristic areas that have a small residential population but attract significant numbers of tourists.

While the PP is generally similar to the resident population (most EPCIs are in light grey on Figure 1C)), the eating population (EP) is usually smaller than the resident population (Figure 1D), with more than 75% of the $RC_{EP}$ in the -5 to -25% range (light to dark blue). This shift can be explained by the fact that children and teenagers consume less food compared to adults, and that commuters have only some of their meals within the area. The only areas where both the PP and EP are substantially larger than the resident population are the touristic areas (from salmon to dark red).

The gap between the residents and the present population (PP) on the territory varies significantly, depending on the spatial and temporal scales. Even at the large spatial scale of French departments,

<figure><img src="image_4.png" /><figcaption>Figure 2: Variation of the gap between the residents and the present populations (PP) depending on the spatial and temporal scale. A. Change in the $RC_{PP}$, as defined in equation 11 at the scale of departments (top) and regions (bottom). B. $RC_{PP}$ for cities within the Greater Paris Metropolis (black line) or close to it, over the whole year (left) or a single week (right). The city of Paris is delineated by a white dashed line. C. $RC_{PP}$ for the touristic city of Agde and its surroundings over the whole year (left) and during summer time (June–July–August, right).</figcaption></figure>
there can still be a discrepancy greater than 10% between the residents and the PP (Figure 2A, top, with a maximum range of -9 to 13%). This decreases at the regional scale but still reaches almost -5% for the Île-de-France region (Paris) and more than 7% for Corsica.

The smaller the spatial scale, the greater these changes will be. For instance, cities within or close to the Greater Paris Metropolis (black line) host populations that differ substantially from their residents alone, both over a whole year (Figure 2B left) and a single week (right). The areas with the largest positive changes (in red, with PP greater than twice the residents) are the areas around CDG airport in the north, Disneyland Paris in the east, the Rungis market in the south, and the center of Paris. The marked difference between yearly (right) and weekly (left) changes shows the importance of choosing the relevant timescale with respect to the question at hand: almost all areas gain population over a week while most lose population over the whole year due to residents' vacations. Similarly, touristic areas like Agde and the surrounding cities, on the Mediterranean coast, show major changes between the yearly (Figure 2C left) and summer-time populations (on the right).

The contribution of the various population equivalents to the present population (PP) led us to classify the areas into four main categories (Figure 3A), depending on the relative contribution of each population to the PP — see Supplementary Material for more details about the precise classification criteria. Touristic areas are characterized by a touristic contribution to the PP that is larger than 10%. Autonomous areas have a balanced mix of population equivalents, whereas the two remaining areas are characterized by the commuter population equivalents: attraction areas are characterized by an incoming commuter population that accounts for more than 10% of the active population; and areas under influence see more than 10% of their active population leave to work or study elsewhere.

Most “influenced areas” have a PP that is at least 6% lower than its resident population, meaning that they lose more than just the residents that go on vacation, and almost all of them have a negative $RC_{PP}$, that is, a present population equivalent that is smaller than the resident population (Figure 3B and supplementary Figure A1). The majority of autonomous areas have a balanced $RC_{PP}$, between -6 and 0%, some with a stronger touristic and commuter contribution that places them in the positive range. Most attractive areas offset the departures of their residents on vacation with large influxes of commuters, to the extent that they have a positive (or at least close to positive) $RC_{PP}$. Finally, the touristic areas are the only ones that consistently gain population over a year, with $RC_{PP} \ge 0$. They are also the only type of territory where most areas have an eating population that is larger than the resident population.
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>Figure 3: A. Ternary plot of the relative contributions from residential, commuting, and touristic activities to the present population (PP) of an area for all French inter-municipal cooperation areas (EPCIs) and the 10 largest cities. The touristic EPCI marked by a star is used as an example to show how to read this diagram: its residents contribute to slightly more than 57% of the PP (full orange line), its commuters contribute to around 5% (dashed orange line), and the tourists contribute to around 37% (dotted orange line). Touristic areas are defined as those receiving more than 10% of their present population from tourism. Attraction areas have more than 10% of the active population coming from outside the territory while influenced areas lose more than 10% of it to other areas. Autonomous areas lie in between. B. Distribution of the relative change between the PP (left) or EP (right) compared to the census population. C. Map of the EPCIs classified as attraction, autonomous, influenced, and touristic areas. D. Detail of the specific contributions of different populations to the PP for each of the four types of territory (highlighted by dotted white contours on the inset in B). MGP: Métropole du Grand Paris (Greater Paris Metropolis); PdM: Pays de Montereau; PMF: Plaine et Monts de France; VEA: Val d'Europe Agglomeration (where Disneyland Paris is located).</figcaption></figure>
# 4. Discussion

