Growth and Scale of Living Systems

Zubair Talib
6 min readJan 16, 2023

The principles and science behind scaling of organisms and cities

Photo by Anders Jildén on Unsplash

Life is beautiful, complex and incredibly varied with more than 8 million difference species on Earth alone. Is there any rhyme or reason for how large animals can grow? Or for that matter how small they can be? How long they can live? What about “almost living” entities like cities and companies…are there any principles or laws that govern their growth?

These are some of the questions that Geoffrey West addresses in his captivating book Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies”.

Scale by Geoffrey West

This book asks some of the most basic questions about life and uses data and scientific methods to attempt to understand the governing principles and concepts for developing a predictive, mathematical framework for understanding some key aspects of life and society.

This blog will aim to share just a few high-level observations. If you want to read a more detailed review this is a nice blog and this is a detailed book summary.

Scaling of Organisms

The base observation of the book itself is quite fascinating, namely that each organism or animal is, on average, a scaled version of each other. And the same is true for cities and companies. Here are some compelling scaling observations.

Source WSJ

As the above image shows, mammals’ energy use scales sub-linearly. Concretely, this means that as the size of an animal doubles, the energy requirements are less than double — specifically the energy requirements only increase by 3/4 (75%) instead of 100% as you’d expect for double the size of creature. This is to say that larger animals are more energy efficient, pound for pound, than smaller animals.

Interestingly a number of other biological traits scale in a similar fashion, for example, heart rate decreases by a similar factor, whereas life span increases by the same factor — as we can observe mice have very fast heart rate, but live for short lifespans and elephants have very slow heartbeats and live for much longer lifespans — all in similar scaling fashion.

Science believes much of the aging process has to do with the activity of the metabolic process 1) wear and tear associated with the friction of blood pumping and moving through blood vessels and 2) chemical damage from the by-products of the production of ATP (energy molecules). Giving the faster metabolic processes of smaller organisms it makes sense that their lifespans are shorter, or said conversely as the organism scales and becomes more energy efficient, the organism is able to have less wear and tear in those energy production processes and have a longer life span.

Limits to Growth

The other interesting observation around biological scaling has to do with limits to growth. The first is about the allocation of energy between growth and maintenance. Initially almost all energy available is used for growth. But as the organism grows and doubles in size, the number of cells double, and the amount of energy required for maintenance also doubles. The supply of energy (metabolic rate) only scales at the 75% rate — so there is less than double the amount of energy for such maintenance. As the organism grows, more and more of the supply energy must be used in maintenance and there is a decreasing amount of energy available for growth.

The second factor for limits to growth has to do with straightforward structural physics. The book uses Godzilla as a fictional example. At 60x the height of a human, Godzilla would have 60³ (216,000) the amount of volume or mass of a human. However the bones or leg structure would only have 60² (3,600) times the cross-sectional area or strength of human legs. Since the fundamental bone material and composite cells are evolutionary similar — its unlikely they would be able to be 60x fundamentally stronger.

Principles and Underlying Understanding

Substantial research has gone into understanding and explaining why organisms scale in the observed manner and the particular study referenced in this book has been around network theory and the distribution of energy, materials, and information. These theories and principles are interestingly common in animals, cities, and perhaps other “organisms”. The author shares a few key insights:

Networks are space-filling meaning that they services all “terminal units” — that is that blood, oxygen, and energy need to flow to cells in an organism, or water, electricity need to flow to all houses or people in a city, etc.

Terminal units are invariant meaning that the final terminal unit is of similar form. Again this is the understanding that cells in a mouse, human, or elephant are fundamentally similar due to evolutionary parsimony. And in the case of cities — the final water faucet or electrical receptacle in a home or building across a variety of cities are all the same

The system is optimized for network performance and energy efficiency — either through evolutionary biology or economic forces in a city or company — the systems for distribution of materials have generally been optimized for efficiency and performance.

These attributes helped yield the basic network theory and mathematical formulas for scaling.

Scaling of Cities

While itwas quite interesting to learn about the scaling of organisms, it was even more remarkable to see similar such scaling effects with cities. The first city observation is that the amount of infrastructure required (roads, wire, pipes) grows sub-linearly — that is to stay that as you double the size of the a city, the city requires less than double the amount of such infrastructure (85% instead of 100%). The second has to do with the socio-economic indicators of a city, such as per capita income, number of patents produced per capita, the amount of crime per capita, etc. In this case the socio-economic indicators grow super-linearly, meaning that as city size double, those socio-economics indicators (such as per capita income) grow faster than double (115% instead of 100%).

It is quite fascinating to learn that cities — for all of their differences in culture, style, and industry — have some general common, predictable traits. The current understanding of these scaling patterns is a function of the increased interactions and social lives of people living in big cities. The feeling that life moves faster in the big city is indeed a reality that matches the data!

Learnings and Observations

While I found the particular analysis on animals growth and aging, cities, and companies fascinating — I was most interested in the general approach of taking a systemic view and trying to understand the underlying physics that make each of these systems “go” — if we can learn about them and how they work, we can use that knowledge to plan and adapt.

The most profound implications for me were in terms of cities and humanity as a whole — use of energy, growth of population — and whether our overall civilization will scale and grow like animals and companies that ultimately die — or will we be able to achieve the appropriate balance of growth and maintenance and continue to thrive.

Specifically the author uses the same type of analysis to show the limits of the the typical techno-optimist thinking. The techno-optimist says that in the past when we have been short on resources (food, energy, or otherwise) — we have been able to innovate our way out of that — and in doing so we have been able to sustain exponential growth of population, per capita income, and more.

While the author of course agrees that historically innovations have indeed been able to “re-set” the table and enable the next phase of growth — e.g. the agricultural revolution, the industrial revolution, introductions of fossil fuels, etc. — what he showed is that to sustain the exponential growth of population and the increasing needs of food, energy, and resources those innovations have been required to happen at an increasing rate. While the gap between the first such innovations might have happened from 1000 years, the next one took place in 100 years, and the one after that in 25 years. And to sustain our current level of growth those innovations will need to happen even faster. I found this macro approach and analysis of the complex system that is human civilization to be insightful and hopefully a helpful lens particularly when looking at the energy requirements for growth and how we will manage that going forward.