The urban metabolism of airline passengers: Scaling and sustainability

Abstract

Chinese

Concerns about the negative externalities of air transport suggest it is important to consider the sustainability of growth in demand for air transport. However, there is little agreement on how the sustainability of demand should be evaluated. In this paper, I draw on the extensive literature on allometric scaling in biology, which examines animals’ demand for calories, to provide a novel framework for evaluating the sustainability of cities’ demand for air transport service. Viewing cities as analogous to organisms and airline passengers as analogous to life-sustaining resources, I focus on two questions. First, at what rate do cities metabolise passengers, that is, how many airline passengers does it take to fuel a city of a given size? Second, does this metabolic rate differ for business and leisure passengers, which represent different kinds of urban resources? Using data on airline passenger movement between 103 US metropolitan areas in each year from 1993 through 2011, I find that cities demand airline passengers in proportion to their population size, but when viewed separately, demand for business passengers as a function of city size is much lower than for leisure passengers. Moreover, I find that these patterns have remained relatively stable over the last two decades. The findings suggest that considering passenger type is important in evaluating the sustainability of air transport and the capacity of the air transport system to support cities’ continued growth.

Keywords

air travel metabolism scaling sustainability USA

Introduction

As cities grow, so too does demand for air transport service to and from these cities. The increased demand for and use of air transportation can offer both economic benefits, by fuelling urban economic growth, and social benefits, by facilitating the exchange of information and maintenance of social bonds by city residents. However, it is also associated with a number of negative externalities, including pollution and the need for significant public investment in new infrastructure. While these issues suggest that it is important to consider the sustainability of the growth in demand for air transport associated with the growth of cities, there is little agreement on how the sustainability of demand should be evaluated. In this paper, I draw on the extensive literature on allometric scaling in biology, which examines animals’ demand for calories, to provide a novel framework for evaluating the sustainability of cities’ demand for air transport service.

There is a long history in the social sciences of adopting language from ecology and biology, and metaphorically viewing cities as organisms. Burgess (1925) examined cities as complex systems that ‘metabolise’ people, asking ‘in what way are individuals incorporated into the life of a city?’ (p. 53). In these processes, he reserved a special place for mobility and transportation, contending that ‘mobility is perhaps the best index of the state of metabolism of the city. Mobility may be thought of … as the pulse of a community’ (p. 59). Forty years later, Wolman (1965) adopted this approach to examine cities’ natural resource demands and their role in generating air and water pollution. He explained that ‘the metabolic requirements of a city can be defined as all the materials and commodities needed to sustain the city’s inhabitants’ (p. 179), and understanding urban metabolic requirements and processes is critical to addressing urban environmental issues. More recently, others have continued along this conceptual path, using notions of metabolism to critically evaluate cities’ environmental (Kennedy et al., 2007) and social (Bettencourt et al., 2007) sustainability.

As I demonstrate below, this approach can also be useful for examining the sustainability of demand for air passengers, which are key resources for cities that enable urban growth. This is an abstract conception of sustainability that is not directly connected to issues of environmental sustainability per se, but rather is focused on the fact that bigger cities need more resources to thrive. This approach asks ‘How much more?’ and uses the answer to understand the limits of continued urban growth imposed by the finiteness of resources. Accordingly, as a study of urban sustainability, it is situated not in the contemporary literature on environmentalism and sustainable cities (e.g. Houghton and Hunter, 2004), but rather in an earlier literature on the limits of urban growth (e.g. Wardwell, 1980; Goodall, 1972; Kelley and Williamson, 1982). Adopting this frame, by viewing cities as analogous to organisms and airline passengers as analogous to life-sustaining resources, I focus on two related research questions. First, at what rate do cities metabolise air passengers; that is, how many airline passengers does it take to fuel a city of a given size? Second, does this metabolic rate differ for business and leisure passengers, which represent different kinds of urban resources? Answering these questions provides clues about the sustainability of the resource demands of growing cities. I answer these questions using data from the Bureau of Transportation Statistics on airline passenger movement between US metropolitan areas in each year from 1993 through 2011. I find that cities demand or ‘metabolise’ airline passengers in proportion to their population size, but when viewed separately, demand for business passengers as a function of city size is much lower than for leisure passengers. Moreover, I find that these patterns have remained relatively stable over the last two decades. These findings are important because they raise questions about the sustainability of cities’ demand for air transport, and about the capacity of the air transport system, as cities continue to grow.

