The Secret Rule Behind America’s City Growth: Why Some Cities Flourish While Others Falter

A fascinating new study from the Complexity Science Hub (CSH) in Vienna has uncovered a rule that has quietly guided the growth and transformation of U.S. cities for nearly two centuries. Despite massive economic and technological revolutions — from the rise of manufacturing and railroads to the modern dominance of services, computing, and AI — American cities seem to evolve according to a surprisingly consistent pattern of “coherence.”

In simple terms, coherence describes how well a city’s economic activities “fit together.” A city might change what it produces — shifting from steel to software, for example — but the overall degree of internal connectedness between its industries tends to remain remarkably stable over time.

This study, titled “The Coherence of U.S. Cities,” was published in the Proceedings of the National Academy of Sciences (PNAS) in September 2025. It was conducted by Simone Daniotti, Matté Hartog, and Frank Neffke, who drew upon a massive collection of historical and modern economic data spanning 170 years of American history.

Let’s explore what the researchers found — and why it might change the way we think about urban development, diversification, and economic resilience.

What the Study Looked At

The team analyzed one of the most extensive datasets ever assembled on urban change in the United States. It included:

650 million individual census records from 1850 to 1940
6 million patents showing how innovation spread across regions
Modern employment data from the U.S. Bureau of Labor Statistics (2002–2022)
Additional sources capturing the industrial, occupational, and technological evolution of hundreds of American cities

Using this data, they measured how closely related the jobs, industries, and technologies within each city were — a measure they call coherence.

If two randomly chosen workers in a city tend to have related skills or industries (say, both work in car manufacturing or mechanical engineering), the city has high coherence. If they work in completely unrelated fields (say, one in fashion design and another in aerospace engineering), coherence is lower.

The Consistent Pattern of Coherence

The most striking finding was that, on average, U.S. cities have maintained a steady level of coherence for almost two hundred years.

Even as cities transformed — from the age of craftsmanship in the 1800s to the service-based economies of today — they did so while keeping this internal economic “fit” remarkably constant.

This means cities are not endlessly flexible or chaotic. They adapt, but only within limits. When a city like Pittsburgh transitioned from steelmaking to technology and healthcare, or Boston shifted from heavy manufacturing to education and biotech, they did so in a way that kept their internal economic network cohesive.

According to the researchers, cities can’t just reinvent themselves at random. They need to build new industries that still connect to the old ones — using their existing workforce, infrastructure, and institutional base as a foundation.

The West Coast Experiment

The researchers also looked closely at how the West Coast developed — since cities like Los Angeles and San Francisco emerged much later than older East Coast hubs such as Boston or Philadelphia.

In 1850, during the Gold Rush era, less than half of all export-oriented occupations found across the broader United States existed on the West Coast. But within just fifty years, that share surged to nearly 90%.

That’s a stunning transformation — yet despite this rapid diversification, West Coast cities kept their coherence levels constant, roughly matching those of older, more established cities back east.

In other words, Los Angeles and San Francisco expanded into new fields at lightning speed, but they didn’t do it chaotically. They developed in ways that preserved internal alignment among industries, technologies, and skills.

The Rule of Size: Bigger Cities, Lower Coherence

The study uncovered another consistent law: the larger a city grows, the less coherent it becomes.

Across every era and dataset, coherence drops at a rate of about 4% each time a city’s population doubles.

So as a city expands — drawing in more people, industries, and ideas — it becomes more diverse and complex, but also less tightly connected in its internal structure.

That pattern holds from 1850 to 2022, surviving through revolutions in transportation, communication, production, and technology. From railroads and telegraphs to the internet and artificial intelligence, the relationship between population size and coherence has stayed virtually unchanged.

This suggests there’s something fundamental about how economic activity scales with size — a kind of universal rule of urban organization.

Why Transformations Are Constrained

The key insight from the research is that city transformations are not limitless.

When a city evolves, it must do so while staying “coherent.” It can add new industries or drop outdated ones, but only if the remaining mix of activities still fits together logically and functionally.

