The Powers That Might Be

On the edge of Santa Fe, New Mexico, cacti, pinyon pines, and stunted junipers seem to slumber beneath the remnants of a fierce January snowstorm. As ravens circle overhead, their shadows send the desert cottontails darting about the sparse landscape.

In the frigid hush of these hills, each organism is playing its role in the high desert's idiosyncratic ecosystem. Inside the nearby Santa Fe Institute three researchers are trying to peel back life's feathers, fur, and bark to reveal the formula that makes it all tick. Could it be that the steady rhythms coursing here - from the rabbit's pounding heart to the juniper's roots straining to pull water from the frozen ground - obey some immutable law?

Though he tries not to overstate the reach of their work, Geoffrey West, one of these scientists, can't resist the urge to boast about their latest research. "This has the potential to change the way people think about forests," he says, a grin spreading across his tanned face. West and his collaborators, Jim Brown and Brian Enquist, have gathered at the Institute to put the finishing touches on their latest paper, a comprehensive test of their idea's ability to describe and predict the structure and function of forest plant communities.

They call the idea "metabolic theory," in essence a cognitive framework to describe linkages within and between living things based on commonalities in how they convert resources into energy. Melding first principles of physics, geometry, chemistry, and biology, they've built mathematical models that represent and may even predict the complexities of ecology. The practical applications of their theory, if it continues to stand up to rigorous and broad testing, are practically boundless. It could help wildlife managers determine appropriate reserve dimensions for severely endangered species. It could predict changes in forest dynamics under the stress of global climate change. Nonecological applications such as computer chip design and urban planning could function under these rules. Even oncology is taking notice of metabolic theory. Perhaps unsurprisingly, an idea this ambitious has caused quite a stir.

A 1997 Science paper ¹ introduced the group's theory and has been cited more than 700 times. While attracting a fair share of praise, it has also proved a magnet for criticism. "We've created a cottage industry for critics," says Brown, an ecologist at the University of New Mexico. "There are whole labs out there that get the vast majority of their publications from criticizing our stuff."

And as West, Brown, and Enquist bounce ideas around a glass-walled conference room, they are crafting their strategy to stave off the next round of critiques. "We absorb the criticism and move forward," Enquist says.

West, the team member most likely to voice the excitement for the potential of their theory, is less patient with the deluge of criticism. In his mellifluous British accent, he snipes, "Part of me doesn't want to be cowered by these little dogs nipping at our heels."

At 66, Geoffrey West is the elder statesman of the team. He is also the only nonbiologist. A theoretical physicist by training, West led the particle theory group at Los Alamos National Laboratory in the late 1980s and early 1990s. These were distressing times as physics seemed to be losing ground to biology in the public and political consciousness. In 1993, Congress pulled the plug on the Superconducting Super Collider that was to be built in Texas, and West says he heard the chorus growing louder: "Physics was the science of the 19^th and 20^th centuries, and biology is the science of the 21^st century." West realized that biology would, in fact, become a more dominant discipline, but the implication that physics' demise was a necessary corollary to this progression angered him.

Nevertheless, West began thinking about biology. His own mortality was partially to blame. "I was now into my fifties, and I was very conscious of aging and dying," he says. He struggled with biology's lack of theory and inability to answer key questions: "Why can I only live on the order of 100 years? Why can't I live a million years? Why is it if this piece of flesh that is me happened to have been a mouse, it would have in fact been dead after a few years?"

So, West looked for answers as he combed the aging and gerontology literature, replete with data but devoid of fixed rules. Then West discovered the writings of Swiss-American physiologist Max Kleiber, who had taken precisely the kind of integrative approach West was looking for.

In 1932 Kleiber measured an array of animals ranging in size from rats to cattle and showed that metabolic rate was proportional to body mass raised to the power of ³/₄ across the board.

This ³/₄-power relationship between metabolic rate and body size, dubbed Kleiber's law, supplanted a ²/₃-power relationship previously thought to describe accurately the relationship between mass and metabolic rate in animals. This early formula used Euclidean geometry - namely the ratio between surface area (length²) and volume (length³) - to explain the difference in metabolic rate for organisms of different sizes. This surface area-to-volume ratio gave the metabolic rate of a particular organism as proportional to its mass raised to the power of ²/₃.

Kleiber used a more robust data set to construct a more accurate model for the scaling of metabolism with body size, but he failed to suggest an adequate physical explanation for the relationship. He simply let his data construct the model. So Kleiber's law, while supported across a broad range of animals and corroborated by his successors, remained devoid of a mechanistic underpinning for decades. It was the kind of puzzle that attracted West: "I looked at all these and said... I can't believe this isn't a central piece of biology."

Other well-established scaling laws show several characteristics of living things changing steadily with changes in body size. For instance, an animal's lifespan is proportional to the ¹/₄ power of its mass; the cross-sectional area of a mammal's aorta is proportional to the ³/₄ power of its total mass; heart rates vary as body mass to the negative ¹/₄ power; and the density of individuals inhabiting an area tends to scale to body mass at the negative ³/₄ power. "It obviously can't be some diabolical accident that all these things scale," West says. "That got me thinking about where all these scaling laws came from."