## 4.1. Significance of the results, comparison with the literature

We provide a consistent framework, based on publicly available and periodical demographic data, that can be used to assess the present population over a certain period of time in an area. The concepts and data used are a common standard in an international context, allowing for replication in any country where such data is available. This method, based on population equivalents rather than individuals, enables one to account for the variety of populations that spend time in the area (residents, commuters, tourists) and the different ways and periods in which this area is used (residential, occupational/educational, or touristic use). Compared to previous studies, we provide detailed formulas for the population equivalents and discuss the different sources of data that can be used to compute them (Supplementary Material D). We also discuss key conditions that must be verified to make the calculations consistent across all geographical scales, such that there are no double-counts or missed contributions (Supplementary Material A).

Using this population-based approach, we show that, at the scale of municipal and inter-municipal areas in France, most locations have a present or eating population that is lower than their resident population (at least 75% of areas for the PP and up to 90% for the EP). Since annual food consumption is directly proportional to the EP, this also means that most areas have a lower food consumption compared to estimations in previous studies that used the resident population. This directly contradicts the oft-formulated hypothesis (Goldstein et al. 2017; Barles 2009; Niza et al. 2009) that such calculations underestimate the consumption because they do not account for population flows, and in particular for additional non-resident population such as commuters or tourists, in large urban areas. Since the time that residents spend away from the area — e.g. for vacation or family visits, so far mostly ignored in previous studies — is the main contributor to the reduced present population, this also means that studies that overlook this factor risk over-estimating food consumption in the area, especially if they consider additional incoming populations like commuters or tourists.

This comprehensive population-based approach also provides further insights to complement consumption indicators in material accounting methods (European Commission. Statistical Office of the European Union. 2018). A comparison of the work of Bahers et al. (2019) and Barles (2009) — two of the few French urban metabolism studies applying the Eurostat material accounting method — with the results of this study (Table 2), yields insights on the contribution of food consumption to DMC. Both studies used the broader category of agricultural biomass, including animal feed or industrial material in addition to food.