Think of it like a biological organism. A city can grow new organs, but it can’t rearrange them arbitrarily — the system has to keep working as a whole.

This is why some cities struggle to adapt while others thrive. The challenge isn’t just adopting new technologies — it’s finding a transformation path that doesn’t disrupt the economic web that keeps the city functional.

Lessons for Policy and Urban Development

For urban planners and policymakers, these findings come with clear lessons.

The urge to diversify — to become a “tech hub” or a “green economy leader” — is natural and often encouraged. But the study warns that diversification must be balanced with coherence.

Every city has a limited capacity for diversity based on its size, workforce, infrastructure, and local institutions. Trying to stretch beyond that can weaken the foundation that holds the local economy together.

The authors point out that larger cities can support a wider range of industries because their networks and resources are broader. However, even large urban centers face boundaries on how unrelated their industries can become.

That’s why smaller cities should focus on deepening and expanding adjacent capabilities — sectors that naturally connect to what they already do well — rather than chasing every new trend.

For example, a city with a strong base in automotive manufacturing might successfully evolve into electric vehicle design or battery production, but leaping straight into biotech or aerospace would likely be too big a jump.

In short, successful cities grow by building on what they already are, not by abandoning their roots.

What “Coherence” Really Means

The study defines coherence as the economic glue that binds a city together. It combines three related ideas:

Variety – how many different industries or occupations a city hosts.
Balance – how evenly those industries are distributed across the workforce.
Disparity – how different those industries are from one another.

A highly coherent city, like Detroit in its car-making prime, has a smaller number of tightly connected industries. A less coherent city, like New York, might have hundreds of unrelated sectors — from fashion and media to finance and healthcare.

Neither model is “better.” The key is that cities tend to preserve a consistent internal relationship between these factors over time, even as the actual industries change.

A Universal Rule of Urban Evolution

One of the most remarkable aspects of this research is that it finds a stable scaling relationship — meaning the connection between coherence and population size doesn’t depend on the time period or type of data used.

This rule holds across the Industrial Revolution, the rise of computers, and even the AI era. Despite radical shifts in technology and demographics, the underlying relationship remains the same: bigger cities can support more diversity, but always within a predictable limit.

This suggests that the way human societies organize economic activity follows deep, consistent patterns — a finding that aligns with previous work in complexity science and urban scaling theory.

Broader Context: Why This Matters

This study fits into a broader effort to understand cities as complex systems — networks of people, skills, technologies, and infrastructure that evolve over time.

Previous research in complexity economics has shown that cities drive innovation by clustering related industries and knowledge. That clustering fuels creativity and productivity — but also sets natural limits on how much diversity a system can handle before it loses coherence.

The concept of coherence could also help policymakers forecast how cities might adapt to automation, AI, and climate change. As economies shift toward new technologies, cities that preserve their internal coherence are likely to be more resilient, while those that stretch too far may find themselves fragmented.

The Bigger Picture: Why Some Cities Succeed

When we look at why cities like Boston, Austin, or San Francisco continue to reinvent themselves while others stagnate, this study offers a clue.

These cities don’t just add new industries — they build connected ones. Boston didn’t randomly become a biotech hub; it evolved from its base in higher education and medical research. San Francisco’s tech boom didn’t appear out of nowhere; it grew from a foundation of electronics, engineering, and university-driven innovation.

Cities that grow coherently can transform without breaking the internal web that supports them. Those that don’t — that try to leap into unrelated sectors — risk economic collapse or long-term decline.

In Summary

Across 170 years, American cities have changed enormously in what they produce — but not in how they evolve.

From the mills of 1850 to the microchips of today, every city has balanced its desire to diversify with an invisible constraint: the need to remain coherent.

The study’s main lesson is clear — growth, innovation, and transformation are all possible, but they have to happen within the boundaries of a city’s existing capabilities and connections.

That hidden rule — coherence — might just be the secret reason why some cities manage to thrive while others fade away.

Research Reference:
The Coherence of U.S. Cities – Proceedings of the National Academy of Sciences (2025)