West focused on this conundrum, and he searched for answers in the geometric architecture of biological transport networks, such as the mammalian vascular system that delivers resources. Then in 1995, he received a call from his friend and former Los Alamos colleague, Mike Simmons, who had become the vice president for academic affairs at the Santa Fe Institute and who knew of West's new forays into biology. Simmons told West of two ecologists from the University of New Mexico in Albuquerque who happened to be pondering similar questions about biological scaling and Kleiber's law.

The two ecologists were Brown and Enquist. Through painstaking statistical analysis of plant data in the literature, Enquist, who was Brown's graduate student at the time, had shown that Kleiber's law applied even to trees. Yet, they had arrived at the same impasse as West and many before them: explaining the fundamental physical mechanism operating at the root of this pattern.

That explanation proved elusive. Kleiber's law suggests the presence of some fourth dimension as opposed to the more familiar three-dimensionality inherent to the ²/₃-power law. What extra-dimensional physical characteristic could explain the observation that, when corrections are made for body size, virtually all living things convert resources at a similar rate?

Like West, Brown and Enquist suspected that the answer to this question lay in the geometry of transport systems. The ecologists constructed theoretical networks using a branch of mathematics called graph theory, but the systems they built functioned at rates proportional to the ¹/₃ power or ²/₃ power of their size. Enquist and his advisor realized that they needed help to solve the problem.

Brown and Enquist arranged to meet West at the Santa Fe Institute to discuss the scientific questions that had been vexing them. Though 20 years his junior, Enquist says he felt an immediate intellectual connection to West. "It was very weird meeting him for the first time because he was this long-lost brother," he remembers. "He could relate to [Jim and me] in terms of the ideas we we're thinking about." And ultimately, West would provide the key for successfully modeling an ideal biological resource-transport system.

That key was fractal geometry. In these branched structures, where each subunit is an approximation of the whole structure, was the fourth dimension that was necessary to explain the anatomic origin of Kleiber's law. "It was immediately clear that what Geoffrey was bringing to the table, which was very novel to what Jim and I had been thinking about, was the notion of self-similarity and the fractal," says Enquist. "That gave us the language to codify all of this."

This first meeting grew into a weekly event. Enquist, now an established plant ecologist at the University of Arizona, remembers the hour-long drives fondly. "I would have a time with no telephones, no interruptions, where Jim and I could just talk about things."

After a year's worth of meetings, the team had constructed a model that proposed a mechanistic explanation for Kleiber's ³/₄-power law. The model described space-filling networks that, obeying established geometric and physical principles and operating under three important underlying assumptions, optimize the transport of metabolism's raw materials through living things.

The model was built on three assumptions: 1) The networks were constructed of tubes that branched in fractal-like patterns; 2) The networks minimized the amount of energy needed to transport materials through the system of tubes; and 3) The size of the terminal units at the ends of this system (i.e., capillaries) did not vary with overall body size. These provided an idealized network that is a reasonable approximation of real-world biological transport systems. For example, mammalian vascular systems are highly branched, and capillary size is relatively invariant across mammals of different size. Thus, it is conceivable that natural selection has endowed mammals with a maximally efficient vascular system.

In April 1997 West, Brown, and Enquist published their groundbreaking paper. Employing a slew of complex mathematical equations - what Enquist refers to as "pyrotechnics" - they provided mathematical justification for their theory. They also tested their model against measurements taken for several characteristics of vascular and respiratory systems in several mammalian species. The model predicted the observed values exceedingly well. West, Brown, and Enquist had built a predictive model that seemed to resolve the central role of body size in much of biology, and in doing so, provided the most robust mechanistic explanation yet for the pattern that Max Kleiber had revealed more than 65 years before. Their metabolic theory was born.

The paper would form the cornerstone for the group's subsequent work, and it was far from subtle. Writing that "quarter-power allometric scaling is perhaps the single most pervasive theme underlying all biological diversity," West, Brown, and Enquist left themselves open to criticism.

Just two months before the Science publication, Jan Kozlowski and January Weiner of Jagiellonian University in Krakow published a paper in American Naturalist. ² The Polish biologists proposed a vastly different explanation for the prevalence of Kleiber's law.

COURTESY OF KNUT SCHMIDT-NEILSEN

Kozlowski and Weiner constructed a model that showed wide variation in the scaling of metabolic rate (from mass to the ²/₃ power to mass to the power of 1) within species that, when plotted across different species, produces the ³/₄ power seen in Kleiber's law. Their model suggests that Kleiber's law is simply a statistical artifact and not the result of some underlying structural or functional commonality between living things.

Though not a direct response to metabolic theory (the two teams claim not to have been aware of each other's work at the time), Kozlowski and Weiner's argument did illustrate a fundamental departure from the theory's foundation. Biological diversity, they say, defies encapsulation by a single, reductive model.

"For me, [West, Brown, and Enquist's] models represent oversimplification," says Kozlowski, on the phone from his Krakow office. "They want to explain, with this one simple parameter [body size], everything up to a very broad scale. I'm not so optimistic," he continues. "I believe that nature is much more complex than that."