In the case of two intermediary French cities, Rennes and Le Mans, (Bahers et al. 2019), there is a large gap between food consumption and DMC for biomass leaving 78% and 79% of the DMC uncharacterized for both cities. While in line with Barles (2009), food related waste treated outside of the area was excluded from the calculation of DMC and no longer figures in the uncharacterized fraction, waste treated inside the area is considered. Nevertheless, the extent of food waste known from the literature (an average of 17% of food available to consumers wasted at distribution and consumption worldwide, UNEP 2021) cannot explain a four-fold increase in DMC. The transformation of agricultural biomass, not only produced in large farmland areas on the outskirts of both cities (respectively 34% and 55% of the EPCI of Le Mans and Rennes consist of farmland) but also imported, would be another area for investigation. In the case of the Paris metropolitan area (Barles 2009), 57% of the DMC remains uncharacterized for Paris itself. The FC and DMC are closer for Paris Petite Couronne (PPC) and Île-de-France but the 30% discrepancy for these two areas can still not fully be explained by food waste alone. For Île-de-France, half of which is dedicated to farming (48% of its surface area, mostly under cereals and other crops), the discrepancy may be explained by biomass processing taking place in the area. Overall, this shows that further insights are necessary to better understand the patterns of material transformation (including urban food consumption and waste) of intermediary cities and large metropolitan areas, both in France and worldwide.
<table><caption>Table 2: Comparison between resident ($P_r$) and eating (EP) populations, as well as food consumption (FC) — calculated by means of the new model — and previous DMC calculation for food and agricultural products, using material flow analyses for five territories in France. Food consumption is computed by considering all INCA 3 groups except tapwater and hot beverages ($C_{adult}$ = 1952 g/day). $\delta$ = (DMC - FC) / DMC is the fraction of the DMC that is not explained by human food consumption. PPC is Paris and the three surrounding départements (92, 93, 94). *Tourism data is estimated from 2015 and 2018 values. †Estimated using the 2019 value of the $RC_{EP}$.</caption><thead><tr><th>Territory (year)</th><th>P<sub>r</sub></th><th>EP</th><th>FC (kt)</th><th>DMC (kt)</th><th>δ</th><th>Source</th></tr></thead><tbody><tr><td>Rennes Métropole (2012)</td><td>408,549</td><td>384,162*</td><td>274</td><td>1,277</td><td>78 %</td><td>Bahers and Giacchè (2018)</td></tr><tr><td>Le Mans Métropole (2012)</td><td>184,446</td><td>177,902*</td><td>127</td><td>625</td><td>79 %</td><td>Bahers et al. (2019)</td></tr><tr><td>Paris (2003)</td><td>2,166,000</td><td>2,314,000†</td><td>1,650</td><td>3,870</td><td>57 %</td><td>Barles (2009)</td></tr><tr><td>PPC (2003)</td><td>6,321,000</td><td>5,920,000†</td><td>4,220</td><td>6,000</td><td>29 %</td><td>Barles (2009)</td></tr><tr><td>Île-de-France (2003)</td><td>11,259,000</td><td>10,100,000†</td><td>7,200</td><td>10,300</td><td>30 %</td><td>Barles (2009)</td></tr></tbody></table>

## 4.2. Policy relevance

The population-based approach developed in this study is useful for policy-making, particularly in the field of food systems, as policymakers are increasingly re-engaging with food-related issues. To implement territorial food projects, local authorities lack methods and tools to conduct a quantitative assessment of their food system as an initial step. In this regard, open-access, open-source tools, such as the one developed by the authors for the French case (lien gitlab), can contribute to providing local authorities with the knowledge needed to quantify food consumption at the territorial scale. Strategies for strengthening cities' self-sufficiency and recoupling production and consumption benefit from this study's approach (Tedesco et al. 2017).

The composition of the present population, and the eating population in the case of food, provides useful insights to design targeted policies for the socio-ecological transition in the field of food, and potentially also for the public service sector (energy, transport, etc). Types of population and use patterns of a given area determine an its specific profile, structured in this study as influenced, residential, attractive, and autonomous areas. While attraction areas characterized by a comparably high number of commuters and tourists can use restaurants and canteens to offer locally-sourced food services or set up waste reduction initiatives, influenced areas can address the specific needs of busy commuters who often resort to practices that are mostly wasteful and unsustainable (Dobernig and Schanes 2019; Schanes et al. 2018).

## 4.3. Limitations

The main limitation of this study stems from the need to dis-aggregate data at local scales (especially for EPCIs and municipalities) since some of the parameters used are national averages or estimates that may not precisely account for the specificity of local areas. For the time spent at the usual place of residence and at the place of work or study, we used national averages that may display variations depending on the local socio-economic context. For the contribution of tourism, we made assumptions about the distribution of overnight stays from data available at national and département scale that may not precisely reflect the actual choice of accommodation by local tourists. Furthermore,
tourism data may be incomplete for overnight stays at friends and family, as well as for nights spent
in platform-based tourism, such as Airbnb.