Airline passengers as key urban resources

Modern cities require a wide range and large volume of resources to sustain their activities and grow. It would go beyond the scope of this, and perhaps any, paper to catalogue all the resource requirements of cities, but in the broadest terms they include things such as natural resources (e.g. land, air and water), energy (e.g. oil and electricity), life-sustaining resources (e.g. food), and infrastructure (i.e. systems for moving and delivering these resources). Some of these key resources have always been a prerequisite for urban growth (e.g. water), while others such as the infrastructure to support information and communication technology are newer requirements for development (Tranos, 2012). Although all of these resources are important for cities, they are all required to support the activities of people, which represent the most critical urban resource. Indeed, it may seem so obvious as to not be worth stating, but cities need people to thrive. Moreover, for modern cities to thrive, they now depend in part on non-local populations (Neal, 2011a), including people who arrive by air from other areas to engage with the city.

Airline passengers serve as key urban resources in a number of ways, including as economic, informational, social and symbolic resources. First, the most widely studied impact of airline passengers on cities is in their role as economic resources, where they can spur job growth not only in the transportation and tourism sectors, but also in the wider economy (Brueckner, 1985; Chi and Baek, 2013; Debbage and Delk, 2001; Goetz, 1992; Neal, 2010; Taaffe, 1956). Moreover, a number of studies have demonstrated that airline passengers are not merely associated with, but are causally responsible for, urban economic growth (Brueckner, 2003; Button and Lall, 1999; Irwin and Kasarda, 1991; Ivy et al., 1995; Neal, 2011b, 2012). Second, airline passengers serve as informational resources for cities, acting as conduits through which new ideas are imported into and exported from cities. Although information can now move quickly from place to place via electronic channels such as the internet, person-to-person information transmission remains important. Third, airline passengers serve as social resources, allowing a city’s local population to stay in face-to-face contact with friends and family living elsewhere, and thus providing a city’s residents with a sense of social connectedness. Finally, airline passengers can serve as a symbolic resource that enhances a city’s status and reputation as an important location, with both researchers and city boosters grounding claims of ‘world city’ or ‘global city’ status in data about a city’s centrality in the global air transport system (Derudder et al., 2007; Hedrick-Wong and Choong, 2015; Rimmer, 1998; Smith and Timberlake, 2001).

When thinking about airline passengers as resources, precision concerning the unit of analysis is critical. Airline passengers serve as key resources for cities in the ways noted above, but airline passengers are also key resources for airports and air carriers. However, there is an important distinction to be made. Airline passengers’ enplanements serve as key resources for airports and carriers because it is the passengers’ enplanement and carriage itself that generates revenue for airports and carriers. In contrast, passengers’ arrival at a final destination serves as a key resource for cities because, upon arriving at his or her destination, the passenger then disengages with the airport and carrier, and instead engages with the destination itself. This distinction is most relevant in the context of hub airports, where a significant proportion of passengers are merely passing through en route to other destinations. Thus, the large passenger volume at hub airports may represent a large volume of key resources for the airport and the specific carriers operating there, but not necessarily for the cities where those airports are located. For this reason, in the discussion and analysis that follow, I focus on cities’ demand for terminally inbound passengers, that is, airline passengers who have the city as their final destination.

Metabolism, scaling and sustainability

Living creatures thrive by taking resources from their environment (e.g. food, water, sunlight), and converting or metabolising these resources into energy that enables growth. Similarly, cities thrive in part by receiving airline passengers (resources) from the air transport system (the environment) and ‘metabolising’ them into job creation, information exchange, social connectedness and global status that enable urban growth (energy). Although not a process of biochemical metabolism, this metaphor can be extended to cities in a number of conceptually useful ways. First, just as an animal ceases to grow when its nutrient intake falls below its metabolic requirement, similarly a city’s growth will slow or stop when its airline passenger intake falls below its needs (Brueckner, 2003; Button and Lall, 1999; Irwin and Kasarda, 1991; Ivy et al., 1995; Neal, 2011b, 2012). Second, just as different animals have different resource requirements (e.g. an elephant needs to eat more than a mouse), different cities have different resource requirements (e.g. New York requires more airline passengers to experience growth than does Omaha). Understanding the sustainability of continued urban growth can thus be reframed (in part) as a question about cities’ metabolic requirements for airline passengers.

