Technology Trends

In “Life on the Scales,” Science News recently wrote that some simple mathematical equations, known as quarter-power scaling laws, can explain the metabolic rates of living organisms. For example, “an animal’s metabolic rate appears to be proportional to mass to the 3/4 power.” And this “3/4-power law appears to hold sway from microbes to whales, creatures of sizes ranging over a mind-boggling 21 orders of magnitude.” The ecologists, physicists and chemists behind this research are now successfully applying this equation to plants, fish, full ecosystems and even biology and genetics, by adding a new key parameter: temperature. Please read this fascinating article for many more details and references. But save some time to read another long article, “Ecology’s Big, Hot Idea,” published by PLoS Biology, which states that “the way life uses energy is a unifying principle for ecology in the same way that genetics underpins evolutionary biology.” Read more…

The Science News article starts with a simple observation. Although a mouse has a shorter life than an elephant, both clock approximately the same number of heartbeats during their lives. Simply, their metabolisms are different. Now, let’s go back several decades ago.

Scientists have long known that most biological rates appear to bear a simple mathematical relationship to an animal’s size: They are proportional to the animal’s mass raised to a power that is a multiple of 1/4. These relationships are known as quarter-power scaling laws. For instance, an animal’s metabolic rate appears to be proportional to mass to the 3/4 power, and its heart rate is proportional to mass to the –1/4 power.

In subsequent decades, biologists have found that the 3/4-power law appears to hold sway from microbes to whales, creatures of sizes ranging over a mind-boggling 21 orders of magnitude.

But nobody had an explanation for this scaling law – until 1997.

The beginnings of an explanation came in 1997, when ecologist James Brown of the University of New Mexico in Albuquerque, physicist Geoffrey West of Los Alamos (N.M.) National Laboratory, and Brian Enquist, an ecologist at the University of Arizona in Tucson, described metabolic scaling in mammals and birds in terms of the geometry of their circulatory systems. It turns out, West says, that Rubner was on the right track in comparing surface area with volume, but that an animal’s metabolic rate is determined not by how efficiently it dissipates heat through its skin but by how efficiently it delivers fuel to its cells.

The idea, West says, is that a space-filling surface scales as if it were a volume, not an area. If you double each of the dimensions of your laundry machine, he observes, then the amount of linens you can fit into it scales up by 2³, not 2². Thus, an animal’s effective surface area scales as if it were a three-dimensional, not a two-dimensional, structure.

This law also can be applied to plants, fish, or even cancer growth rates — providing you add a new parameter: temperature.

In 2001, after James Gillooly, a specialist in body temperature, joined Brown at the University of New Mexico, the researchers and their collaborators presented their master equation, which incorporates the effects of size and temperature. An organism’s metabolism, they proposed, is proportional to its mass to the 3/4 power times a function in which body temperature appears in the exponent.

When the researchers filter out the effects of body temperature, most species adhere closely to quarter-power laws for a wide range of properties, including not only life span but also population growth rates. The team is now applying its master equation to more life processes — such as cancer growth rates and the amount of time animals sleep.

Now, it’s time for two key quotes [which don't appear in bold characters in the original article.]

“We’ve found that despite the incredible diversity of life, from a tomato plant to an amoeba to a salmon, once you correct for size and temperature, many of these rates and times are remarkably similar,” says Gillooly.

“Metabolic rate is, in our view, the fundamental biological rate,” Gillooly says. There is a universal biological clock, he says, “but it ticks in units of energy, not units of time.”

Then the researchers applied their master equation to ecosystems such as forests, and even to evolutionary biology, trying to answer this question: “Why do the fossil record and genetic data often give different estimates of when certain species diverged?”

When the researchers use their master equation to correct for the effects of size and temperature, the genetic estimates of divergence times — including those of rats and mice — line up well with the fossil record, says Allen, one of the paper’s coauthors.

As I wrote in the introduction, don’t miss this other paper by John Whitfield in PLoS Biology on a similar subject, “Ecology’s Big, Hot Idea.” Here are the two first paragraphs.

Life is complicated. It comes in all sorts of shapes, sizes, places, and combinations, and has evolved a dizzying variety of solutions to the problem of carrying on living. Yet look inside a cell and life takes on, if not simplicity, then at least a certain uniformity — a genetic system based around nucleic acids, for example, and a common set of chemical reactions for turning food into fuel. And looked at in broad swathes, life shows striking generalities and patterns. Every mammal’s heart will beat about one billion times in its lifetime. Both within and between species, the density of a population declines in a regular way as the size of individuals increases. And the number of species in all environments declines as you move from the equator towards the poles.

Wouldn’t it be good if there were a simple theory that used life’s shared fundamentals to explain its large-scale regularities, via its diversity of individuals? In the past few years, a team of ecologists and physicists have come up with just such a theory. At its heart is metabolism: the way life uses energy is, they claim, a unifying principle for ecology in the same way that genetics underpins evolutionary biology. They believe that energy use, in the form of metabolic rate, can be understood from the first principles of physics, and that metabolic rate can explain growth, development, population dynamics, molecular evolution, the flux of chemicals through the environment, and patterns of species diversity — to name a few.

If you don’t have enough time today, print the two articles I mentioned and read them next weekend. I promise you will not waste your time.

Sources: Erica Klarreich, Science News, Vol. 167, No. 7, p. 106, February 12, 2005; John Whitfield, PLoS Biology, Vol. 2, Issue 12, December 14, 2004

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