The main source of uncertainty that was identified, based on sensitivity analysis, was related to
overnight stays at friends and family, which is the largest share of tourism in France (cf. Supplementary
Material). This may not be accurately captured by surveys of the French statistics agency; it is
estimated at national scale only, and there was no available information about where these overnights
stays take place. Three different distribution rules were tested, according to: a) the resident population
(this is the rule used to compute the results in the main text); b) the number of secondary houses in the
area; and c) the local capacity of commercial accommodation. Sensitivity analysis showed that, in 90%
of EPCIs, changing the distribution rule led to an error in the evaluation of the present population
(PP) that was lower or equal to 10%. However, in the remaining EPCIs, the estimated PP could
vary by up to 40% (see supplementary Figure A3). Furthermore, the choice of rule had a significant
impact on the sensitivity of the PP to the precise value of the number of nights spent at friends
and family: the resident population rule was almost completely insensitive to the exact number of
overnight stays, whereas the other rules led to notable variations in the local PP estimation. A similar
issue was encountered for nights spent in commercial accommodation at scales smaller than French
departments, where detailed data is not available. To overcome this issue, we chose to distribute these
overnight stays according to the local capacity of commercial accommodation, though this may not
match the exact local occupation rate.

Other types of data, such as daily travel surveys (Vallée and Lenormand 2024) or mobile phone tracking (European Commission. Statistical Office of the European Union. 2023; Lévy et al. 2023), may capture individual mobility through transport infrastructure, shopping centers, and leisure spaces. These places of daily activity, in addition to those related to residence, work and tourism, may be associated with food consumption practices. Their use could thus enable one to further refine estimates of the present population over certain time periods and spatial areas. However, they are usually not easily accessible and cover a subset of the population. Furthermore, mobile phone data does not contain any relevant socio-demographic information about the individuals or the reasons for their movements, which makes it difficult to use when estimating food consumption.

**5. Conclusions**

Providing a standardized and actionable method to estimate the present population is an important
step for urban metabolism studies. The comprehensive population-based approach presented in this
study provides a more accurate approach than previous studies to characterize urban food consumption
and analyze which populations are involved. It also shows that territorial analyses that rely on
population data to assess specific material flows should take the discrepancy between the present
population and the resident population into account, especially for touristic and metropolitan areas
that can display major seasonal variations and large population movements.

Applicable to any administrative unit, from small municipalities to large regions, this framework
enables bottom-up estimations of some activities, such as part of a city's energy demand, environ-
mental footprints, or nutrient flows, that depend on the time spent by people in the area. Given the
publicly available census data used, the framework can be adjusted to countries with similar legal
data structures available from national statistics authorities. Standardized guidelines for the present
and eating population concepts, in collaboration with the socio-metabolic research community, would
facilitate comparison between studies. Per capita material or energy flows could be normalized by the
present population or one of its variants to provide a deeper understanding of a city's material use by
limiting the impact of population changes as a source of variation.

The presented framework opens up a range of possibilities for future research, including physically
consistent modeling of diet shift, reduced mobility, and nutrient recovery scenarios, as well as for
designing urban demand-side policies towards more sustainable cities.
# Acknowledgments

This work was supported by the INRAE Metaprogramme BETTER (Bioeconomy for Urban Areas). The work of Tanguy Fardet was funded by a Postdoctoral Fellowship from the Marie Skodowska-Curie Action of the European Commission. We thank the French Complex Systems Institute for providing us with their meeting room in Paris, thus greatly facilitating the writing process. We also thank François Michelot for fruitful discussions, as well as Helga Weisz and Sabine Barles for their feedback on an earlier version of the method.

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# A. Consistency of present population (PP) and legal population in the case of residents

## A.1. Time consistency

The total time $T$ is split into two main periods:

* the time spent on touristic activity, $t_t^{(s)}$,

* the days where the resident is present in the area (at least in the morning and the evening), $d_p$, split into "commuting" and "non-commuting" days, $d_p = d_c + d_{nc}$

with $T = t_t^{(s)} + d_p$, and $d_p = t_r^{(s)} + t_c^{(s)}$, such that:

$$T = t_t^{(s)} + \underbrace{\left(d_{nc} + \frac{d_c}{2}\right)}_{t_r^{(s)}} + \underbrace{\frac{d_c}{2}}_{t_c^{(s)}}. \qquad (13)$$

The days dedicated to touristic activity are further split into main parts, based on data about nights spent in different locations (one "night" is considered as 24h spent locally by one person):
• nights spent abroad, $N_{t,r}^{(out)}$,