Kleiber (1932) found that the amount of resources (in calories) required to support an animal’s growth was directly related to their size (in kilograms):

calories = kilogram s^{3 / 4}

(1)

\log (calories) = 3 / 4 \times \log (kilograms)

(2)

This empirical regularity suggested that, in terms of metabolic requirements, an elephant is simply a really big mouse. Although Kleiber’s Law remains contested among biologists, the broader notion of allometric scaling – that a system’s consumption of resources is a non-linear function of its size – has since been extended to a range of urban phenomena (Batty, 2009). Samaniego and Moses (2008) and Changizi and Destefano (2010) have shown that US cities’ number of highways, number of highway exits, average number of lanes and average cross-city travel speed all scale non-linearly with the city’s land area. Similarly, Bettencourt et al. (2007) have shown that a wide range of key urban resources including electricity, water, gasoline and houses scale non-linearly with city population in the USA, Germany and China. These scaling relationships suggest that just as animals’ metabolic requirements depend on size, so too do cities’.

Examination of allometric scaling relationships often focuses on the value of the scaling exponent, which has implications for the sustainability of the metabolic requirement. When the exponent is exactly 1, this indicates that the number of resources needed is strictly proportional to size: each one unit of growth requires one extra unit of resource. The implications of the scaling exponent for sustainability are more clearly illustrated when it differs from 1. When the exponent is below 1 (sub-linear scaling), this indicates an economy of scale: fewer resources are needed for each additional unit of size. Kleiber’s (1932) derived exponent of 0.75 indicates that although an elephant needs more food than a mouse, it needs less food per kilogram than a mouse. Some have interpreted this as evidence for an evolutionary trend toward efficiency in nature. In the case of cities, Bettencourt et al. (2007) found that the scaling exponent for types of urban infrastructural resources was below 1. For example, they estimated the exponent associated with gasoline sales as 0.79, suggesting that although more gasoline is used in large cities than in small cities, less gasoline is used per person in large cities than small cities. For key urban resources that exhibit sub-linear scaling, cities can do more with less. Although there may be an upper limit on urban growth because the total supply of these resources is finite, reaching that upper limit may take a long time because for the largest cities additional growth requires few additional resources (c.f. Zeno’s paradox).

When the scaling exponent exceeds 1 (super-linear scaling), this indicates an increasing return to scale: more resources are needed for each additional unit of size. This means that as the entity grows in size, its requirement for resources grows even faster. Super-linear allometric scaling is generally not observed in nature, but can arise in man-made systems such as cities. For example, Bettencourt et al. (2007) estimated the exponent associated with employment in private research and development as 1.34, suggesting not only that there are more such jobs in large cities than small ones, but also that there are more of these jobs per person in large cities. For key urban resources that exhibit super-linear scaling, cities do less with more. Thus, although a strict upper limit on urban growth is imposed by the finiteness of resources, cities may reach this upper limit quickly because for the largest cities additional growth requires an enormous number of additional resources.

Recently, attention has turned to understanding the origin of allometric scaling relationships. One explanation points to the properties of the networks used to deliver resources. West et al. (1997) and Banavar et al. (1999) contend the distribution of resources through efficient branching networks (e.g. capillary systems of mammals, the root systems of plants, and the river systems of mountains and flood plains) implies a sub-linear allometric scaling relationship. The hub-and-spoke organisation of post-deregulation US air carriers resembles the branching resource distribution networks observed in nature, suggesting that it may be an efficient system for delivering passengers from one airport to the next. However, the network of airline passengers’ movements from origin to destination does not resemble a branching network, suggesting that the hub-and-spoke arrangement is an inefficient system for moving passengers from where they are to where they want to be (Neal, 2014a). As with Kleiber’s Law, the biological and mathematical foundations of the relationship between network structure and allometric scaling exponents remain contested (Painter et al., 2000). However, it does suggest a possible link between the sustainability of cities’ demand for airline passengers and the structure of the air transport network.

