Geoffrey West, a theoretical physicist, has discovered some remarkable scaling laws that turn out to be useful in many domains, including biology, urban planning, economics, and corporate strategy.
West researched the food consumption of animals (including humans) and found that larger animals use energy more efficiently than smaller ones. For instance, imagine a woman and her dog are out for a walk. The dog weighs 60 pounds, and the woman weighs 120 pounds. Since the woman weighs twice as much as the dog and has twice as many cells, you would assume she would need twice as many calories each day to maintain her basal metabolic rate, right? But she doesn’t. She only needs about 75 percent more calories than her dog.
Now the woman and her dog spot a deer, and that deer weighs 240 pounds, twice as much as the woman and four times as much as the dog. It turns out the deer only needs about 75 percent more food than the woman to maintain its basal metabolic rate. It is four times as heavy as the dog but needs only about three times as many calories.
West found that you could continue identifying heavier and heavier animals — the Siberian Tiger is eight times as heavy as the dog, the California Sea Lion is 16 times as heavy as the dog — and for each doubling of weight, the animal would only need three-quarters more food. These ratios hold for ever-larger animals all the way up to the blue whale and also for ever-smaller animals down to the tiny mouse.
There is, of course, lots of internal variability within each species. Some animals of the same species eat more food than others, like my 35-pound dog Miss New York (rest her soul) who could manage to wolf down an entire roasted chicken and then pass out for half a day.
Speaking of sleep, West found there’s a relationship between an animal’s size and the amount of sleep it needs. An elephant only needs a few hours of sleep per day, while a fruit bat may sleep for 20 hours.
West identified many such relationships between size and other attributes. Larger animals use less energy per pound than smaller ones. Larger animals have slower heart rates per pound. Larger animals tend to grow at a slower pace but then live longer. Larger animals have more efficient networks to carry nutrients and oxygen through their bodies. In all these examples, nature has awarded a size premium to the larger animals.
As interesting as these observations are, if you look deeper, you notice another crucial perspective. You can plot the ratios on a graph, with the horizontal axis representing size and the vertical axis representing calories or sleep or any of the other attributes, and you would probably expect to see a hive of dots scattered across the graph with a general upward-sloping trend. In other words, you would expect to see a lot of variability among the menagerie of animals who each evolved independently over millions of years, from mice to cats to dogs to horses to deer to tigers to sea lions to whales. You might expect to see an organic, chaotic graph, but you don’t. What you see is remarkably tidy. What you see is a straight line of animals lined up in an orderly row with surprisingly little variation above or below the trend line. This signifies an impressive consistency in the scaling ratios all across the animal kingdom.
West began searching for similar scaling ratios in other areas and, sure enough, he found them. Just as animals enjoy a size premium, so do cities. If you double the population of a city, you more than double its economic output per capita as well as its innovation output per capita, as measured by the number of patents created. The list continues. You more than double its amount of social interaction. You more than double the efficiency of its infrastructure, as measured by the length of its roads and electrical lines relative to its population. Again, the cities line up neatly along the scaling line with surprisingly little variation.
What about companies? Do they also enjoy a size premium? They sure do! If you have two companies, one with twice as many employees as the other, the larger one will create more than twice as many assets per capita and generate more than twice as much income. From the smallest family company all the way up to the Amazons and Walmarts with their millions of employees, these scaling ratios of companies follow a stable, orderly scaling law.
Economists use the terms “economies of scale” or “increasing returns to scale” to describe these relationships. Physicists call this “superlinear scaling” or, in the case of needing fewer and fewer resources as they grow, “sublinear scaling.”
In his book Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies, West wondered if there could be “any analogous hidden order underlying all of this complexity and diversity. Could there conceivably be a few simple rules that all organisms obey, indeed all complex systems, from plants and animals to cities and companies?”
The existence of the similarities suggested there is a common framework within all these different complex dynamics.
In a parallel study alongside his research into how complex systems scale, he began wondering what limits restrict the same complex systems and prevent them from scaling indefinitely. If there are advantages to being large — and his research unambiguously showed there are — why don’t animals grow to be the size of mountains, trees grow to the height of skyscrapers, or cities grow to service a billion residents?
West observed that scaling laws develop from the structure of their internal networks. In the case of animals, their cells and blood vessels allow them to grow. In the case of cities, it’s their transportation and communication systems. These networks function best when they optimize resource distribution. For instance, larger animals have less external area per pound than smaller ones, so they don’t have to generate as much relative heat, so their metabolisms don’t have to work as hard, so they don’t need as many calories. However, animals eventually get to such a vast size that their resource distribution begins to become more difficult, thereby limiting their ability to grow further.
If an animal were to become gargantuan, its heart would have to work like an industrial-sized filtration system to pump its blood through all its veins to all the extremities of its body, and that size may not be optimal for resource distribution.
The point is made vividly clear with the Brontosaurus. With its immense prehistoric size, if something caused a pain in its tail, it would likely take several seconds to cause a reaction. The nerve signals would travel from its tail all the way up the spine to its brain, and then the brain would trigger a motor response back in the tail. It’s a pity the Brontosaurus isn’t around today to participate in West’s research.
West found a remarkable example of this size-resource relationship in the heartbeats of mammals. Larger animals tend to live longer than smaller animals. Elephants generally live longer than horses, which live longer than mice. But mice have faster heartbeats than horses, which have faster heartbeats than elephants. The mouse’s heart may race at 10 beats per second, even in a resting state, while the elephant’s heart beats only once every 2 seconds.
Since small animals with fast hearts have short lives, and large animals with slow hearts have long lives, it occurred to West to ask the question, Do animals of vastly different sizes have the same number of heartbeats in their lifetimes? Amazingly, the answer to the question is yes! Regardless of size, the hearts of most animals beat roughly 1.5 billion times during their lifetimes, on average.
The heart of the tiny shrew, nature’s smallest mammal, races to 1.5 billion in less than a year, while the heart of the largest mammal, the blue whale, may take a century to beat 1.5 billion times.
In a future post, we’ll examine the implications of West’s discoveries for city planners and corporate managers.
Stay tuned!