• nights spent in market accommodation in the country, $N_{t,r}^{(m)}$,

• nights spent in non-market accommodation in the country, $N_{t,r}^{(nm)}$,

with non-market accommodation being further split into nights spent in secondary housing, $N_{t,r}^{(sh)}$, or at friends and family, $N_{t,r}^{(f)}$. The average time spent on holiday for one person is thus given by:

$$t_{t,r}^{(s)} = \frac{N_{t,r}^{(out)} + N_{t,r}^{(m)} + N_{t,r}^{(sh)} + N_{t,r}^{(f)}}{P_{\text{legal}}} \quad (14)$$

If we define the total number of person-days that are not spent on commutes as $D_{nc} = \sum_{j}(T - d_{c,j})P_{\text{legal},j}$, then for a given population group j, the amount of nights spent in a specific tourist accommodation can be approximated by:

• $N_{t,r,j}^{(out)} = N_{t,r}^{(out)} \frac{P_{\text{legal},j}}{P_{\text{legal}}}$,

• $N_{t,r,j}^{(m)} = N_{t,r}^{(m)} \frac{P_{\text{legal},j}}{P_{\text{legal}}}$,

• $N_{t,r,j}^{(sh)} = N_{t,r}^{(sh)} \frac{P_{\text{legal},j}}{P_{\text{legal}}}$,

• $N_{t,r,j}^{(f)} = N_{t,r}^{(f)} \frac{(T - d_{c,j})P_{\text{legal},j}}{D_{nc}}$.

Since minors cannot be involved in touristic activities except those at friends or family without a supervising adult, all nights except those spent at friends or families are distributed according to the population share, while the latter are distributed according to the total person-days for each age group.

We then define the time spent on touristic activities for residents:

$$t_{t,j}^{(s)} = \min \left( T - d_{c,j}, \frac{N_{t,r,j}^{(out)} + N_{t,r,j}^{(m)} + N_{t,r,j}^{(sh)} + N_{t,r,j}^{(f)}}{P_{\text{legal},j}} \right) \quad (15)$$

Overall, this guarantees that the time spent by any resident group always adds up to T:

$$T = t_{t,j}^{(s)} + t_{r,j}^{(s)} + t_{c,j}^{(s)} \quad (16)$$

Since all durations except $d_{nc}$ are constrained by available data, consistency is ensure by defining:

$$d_{nc,j} = T - t_{t,r,j}^{(s)} - d_{c,j}. \quad (17)$$

## A.2. Consistency of the present population

Since it is not possible to obtain the age groups associated to the nights spent in an area, resident nights are distributed proportionally across all groups while all non-resident tourists nights are associated to the adult population, such that:

$$\text{PPE}_{t,j} = \text{PPE}_{t,r,j} + \text{PPE}_{t,nr,j} = \underbrace{\frac{N_{t,r,j}^{(m)} + N_{t,r,j}^{(nm)}}{T}}_{\text{PPE}_{t,r,j}} + \begin{cases} \frac{N_{t,nr}^{(m)}}{T} & \text{if } j = \text{adult} \\ 0 & \text{otherwise} \end{cases} \quad (18)$$

Combined with the time consistency, the present populations and the contributions from people working or going on holiday abroad always sum up to the total legal population:
<table><caption>Table 3: Parameters used to compute the population equivalents over a year and number of tourist overnight stays for metropolitan France.</caption><thead><tr><th>Name</th><th>Description</th><th>Value</th><th>Source</th></tr></thead><tbody><tr><td>d<sub>c,adult</sub></td><td>Number of commute days per year for non-student adults</td><td>210</td><td>INSEE</td></tr><tr><td>d<sub>c,students</sub></td><td>Number of commute days per year for students</td><td>175</td><td>French public service</td></tr><tr><td>t<sup>(day)</sup><sub>c,j</sub></td><td>Daily commute and work/study time (h/day)</td><td>9</td><td></td></tr><tr><td>t<sup>(s)</sup><sub>c,j</sub></td><td>Yearly hours spent on commute and daily activity</td><td>t<sup>(day)</sup><sub>c,j</sub> &middot; d<sub>c,j</sub></td><td></td></tr><tr><td>N<sup>(out)</sup><sub>t,r</sub></td><td>Nights spent by residents abroad (2019)</td><td>272 &middot; 10<sup>6</sup></td><td>EU + NON EU</td></tr><tr><td>N<sup>(m)</sup><sub>t,r</sub></td><td>Nights spent by residents in market accommodation (2019)</td><td>305 &middot; 10<sup>6</sup></td><td>Hotel + Camping + Others</td></tr><tr><td>N<sup>(sh)</sup><sub>t,r</sub></td><td>Nights spent by resident in secondary housing (2019)</td><td>126 &middot; 10<sup>6</sup></td><td>INSEE</td></tr><tr><td>N<sup>(f)</sup><sub>t,r</sub></td><td>Nights spent by residents at friends or family (2019)</td><td>410 &middot; 10<sup>6</sup></td><td>INSEE</td></tr></tbody></table>