Methods

In each year from 1993 to 2011, city population was measured using the annual estimates of population provided by the US Census Bureau for the largest metropolitan area units defined by the bureau. In most cases, this was the metropolitan statistical area (MSA). However, in cases where the census bureau also defined a consolidated metropolitan statistical area (CMSA, used 1993–1999) or combined statistical area (CSA, used 2000–2011), these larger metropolitan units were used instead. Analysis focused on the largest available metropolitan area unit because this best captures the complete urban agglomeration served by the region’s airports, and mirrors the geographic aggregation of airports performed by AIRNET (see below). Because metropolitan area classifications change over time (e.g. from CMSA to CSA), and because specific metropolitan areas’ status in these classifications change over time (e.g. Atlanta was the Atlanta, GA MSA from 1993 to 1999, but the Atlanta-Sandy Springs-Gainesville, GA-AL CSA from 2000 to 2011), there is slight variation in the sample size and composition over the study period. The models described below are estimated for a total of 101 cities between 1993 and 1999, and for a total of 103 cities between 2000 and 2011, which in both periods represents the entire population of metropolitan areas served by a major airport in the USA.¹

These cities’ annual number of terminally inbound airline passengers was measured using data from the US Bureau of Transportation Statistics’ Airline Origin and Destination Survey (DB1B). These data contain a 10% random sample of airline tickets, and are provided in quarterly intervals at a highly disaggregated level. Specifically, each record indicates a party’s (one or more passengers travelling together on the same ticket) takeoff from one airport, and landing at another airport (i.e. a coupon). To facilitate analysis, these data were aggregated by metropolitan area and transformed to omit layover stops using the AIRNET software (Neal, 2014b). In addition, AIRNET was also used to estimate the number of total passengers travelling for business or for leisure. Because the original data do not contain information about passengers’ travel purpose, these estimates are based on each passenger’s fare and number of travel companions. Specifically, AIRNET flags passengers travelling alone on a ticket costing statistically significantly more than the route’s mean fare as business passengers, and flags passengers travelling with one or more companions on a ticket costing statistically significantly less than the route’s mean fare are flagged as leisure passengers. These data processing steps yielded three variables used to measure cities’ intake of airline passengers as key resources. First, TOTAL_MY measures the total number of passengers having one of metropolitan area M’s airports as their final destination in year Y. Second, BUSINESS_MY measures the estimated number of business passengers having one of metropolitan area M’s airports as their final destination in year Y. Finally, LEISURE_MY measures the estimated number of leisure passengers having one of metropolitan area M’s airports as their final destination in year Y.

Following other urban allometric scaling studies (e.g. Bettencourt et al., 2007; Changizi and Destefano, 2010; Samaniego and Moses, 2008), three OLS regressions were estimated separately for each year from 1993 to 2011:

\log ({TOTAL}_{M}) = α + β_{1} \log ({POP}_{M}) + ε_{M}

(3)

\log (BUSINES S_{M}) = α + β_{1} \log (PO P_{M}) + ε_{M}

(4)

\log (LEISUR E_{M}) = α + β_{1} \log (PO P_{M}) + ε_{M}

(5)

By using the logarithm of the key independent (population) and dependent (passengers) variables, it is possible to estimate the scaling exponent (β) through a linear model. Unlike in many linear models where the interest is in whether the coefficient’s is statistically significantly different from 0 (H₀: β = 0; H_A: β ≠ 0), in these models interest is in whether the coefficient is statistically significantly different from 1 (H₀: β = 1; H_A: β ≠ 1). This hypothesis tests whether the demand for resources is strictly proportional to size (null hypothesis), or exhibits a non-linearity (alternative hypothesis).

Estimating these models using data only on cities and air travel in the USA is a scope condition made necessary by the comparability of spatial units and the availability of suitable air traffic data. Although intra-national samples are common for studies of urban scaling phenomena, and their findings have been replicated in multiple national contexts (Arcaute et al., 2015; Bettencourt and Lobo, 2016; Bettencourt et al., 2007; Changizi and Destefano, 2010; Samaniego and Moses, 2008), it is nonetheless important to consider how these scope conditions may impact the analysis. First, although defining metropolitan spatial units can be challenging in any context, the greater distances between US metropolitan areas makes them and their associated airport catchment areas more discrete than in some other regions. The more discrete spatial distribution of population and cities in the USA may make it a better context for examining allometric scaling phenomena using the cities-as-organisms metaphor because the resources (here, air passengers) can be more clearly allocated to specific organisms (here, cities). The same metaphor, and associated modelling framework, may be fuzzier in contexts where different metropolitan areas and the resources they ‘metabolise’ cannot be as easily distinguished (Arcaute et al., 2015; Bettencourt and Lobo, 2016). Second, unlike in many other countries, there are few alternatives to air transport for medium- and long-range travel in the USA. Thus, to the extent that cities rely on travellers from other places as key resources, a singular focus on air passengers is more appropriate in the USA than it may be elsewhere. Finally, these data include only domestic passengers, but do not include international passengers. Domestic passengers vastly outnumber international passengers at most US airports, including major hubs (e.g. by nearly 10-to-1 in Atlanta), but the opposite is true at many non-US airports (e.g. Schiphol). Thus, the omission of international passengers in a US sample is likely to have little effect on the scaling exponent,² but would be of critical importance in a similar scaling study conducted elsewhere.

