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How Nature Scales Up

How Nature Scales Up

Plants and animals deliver energy through branching networks—veins and vessels—that shape the path of growth and determine its limits. PHOTO: GETTY IMAGES

A simple mathematical relation might explain how everything—from plants to people to cities—develops.

Like a hardcover version of the Veg-o-Matic in those old television commercials, Geoffrey West’s “Scale” is three books in one. The first is among the most fascinating popular-science books I’ve read in a long while, and the other two are consistently provocative. But like that Veg-o-Matic on the shelf, it’s unclear how useful the whole package will be in the end.

Mr. West is a particle physicist whose career was disrupted in 1993 when Congress, with the acquiescence of President Bill Clinton, canceled the Superconducting Super Collider, an enormous particle accelerator that had been in the works for years. The end of the SSC marked the end of U.S. dominance in physics; thousands of Ph.D.s saw their research programs turn to ash. Mr. West, then director of the particle-physics program at Los Alamos National Laboratory, switched to biology and after that, more boldly, to the study of society.

Beginning in the late 1990s, Mr. West and a raft of collaborators argued in a series of articles that a single phenomenon called “scaling” could explain many of the fundamental properties of living organisms. In some sense, this is no surprise. As far back as 1932, the Swiss physiologist Max Kleiber had noted that the metabolic rates of creatures of every sort—the amount of energy they need to stay alive—exhibit what Mr. West calls “an extraordinarily systematic regularity.”

The regularity is shown most commonly by drawing a special kind of graph, in which every increment on the x- and y-axis is 10 times bigger than the previous increment—instead of running from 1 to 2 to 3 and so on, the increments run from 1 to 10 to 100 and so on. When organisms’ metabolic rates are plotted on the vertical axis and their mass on the horizontal one, the result is a dead- straight line—a relationship that holds true for animals as tiny as a mouse (typical weight, .02 kilograms) and as enormous as an African elephant (typical weight, 6,500 kilograms).

This is a scaling law: a relationship between two quantities that holds true at many orders of magnitude. In this case, every species’ metabolic rate “scales” with increasing size. After Kleiber, researchers found that his rule holds true for fish, amphibians, insects and plants—indeed, for every creature from the smallest microorganisms to the biggest whale. “Overall,” Mr. West says, this relationship “encompasses an astonishing twenty-seven orders of magnitude, perhaps the most persistent and systematic scaling law in the universe.” And the correspondence is no isolated phenomenon. “Similar systematic scaling laws hold for almost any physiological trait or life-history event across the entire range of life,” Mr. West writes, including quantities as disparate as “genome lengths, lengths of aortas, tree heights, the amount of cerebral gray matter in the brain, evolutionary rates, and life spans.”

This is remarkable. It was as if Mr. West and his colleagues had discovered that the number of doors, bathrooms and chimneys in every building in the world—a Mongolian yurt, a Cairo apartment and Tom Brady’s moat-surrounded castle in Los Angeles—were described by a single mathematical rule that specified details down to the number of doorknobs. For real estate, the idea is ridiculous. But not, it seemed, for biology.

With two colleagues, Mr. West proposed an explanation in 1997. Roughly speaking, they said that our bodies, like those of every other living creature, are bags of cells. These cells are in some ways surprisingly similar; all must be nourished and directed, and most of them are about the same size, no matter what species they belong to (a few exceptions exist, like brain and fat cells). Thus living things must contain networks—blood vessels, plant veins and so on—that distribute energy, materials and information to cells. Because the cellular endpoints of every network are all about the same size, the “terminal units” of the distributive system must also be about the same size. That is to say, the capillaries (the smallest blood vessels) of all mammals are roughly the same size, as are those of every fish and insect, as are the endpoint veins of leaves and a host of other things.

Big species need more nutrients and energy than small ones, so the network centers—the heart, for mammalian blood systems; the big xylem at the roots, for vascular plants—vary in dimension. Because the endpoints are always the same small size, the network needs to consist of what Mr. West calls a “hierarchical branching network structure,” with big branches unraveling tree-like into smaller ones. But when the big tubes divide into smaller tubes, the branch points will cause eddies or otherwise interfere with the flow—unless they obey certain precise physical properties. Unsurprisingly, evolution keeps nudging organisms toward those properties, which again are similar for every species, because they depend on physical laws that are independent of biology.

As physicists do, Mr. West and his collaborators looted this new understanding to produce all kinds of eyebrow-raising results. That blood pressures in the various branches of the network are the same for every mammal, regardless of size. That the lengths of successive blood vessel branches in every species must decrease by a single constant factor. That the volume of blood in every species is a constant proportion of the body volume, regardless of size. That measures ranging from lung volume to the pumping action of the heart to the frequency of breathing are all covered by scaling laws.

A certain type of reader (me, for example) will find this stuff fascinating—I kept underlining phrases and putting exclamation points in the margins. And this kept going as Mr. West showed how fractals (structures like snowflakes, in which similar patterns repeat at progressively smaller scales) and network dynamics govern birth, growth and development, again in species of every sort. But then, around page 200, “Scale” takes a radical shift. Mr. West begins what amounts to a second book about social science, and here my exclamation points turned into question marks.