$$ \underbrace{\text{PPE}_{r,j}}_{\text{residents at home}} + \underbrace{\text{PPE}_{c,j}}_{\text{residents commuting in the country}} + \underbrace{\text{PPE}_{t,r,j}}_{\text{residents' holiday in the country}} + \underbrace{\frac{t_{c,j}^{(s)}}{T} P_{c,j}^{(\text{out})}}_{\substack{\text{residents commuting abroad} \\ \text{residents on holiday abroad}}} + \underbrace{\frac{N_{t,r,j}^{(\text{out})}}{T}}_{\text{P}_{\text{legal},j}} = P_{\text{legal},j} \quad (19) $$

## B. Specific calculation for tourists in France

In France, the most precise level for tourist nights is the department (2nd administrative level). To extrapolate tourist nights at a more granular scale, e.g. for municipalities, we use the following formula:

$$ N_{t,\text{local}}^{(m)} = \frac{C_{t,\text{local}}^{(m)}}{C_{t,\text{dep}}^{(m)}} N_{t,\text{dep}}^{(m)} \quad (20) $$

where the fraction of the department-level nights $N_{t,\text{dep}}^{(m)}$ retained as local nights $N_{t,\text{local}}^{(m)}$ is given by the ratio of the local capacity $C_{t,\text{local}}^{(m)}$ (e.g. number of rooms for hotels) and the total capacity for the department $C_{t,\text{dep}}^{(m)}$.

The number of nights spent by residents in non-market accommodations locally is computed via:

$$ N_{t,r,\text{local}}^{(nm)} = \frac{R_{s,\text{local}}}{R_{s,\text{France}}} N_{t,r}^{(sh)} + \frac{P_{\text{legal,local}}}{P_{\text{legal,France}}} N_{t,r}^{(f)} \quad (21) $$

$R_s$ the number of secondary residences, is used as a proxy for the distribution of nights spent in secondary housing ($N_{t,r}^{(sh)}$), and the legal population is taken as a proxy for the distribution of nights spent at friends and family ($N_{t,r}^{(f)}$).
<figure><img src="image_9.png" /><figcaption>Figure A1: Classification of the territories into 4 groups. **Left:** 3D plot showing the contribution of tourists to the PP and the absolute or signed ratio of commuters to the active population. Both values are used to discriminate the 4 types of territories. **Right:** Distribution of $RC_{PP}$ by type of territory.</figcaption></figure>

The total number of local tourist nights is thus given by:

$$N_{t,local}^{(total)} = N_{t,local}^{(m)} + N_{t,local}^{(nm)} = \frac{C_{t,local}^{(m)}}{C_{t,dep}^{(m)}} N_{t,dep}^{(m)} + \frac{R_{s,local}}{R_{s,France}} N_{t,r}^{(sh)} + \frac{P_{legal,local}}{P_{legal,France}} N_{t,r}^{(f)} \quad (22)$$