Results

Figure 1 illustrates the results from the three models described by equations (3)–(5) using passenger and population data from 2002. Figure 1(a) shows that cities’ total annual number of airline passengers exhibits a strong scaling relationship with city size (R² = 0.742), and that the scaling exponent was not statistically significantly different from 1 (β = 1.066, n.s.). This indicates that when considering all airline passengers, cities’ demand for airline passengers is strictly proportional to city size. Boston, MA and Charleston, SC lie close to the regression line and offer typical cases that illustrate this finding. In 2002, the Boston CSA was home to 7,430,385 people and received 4,495,100 airline passengers, or approximately 0.6 passengers per capita. The Charleston MSA was home to 566,543 people and received 341,190 passengers, or approximately 0.6 passengers per capita. Thus, although Boston was larger than Charleston by more than an order of magnitude, its per capita demand for airline passengers was roughly the same. To the extent that cities are like organisms that require airline passengers as food, Boston is just a bigger version of Charleston.

Figure 1.

Scaling relationships between city population and inbound airline passengers.

Figure 1(b) shows that cities’ annual number of business passengers also exhibits a strong scaling relationship with city size (R² = 0.782), but that the scaling exponent is statistically significantly smaller than 1 (β = 0.903, p < 0.05). This indicates that cities’ demand for business passengers and the urban resources they represent exhibits an economy of scale. Larger cities may require more business passengers than smaller cities, but they require fewer business passengers per capita because they are more efficient at ‘metabolising’ business passengers into economic growth. Again, Boston and Charleston offer a concrete illustration. Boston received 117,200 business passengers, or 0.016 per capita, while Charleston received 18,400, or 0.032 per capita. Although Boston is ten times larger than Charleston, it demanded half as many business passengers per capita, suggesting that Boston’s greater size allows it to more efficiently convert business passengers into economic growth and symbolic status than Charleston. When it comes to business passengers, Boston is not merely a bigger version of Charleston, but rather it processes these resources differently. As Kleiber (1932) found in nature, bigger cities are more efficient than smaller cities in their metabolism of business passengers.

Finally, Figure 1(c) shows that cities’ annual number of leisure passengers exhibits a strong scaling relationship with city size (R² = 0.676), but that the scaling exponent is statistically significantly greater than 1 (β = 1.263, p < 0.05). This indicates that cities’ demand for leisure passengers and the urban resources they represent exhibits an increasing return to scale. Larger cities not only require more leisure passengers than smaller cities, but they require more leisure passengers per capita. To illustrate, Boston received 2,410,650 leisure passengers, or 0.32 per capita, while Charleston received 95,980, or 0.17 per capita. In the case of leisure passengers, although Boston is ten times larger than Charleston, it demanded more than ten times more business passengers than Charleston, suggesting that Boston’s greater size makes it less efficient at converting leisure passengers into the social connectedness desired by residents.

The relatively large R² values in the three models illustrated by Figure 1 provide evidence of the allometric scaling of cities’ air passenger demand. However, there are some cities that deviate from the trend, demanding more or fewer passengers than might be expected given their size alone. Four cities that exhibit among the largest residuals across these three models are highlighted in each panel of Figure 1, and provide some clues about the non-size factors that are also responsible for the number of air passengers demanded by cities. Cities such as Las Vegas and Orlando that play key roles as both vacation destinations and hosts of business conventions demand many more passengers than their size alone would suggest, while cities such as Allentown and Bellingham that have been struck particularly hard by the effects of deindustrialisation demand many fewer passengers than expected for their size. Thus, while some variation is expected in any empirical sample, and is limited in this sample, size-independent factors help explain some of the more extreme outliers.