There is a long, rich tradition of physicists contributing to biology. Physicist Erwin Schrödinger’s “What Is Life?” (1944) was a major inspiration for molecular biology; DNA pioneers like Francis Crick, Max Delbrück, Walter Gilbert and Sidney Altman began their careers as physicists (all won Nobels). When it comes to physicists’ contribution to the human sciences, such as sociology and anthropology, the record is scantier. There’s a reason for this disparity, and the later portions of “Scale” highlight the limitations of the physicist’s approach. Physicists attack problems by stripping them to their most fundamental parts and throwing away inessential details. In the case of metabolism, Kleiber and his successors ignored huge differences among mammals, birds, fish and bacteria and treated the whole lot as, in effect, having just two properties—metabolic rate and mass.

The approach was successful at explaining many observed physiological features of plants and animals. But the success isn’t as clear-cut when Mr. West tries to create what he calls a “Science of Cities.” The author points out that modern cities, like bodies, depend on transportation and supply networks—roads, gas lines, water conduits, electric cables. Because these networks must reach every home, they scale in a manner analogous to networks in the body. Ancillary quantities like the number of gas stations and power substations per capita also scale. So exact is this scaling that it leads Mr. West to contend that, “despite appearances cities are approximately scaled versions of one another: New York and Tokyo are, to a surprising and predictable degree, nonlinearly scaled-up versions respectively of San Francisco and Nagoya.”

Intriguingly, infrastructure per capita decreases with increasing city size—that’s the “nonlinear” in the previous sentence. Thus larger cities use fewer resources per person than smaller cities, and so Mr. West argues that “on average the bigger the city, the greener it is.” Secure in their superior sustainability, New Yorkers have another reason to sneer at denizens of smaller places.

More than that, Mr. West says, urban scaling laws appear in “quantities with no analog in biology such as average wages, the number of professional people, the number of patents produced, the amount of crime, the number of restaurants, and the gross urban domestic product.” Again, the exactitude of the scaling is remarkable. The relationship of urban GDP to population follows a scaling law, but so does something as seemingly unpredictable as the average walking speed of pedestrians in a city.

Unlike the case of infrastructure, in which bigger cities end up with proportionately less, larger cities end up with proportionately more crime, pollution and disease. On the other hand, Mr. West says, “the bigger the city, the more each person earns, creates, innovates, and interacts.” In general, he argues, bigger is better.

Really? Mr. West is apparently suggesting cities get better indefinitely. Surely this cannot be correct—it implies that diminishing returns do not apply. Congestion by itself drives up resource use. As buildings get packed together, for example, they need ever-larger systems to pump in fresh, conditioned air. Meanwhile, heating and ventilation systems pour out hot exhaust, creating the “heat islands” that are a familiar urban plague, and themselves drive up air-conditioning use even further—a dyseconomy of scale of precisely the kind Mr. West seems not to take into account.

El Paso, Texas, and Washington, D.C., have similar populations (about 680,000), so they are presumably similar in the physical attributes Mr. West measures. But the experience of living in each city is dramatically different. Washington (median household income, $70,848) is almost twice as wealthy as El Paso ($42,772). But FBI statistics show that El Paso has a murder rate of 2.5 per 100,000, and is one of the safest big U.S. cities, whereas Washington, D.C., with a murder rate of 24 per 100,000, is notorious for its unsafe areas.

Environmentally, too, the cities are different: El Paso emits almost twice as much carbon dioxide as Washington. Yes, Washington has a big subway and El Paso has a struggling bus system. But that difference can be explained not by networking behavior but by politics, economics, geography and history—factors that also contribute to the cities’ different levels of crime and income. Does it make any sense to treat the cities as fungible?

Despite the questions it raises, Mr. West’s Book No. 2 is almost as interesting as Book No. 1. And toward the end of “Scale,” Book No. 3 suddenly heaves into view. Not even 50 pages long, it consists of an abbreviated discussion of businesses, firms and corporations. Again, he asks a scaling question: “Is Walmart a scaled-up Big Joe’s Lumber?” Again, the answer seems to be “yes,” but he is tentative about it. Still, in contrast to his science of cities, his proposed “science of companies” seems promising. Companies, unlike cities, share a single goal: profit. And, like organisms, they are subject to relentless selection pressure, nudging them toward efficiency.

One can imagine using scaling laws to evaluate the role of management or corporate structure, but the ultimate conclusions are still to come—the subject, perhaps, of a sequel. I’d look forward to reading that book. In the meantime, we have “Scale”—an overstuffed, often exhilarating, sometimes frustrating introduction to a new way of looking at life.

Charles C. Mann reviews “Scale” by Geoffrey West. June 23, 2017

—Mr. Mann is the author of the forthcoming “The Wizard and the Prophet: Two Remarkable Scientists and Their Dueling Visions to Shape Tomorrow’s World.”

Appeared in the June 24, 2017, print edition as ‘Nature’s Rules for Growth.

Water Technologies Canada Inc.

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