<table><caption>Table 4: Parameters used to compute the present population over an area.</caption><thead><tr><th>Name</th><th>Description</th><th>Source or value</th></tr></thead><tbody><tr><td>$N_{t,r}^{(m)}$</td><td>Nights spent in market tourism accommodation by resident tourists</td><td>Resident nights (market)</td></tr><tr><td>$N_{t,nr}^{(m)}$</td><td>Nights spent in market tourism accommodation by non-resident tourists</td><td>Non-resident overnight stays (market)</td></tr><tr><td>$N_{t}^{(m)}$</td><td>Nights spent in market tourism accommodation by all tourists</td><td>$N_{t,r}^{(m)} + N_{t,nr}^{(m)}$</td></tr><tr><td>$N_{t,r}^{(sh)}$</td><td>Nights spent in secondary housing by resident tourists</td><td>Resident overnight stays in secondary housing</td></tr><tr><td>$N_{t,r}^{(f)}$</td><td>Nights spent at friends or family by resident tourists</td><td>Resident overnight stays at friends or family</td></tr><tr><td>$N_{t,r}^{(out)}$</td><td>Nights spent abroad by resident tourists</td><td>Resident overnight stays (abroad)</td></tr></tbody></table>

## C. Classification of the territories

## D. Alternative definitions or data for the population equivalents

### D.1. Using different data sources

Depending on the data available, the different population types can be constructed independently of commuter data, using (un)employment, retirement, and education data instead.
The commuter population, which is effectively people working and studying locally (we will call them “active”, here), can equivalently be computed as:

$$PPE_{c,j} = PPE_{a,j} = \frac{t_{c,j}^{(s)}}{T} P_{a,j} \quad (23)$$

with $P_{a,j}$ being the “active” population, defined here as the sum of the working and studying populations for age group j.

The legal population stays

$$PPE_{r,j} = \frac{t_{r,j}^{(s)}}{T} P_{\text{legal},j} + \frac{t_{c,j}^{(s)}}{T} P_{r,j}^{(\text{sedentary})} \quad (24)$$

with

$$P_{r,j}^{(\text{sedentary})} = P_{\text{legal},j} - P_{a,j}. \quad (25)$$

## D.2. Using non-positive contributions in intermediate “population equivalents”

To make definitions simpler, at the detriment of having them positive, one can also define the total population equivalents as a sum of other intermediate contributions that are not independent.

The residential contribution is computed using all present days, including those where some commute happens:

$$PPE_{r,j}^* = \frac{d_p}{T} P_{\text{legal},j} \quad (26)$$

To compensate, the commuting contribution is given by:

$$PPE_{c,j}^* = \frac{t_{r,j}^{(s)}}{T} (P_{c,j}^{(\text{in})} - P_{c,j}^{(\text{out})}) \quad (27)$$

where resident leaving the area ($P_{c,j}^{(\text{out})}$) during commute time have a negative contribution, which can lead to $PPE_{c,j}^* < 0$.

The touristic contribution remains unchanged:

$$PPE_{t,j}^* = PPE_{t,j} \quad (28)$$

This leads to:

$$PP = \sum_{j} PPE_{r,j}^* + PPE_{c,j}^* + PPE_{t,j}. \quad (29)$$

# E. Sensitivity analysis

## E.1. Distribution of visits to friends and family

The main source of tourism-related population movement available in statistical data is residents visiting friends or family. Unfortunately, the amount and destination of these visits is unknown and changes in the way these fluxes are distributed is the main source of uncertainty in the calculation of the present population (PP) for some areas.

We consider three ways in which nights spent at friends and family could be distributed:

* as friends and family are residents, these overnight stays might simply be dispatched according to the population in an area (i.e. the number of residents) – this is the assumption that was used in the main text;

* since hosting people requires space, these overnight stays might preferably be spent in places where these friends and family have secondary houses;
* finally, people may preferably visit friends and family that are in areas of touristic interest.

Of course, one could imagine an infinity of ways to distribute these overnight stays, but these three possibilities are already different enough that they provide an idea of how significantly such changes could affect the PP. Furthermore, the real distribution is likely to be explain at least partly by each of these three contributions.