Figure 1 examines the allometric scaling relationship between airline passengers and city size for a single year, 2002. To examine whether these findings – proportional scaling for all passengers, economy of scale for business passengers, and increasing return to scale for leisure passengers – are unique to this one year or a more stable pattern, Figure 2 plots the scaling exponent in each year from 1993 to 2011. The shaded region around the line shows the 95% confidence interval around each year’s estimated scaling exponent, and thus highlights when the exponent was statistically significantly different from 1. Figure 2(a) highlights that cities’ demand for total airline passengers was proportional to size (i.e. β ≈ 1) in every year of the study period. Figure 2(b) demonstrates that although cities’ demand for business passengers exhibited an economy of scale in some years (including, as Figure 1(b) shows, in 2002), in other years cities’ demand for business passengers is proportional to size. Finally, Figure 2(c) shows that cities’ demand for leisure passengers has exhibited an increasing return to scale (i.e. β > 1) in every year of the study period.

Figure 2.

Scaling coefficients for population versus inbound passengers, by year.

Discussion and conclusion

These results offer three key lessons. First, they serve to reinforce the notion that when exploring urban phenomena through airline transportation, distinguishing passenger types are critical (c.f. Chen, 2000; Lassen, 2006; Neal, 2010, 2014a; Ostrowsky et al., 1994; Uriely, 2001). Without making such a distinction, it appears that cities’ demands for airline passengers is simply proportional to their size: bigger cities demand proportionally more passengers. However, this analysis of separate passenger types reveals that this apparent proportional-to-scale relationship actually masks two opposite relationships – sub-linear for business passengers and super-linear for leisure passengers – which have notably different implications for cities prospects for growth.

Second, these results replicate patterns observed in other studies of urban scaling phenomena. For example, Bettencourt et al. (2007) found that cities display an economy of scale in their requirements for ‘material quantities … associated with infrastructure’, which scale sub-linearly with city size (β ≈ 0.8). Although business passengers are not examples of material infrastructure such as roads or electrical cables, they can nonetheless be viewed as a kind of ‘human infrastructure’ for economic activity. That is, in the same way that roads provide conduits for the movement of people, business passengers provide conduits for intercity economic transactions. Accordingly, consistent with prior studies findings, I find that cities display an economy of scale in their demand for business passengers, which scale sub-linearly with city size in many years during the study period (e.g. β ≈ 0.9 in 2002). Conversely, Bettencourt et al. (2007) also found that cities display an increasing return to scale in their requirements for ‘quantities related to … the intrinsically social nature of cities’, which scale super-linearly with city size (β ≈ 1.2). Because they come to cities to engage in cultural events and activities through visits to museums and restaurants, and to renew and reinforce social relationships through visits to friends and family, leisure passengers represent a clear expression of the social side of cities’ activity. Again consistent with prior findings, I find that cities display an increasing return to scale in their demand for leisure passengers, which scale super-linearly with city size (β ≈ 1.26 in 2002).

Finally, these results illustrate a potentially helpful new way to think about the sustainability of urban growth. Bigger cities need more key resources to thrive than smaller cities. Moreover, because resources are finite, there is an upper limit on how big a city can become and still thrive, even if it is difficult to know precisely what this upper limit is. However, when trying to understand the sustainability of urban growth, identifying the upper limit of city size may be less pressing than identifying how soon that limit might be reached. This study suggests that the answer depends on a nuanced understanding of the types of resources in question. Airline passengers represent a type of resource that fuels cities, by supplying them with labour, information, money, social connection and status. As cities get larger, they require more airline passengers to meet their needs. But, at what rate does a city’s requirement for airline passengers increase as it grows, or to use a biological metaphor, at what rate does a city metabolise airline passengers? When airline passengers are considered as a single undifferentiated type of resource, cities’ demand increases proportionally with their size. This is consistent with a naïve assumption that bigger cities need more resources, and might be viewed as a kind of baseline against which the sustainability of cities demand for other resources might be evaluated.

However, airline passengers are not a single type of resource. There are different types of airline passengers – business and leisure – that provide fuel for cities in different ways, and as these results demonstrate, are metabolised at different rates. Specifically, a city’s demand for business passengers scales with population sub-linearly, while its demand for leisure passengers scales super-linearly. The implications of these differing scaling relationships for the sustainability of urban growth are easier to see when viewed in terms of passengers demanded per capita for cities of different sizes. Figure 3 illustrates the predicted per capita demand for business and leisure passengers, based on the average scaling exponent observed across the study period, for cities ranging in size across four orders of magnitude.

Figure 3.

Per capita passenger demand, by passenger type and city size.

