"The metabolic requirements of a city can be defined as all the materials and commodities needed to sustain the city's inhabitants at home, at work, and at play.” – Abel Wolman [1]
Writers and scientists have often used the analogy of a city as a living organism, Manhattan as a termite mound. Scientists have applied that analogy in a search for lessons in sustainable urban planning.
A new study in PNAS builds upon the idea that cities follow predictable biological principles. Their challenge to the assumption that bigger cities are more sustainable than small ones will help us to better understand both the biology of our cities and, more importantly, how science grows through refinement.
A Grand Analogy – Cities as Bodies
“Cities are sustained by similar network systems such as roads, railways, and electrical lines that transport people, energy, and resources and whose flow is therefore a manifestation of the metabolism of the city.” ― Geoffrey West
Imagine a bustling human body, a network of cells, blood vessels, and organs, all working together. This is the analogy through which urban theorists first approached cities: populations as “body mass,” roads as “vascular systems,” and CO₂ emissions as metabolic waste.
Scientists then crossed disciplines to cross-pollinate their work with a rule describing how biological systems change with size, Kleiber’s Law. Max Kleiber found that the energy that animals required daily to sustain their bodies, their metabolic rate, scaled in proportion to their size. Mice have a lower metabolic rate than elephants. Urban scientists applied this to cities: population as mass, and infrastructure or emissions as metabolism. The “found” elegant power laws suggesting that bigger cities, like bigger animals, function with systemic efficiency.
It was a bold first draft of a theory. However, like any scientific first draft, it had its flaws.
Cracks Appear in the Analogy
While Kleiber’s Law applies well to biological organisms and is useful in considering urban planning, it falters when scientists apply the biology underlying Kleiber’s Law to cities.
- Fuzzy Species Boundaries: Unlike an animal with clear skin or a shell, a city’s boundaries are arbitrary. Where exactly does New York City end? In the five boroughs? Or do we need to include the commuter areas, within an hour, the tri-state? Each choice yields different scaling exponents, making the scientific findings boundary-dependent.
- Ignoring Internal Complexity: Measuring averages, the “whole-istic” view is often easiest, but hides what happens within. It describes a human by weight and heart rate, but ignores whether their lungs are strong or weak, or whether their cells are functioning properly. This neglect of the key processes that account for the aggregate average and the neighborhood variability within cities means that the processes shaping cities are obscured.
While urban science found a helpful analogy, further study discovered its blind spots, and science began to self-correct by questioning its own tools.
A New Tool – A High-Resolution Scan
Planners have long postulated that bigger is better because large urban areas require fewer resources and energy per capita and generate more wealth. However, this was not easy to model due to the ad-hoc way city boundaries are often drawn. To resolve these fuzzy boundaries, the current researchers “rescaled” 100 cities around the globe, breaking them down into units that could be more equitably compared across variously sized urban areas. Instead of comparing New York to Lagos as aggregate wholes, they analyzed that intraurban variability block by block.
Based upon millions of data points from these different city units, they found a scaling law, like Kleiber’s, that connects population size to transport networks, economic activity, and CO2 emissions.
Here are their significant insights:
- Boundaries are conveniences, not natural laws. Urban dynamics spill beyond city lines. For example, Paris’ CO₂ scaling changes depending on the boundary you draw.
- Details matter. Hot spots in Phoenix, identified at 250 m resolution, show how targeted transit lanes can cut emissions more effectively than city-wide averages.
- Cities are adaptive systems, not top-down machines. The use of Medellín’s outdoor escalators reshaped transit flows organically, more effectively than the central planner’s rigid planning ratios.
- Key ingredients scale together one-to-one. Shenzhen’s population growth paralleled rises in intersections and emissions, until metro expansions broke the link, proving design matters.
- Underlying math is universal. Despite local quirks, rescaled distributions of people, intersections, and CO₂ collapse onto the same master curve for London, Lagos, and Los Angeles. It seems for cities, size doesn’t matter.
Overall, the findings reframe cities as complex adaptive systems, not machines. Like our body, they are not centrally commanded but emerge from distributed interactions.
Science Self-Corrects
Here is the larger lesson: this paper is not just about cities; it describes how science advances. Begin with a hypothesis, the Kleiber-inspired analogy gave urbanists their first organizing principle. Identify the limitations. In this instance, boundary biases and the neglect of intraurban variability. Refine the methodology and tools, more granular, high-resolution data allowed a shift of focus from averages to distributions. Build upon the shoulders of the proceeding work, Kleiber’s Law is a “special case,” describing a broader, universal framework.
This is science’s self-correcting rhythm: theories emerge, are tested, challenged, refined, and expanded into deeper truths. Just as biology advanced from describing anatomy to decoding DNA, urban science has advanced from city-wide averages to the universal mathematics of intraurban life.
Why This Matters
Science thrives by iteration, each step building on, correcting, or transcending the last. Science does not “flip-flop,” it self-corrects. Our word choice matters because flip-flop comes with its own baggage of ignorance and, of late, intentionality. The scientific method, the action of science, is self-correcting, a phrase that reflects a more humble introspection. This paper, in providing insights into the hives we call cities, exemplifies how science continually improves upon itself: through analogy, critique, refinement, and the discovery of more profound universal truths.
“The lesson is clear: neither science nor data are democratic. Science is meritocratic and not all data are equal.”― Geoffrey West
[1] Abel Wolman is the engineer who brought chlorinated water and a drastic reduction in communicable diseases to our water systems.
Source: A stochastic theory of urban metabolism PNAS DOI: 10.1073/pnas.2501224122