<figure><img src="image_10.png" /><figcaption>Figure A2: Sensitivity of the PP to the number of nights spent at friends and family and the way they are distributed spatially at the communal level. Left: impact of changing the distribution of overnight stays to follow that of secondary houses on the distribution of relative changes (top) and on the associated map (bottom). Center: distribution of overnight stays according to market capacity. Right: distribution of overnight stays according to the residents. The number of overnight stays is also varied: either divided by two (dashed lines) or multiplied by two (dotted lines). The maps represent the situation for the initial number of overnight stays.</figcaption></figure>

Though the distributions remain qualitatively similar at both communal (Figure A2) and EPCI levels (Figure A3), there can be significant quantitative variation in the PP of an area depending on the chosen hypothesis. Indeed, even at the EPCI level, though most of them (roughly 90%) display lower than 10% variations, especially for areas with more than $10^4$ PP, some results may change by up to 40% for touristic areas depending on the hypothesis for nights spent at friends and family.

## E.2. Remote work

Compared to the hypothesis on tourism, remote work plays a much smaller role except in very specific areas. As shown in Figure A4, even under a highly unrealistic hypothesis of 60% of the whole population working remotely 3 days a week, 95% of the communes do not display relative errors higher than 5% in the PP calculation.
<figure><img src="image_11.png" /><figcaption>Figure A3: Sensitivity of the PP to the number of nights spent at friends and family and the way they are distributed spatially at the level of EPCIs. Left: impact of changing the distribution of overnight stays to follow that of secondary houses on the distribution of relative changes (top) and on the associated map (bottom). Center: distribution of overnight stays according to market capacity. The number of overnight stays is also varied: either divided by two (dashed lines) or multiplied by two (dotted lines). Bottom right: reference map for the distribution of overnight stay according to the residents. All maps represent the situation for the initial number of overnight stays. Top right: distribution of relative errors between the secondary houses or market capacity hypotheses and the reference hypothesis (residents) depending on the PP of the EPCI, for the original number of overnight stays.</figcaption></figure>

## F. Geography and population of Metropolitan France

Located at the westernmost edge of Europe, France, in its metropolitan part, covers 551,695 km². The territory features varied yet generally moderate topography. Metropolitan France has a population of 66.1 million (as of January 2024). The distribution of the French population across mainland territory shows significant disparities: concentration around major cities, increasing attractiveness of coastal and southern regions, and low-density areas - commonly referred to as the "diagonal of low densities" - stretching from the northeast to the southwest, including alpines zones.

France geographical characteristics endow it with a diverse range of landscapes and natural environments, contributing to its ecological richness and tourism appeal. With 90 million international tourists in 2019, France is the world's leading tourist destination.

**Territorial organization:** France has a complex and structured territorial organization with several levels of local authorities. The organizational structure reflects both the geographical diversity of mainland France and its administrative history. It is part of a gradual decentralization process while maintaining a degree of centralization typical of the French state. Metropolitan France comprises 12 regions, 96 departments, and nearly 35,000 municipalities. Several authorities have special statuses, such as the City of Paris, the Metropolis of Lyon and the Collectivity of Corsica. Additionally, municipalities are grouped into Public Establishments for Inter-municipal Cooperation (EPCI),
<figure><img src="image_12.png" /></figure>

Figure A4: Impact of remote work on the PP under 3 different hypotheses. The first one is the current average for remote work in France: 20% of the population doing one day of remote work a week (continuous lines). The second is the average for the Île-de-France region, where Paris is located: 40% of the population working remotely for 2 days a week (dashed lines). Last hypothesis is the highest average rate of remote work for specific populations in that area, with 60% working remotely 3 days a week. On the left, the discrepancy that would arise in the relative change between PP and residents is shown. On the right, the relative error between the data in the main text (not accounting for remote work) and the PP under the three remote work hypotheses is shown. The contour lines delimitate 95% of the distribution for each of the three hypotheses and the histogram show the full distribution for the third one, with the highest rate of remote work.

with 1,254 in 2024, including community groupings like "communauté de communes", "communautés d'agglomération" and metropolitan areas. EPCIs are legal entities formed by multiple municipalities that collaborate to deliver high-quality public services, either because they cannot sustain them individually or because coordination across large territory is more effective. They share responsibilities for mandatory functions (economic development, waste management, etc.) and optional ones (environmental protection, tourism development, social initiatives, etc.). Local authorities are not explicitly responsible for food, but they do take action in this area through other responsibilities, such as school catering (middle school for departments, high school for regions), social action or economic development.