Helene Muller-Landau studies the ecology of tropical forests and published two papers last year that challenge metabolic theory's ability to accurately model several aspects of community dynamics in tropical forests. ^3,4 Muller-Landau, a conservation biologist at the University of Minnesota, and colleagues found that trees in a natural tropical forest ecosystem grow at different rates than metabolic theory would predict. ³ They reasoned that this was due to the prominent light limitation in such environments; a variable unaccounted for in West, Brown, and Enquist's metabolic theory. In a second paper, ⁴ the Muller-Landau group measured trees in natural, mixed-age forests. They found a deviation from the size distribution pattern that metabolic theory would predict, and they suggested that dynamics operating in the natural forest ecosystems, like nutrient limitation and disturbance, were the cause of the deviation.

Muller-Landau commends West, Brown, and Enquist's "laudable" efforts, but faults their theory's inability to capture real-world variation. She equates the drive to render ecology down to such a simple model to a quest for mythical treasure. "It's kind of like an ecological El Dorado," she says. "It's nice when things are simple, but the real world isn't always so."

Even if West, Brown, and Enquist retooled what she sees as technical problems with the foundation of their theory, Muller-Landau says that its basic structure would need to be appended in order to model more accurately the natural world. "When you have a simple theory, you have to add bells and whistles to reproduce a more complex pattern," she says.

West, Brown, and Enquist have been adding to metabolic theory as its reach across organism types expands. And the trio, along with a growing corps of collaborators, has constructed more complex models to predict the structure and function of ever-broader swaths of nature. "Muller-Landau raises two good points," says Enquist: namely that growth rates and size distributions in natural forests might deviate from the model's predictions in real-world conditions. Nonetheless, he is adamant: These points "don't invalidate the core of the model."

In 2001, Jamie Gillooly, then a postdoc at the University of New Mexico, in collaboration with Brown and West, added temperature to the core metabolic theory model as a variable necessary to explain the ³/₄ scaling of metabolic rates across organisms from microbes to mammals of varying sizes. ⁵

As Muller-Landau, Kozlowski, and other critics circle around their metabolic theory, West, Brown, Enquist, and collaborators continue to extend the theory's reach. They have applied the fundamental principles of metabolic theory to successfully model a remarkable array of organisms, processes, and life-history characteristics. Their work has even extended to nonecological settings (see sidebar, p. 44).

The three did not anticipate the amount of criticism they would receive. "I was a little unprepared for the magnitude and amount of criticism we got," says Brown, "but if you're doing something important, that's what you'd expect." Moreover, ecology is steeped in the tradition of descriptive science. Brown says the idea of creating a predictive, "overarching theory" is bound to ruffle feathers.

The three aren't cavalier about the importance of the theory, however. "Any model in biology is ultimately wrong," says Enquist, "because they are abstractions of how the real world works." Their theory is more a canvas for the sundry hues of biological variation rather than a "theory of everything," a phrase that others have used to describe their work, but that they avoid. "[Metabolic theory] sets the average, idealized framework for everything else to play off," says West. "Everything else is a variant."

Inside the Institute on a chilly January day, the three scientists strategize over their newest publication. Much has stayed the same since those first meetings a decade ago: the collegial atmosphere, the enthusiastic exchange of ideas, and the constant search for new angles on old questions.

A recent model includes temperature along with mass as a determinant of metabolic rate. Here io is a normalization constant independent of body size and temperature, E is the energy of activation for enzyme-mediated reactions, T is temperature, and k is Boltzmann's constant, which serves as a bridge between temperature and energy.

"What is a tree?" the oddly elementary question comes from West. Enquist with a wink whispers, "This is typical."

The question is meant to ensure that the group is focused on precise definitions and on careful wording. They want to be absolutely sure that all their bases are covered because this latest piece of research represents a major jump in the reach of their metabolic theory. It is the most robust test yet, they say, of metabolic theory's power to predict the structure and function of whole forest communities.

"I'm sure it will be controversial," says West. Enquist agrees and stresses that the statistical analyses in their paper must be airtight. Otherwise, he says, "a big fat torpedo will be headed our way." The attention their work has garnered has helped shape the team's collaboration over the past decade, and their interactions, now, reflect this.

The funding situation also has changed. West has generally obtained funding from the Department of Energy, while Enquist and Brown have maintained National Science Foundation funding. In the ten years since first publishing on metabolic theory, however, the group has won support from the National Center for Ecological Analysis and Synthesis, a Packard Interdisciplinary Science Grant, and the Eugene V. and Clare E. Thaw Charitable Trust. Moreover, Enquist has been featured in the popular press as a rising star in ecological studies.

The attention, though, can get wearisome. As the hills beyond the windows of their meeting room are washed pink in the setting desert sun, West, Brown, and Enquist's heated discussion simmers to a brief pause. Brown leans back in his chair and peers at the ceiling, searching for the answers to hard question as he twirls his eyeglasses between his finger and thumb. West stokes his beard, deep in thought, while Enquist taps away on his laptop, remembering a time 10 years ago when it was a struggle for the three to even reserve a room at the Institute. "Sometimes," Enquist says, "I long for the days when nobody cared."