A small city such as Bozeman, MT must attract around 0.021 business passengers per capita from the finite pool of business passengers to sustain its activity. As such a city grows, the number of business passengers per capita it must attract decreases. Framed in economic terms, the city enjoys a declining marginal cost (in terms of business passengers) of growth, and thus continued growth is easier because it requires fewer and fewer new resources to do so. Of course, at some point the total pool of business passengers will be exhausted by the demands of this and the other cities in the system, which imposes a strict upper limit on urban growth. However, other things being equal, cities’ demand for business passengers as resources places less strain on the growth of individual cities and the US urban system (i.e. allows growth to be more sustainable) than does their demand for other resources that are metabolised less efficiently.

Leisure passengers are one example of a resource that is metabolised less efficiently, and thus which have different implications for urban growth. Figure 3 also illustrates that a small city must attract fewer than 0.2 leisure passengers per capita from the finite pool of leisure passengers to sustain its activity. As it grows, the number of leisure passengers per capita it must attract increases rapidly. Here, framed in economic terms, the city encounters a sharply increasing marginal cost (in terms of leisure passengers) of growth, and thus its continued growth is challenged because it requires more and more new resources to do so. Other things being equal, cities’ demand for leisure passengers as resources places more strain on the growth of individual cities and the US urban system (i.e. allows growth to be less sustainable) than does their demand for other resources that are metabolised more efficiently.

Although business and leisure passengers represent different kinds of resources that cities demand at different rates, which may have implications for the sustainability of urban growth, it is important to note that these resources may not be separable. Because most commercial aircraft typically carry many leisure passengers and just a few business passengers, cities’ demand for business passengers can only be met if they also receive leisure passengers. Indeed, cities’ apparent appetite for leisure passengers may not be essential for their survival, but rather an artefact of the current distribution of business and leisure seats and fares. Under the current model, it would be quite difficult for cities to receive the necessary number of business passengers while simultaneously reducing their consumption of leisure passengers. However, alternate models are possible. Some airlines are exploring business-class-only international routes, but similar shifts in the distribution of passenger types on domestic flights could make it possible to satisfy cities’ needs for business passengers independently of their needs for leisure passengers.

As an initial look at the scaling relationship between airline passengers and city size, this analysis has some limitations, which also identify avenues for future research. First, the data were restricted to cities in a single national urban system and to domestic air passengers. Future studies in this area should examine whether the patterns revealed here are the same in other regions, at the level of the global urban system, and when additional types of transportation are included (e.g. international air passengers, domestic and international rail etc.). Second, the models were estimated cross-sectionally to provide a concrete look at scaling exponents in specific years, but subsequent studies should explore the possibility of panel models designed to explicitly test hypotheses concerning longitudinal trends in scaling exponents. Finally, while this study focused on the sustainability of urban growth in abstract terms by examining differences in the number of passengers that different sized cities require, it did not examine the positive (e.g. economic prosperity) or negative (e.g. air pollution) externalities associated with the growth of air traffic volume. Future research can pair these findings with information about the social, economic and environmental sustainability of urban growth that is facilitated by a steady supply of air passengers.

This study has applied the framework of allometric scaling to understand how urban size and growth is related to airline passengers, which can be conceptualised as a kind of resource that sustains cities’ activities. Separating the effects different types of passengers, which represent different kinds of resources, the results suggest that cities’ decreasing marginal demand for business passengers (i.e. sub-linear scaling with size) makes continued growth more possible or sustainable, while their increasing marginal demand for leisure passengers (i.e. super-linear scaling with size) makes continued growth more difficult or less sustainable. It is worth noting that leisure passengers, for which cities’ demands are unsustainable in the long-run, represent a much larger share of total air passenger volume than business passengers, for which cities’ demands are more sustainable. Does this mean urban growth is unsustainable? Probably not, for now. Unsustainable levels of resource consumption in complex systems can often be resolved through technological innovation (Bettencourt et al., 2007). For example, in the context of transportation, cities once thrived on visitors arriving by car. However, as cities continued to grow, their demand for visitors exceeded the capacity of the highway system. Rather than impose an upper limit on city growth, the development of the air transport system offered a new and higher-capacity way of delivering visitors to cities, allowing cities to continue growing (Batten and Thord, 1995; Marchetti, 1985). Perhaps we are approaching a need for another technological innovation that can meet growing cities’ voracious appetite for people, but it remains unclear whether a suitable innovation might come from inside the air transport system, such as a reorganisation of the network to provide separate service for business and leisure passengers, or will involve something entirely different.

Footnotes

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Notes

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