Scaling Laws & Biodiversity: A 4^th Dimension in our "3-Dimensional" World?

In our 3-dimensional world, why do Dr. Jim Brown and his colleagues search for a 4^th dimension? Biologists have realized for a long time that size and temperature affect metabolic rate in proportion to an organism's mass, but they didn't known how or why. During a discussion about Kleiber's Law, which describes the proportion of an animal's metabolic rate to its body mass, Brian Enquist, then a graduate student, asked the simple question: "Why is it 3/4-power?"

This question has led to a multifaceted body of research that is answering a decades-old question. As Jim recalls, "Brian and I put our heads together to devise a model, but soon realized we needed a mathematician." Brown and Enquist got together with Dr. Geoffrey West, a physicist from the Santa Fe Institute, and the trio devised a model to predict more precisely how metabolic rates increase as body size increases. Their model uses fractal geometry of the blood vascular system to explain the quarter-power scaling law. The idea is that metabolic rates vary in proportion to 3/4-power of an organism's mass; in other words, scaling laws describe how different parts or characteristics of living organisms vary (= scale) in proportion to changes in body size, a phenomenon that Brown calls the 4^th dimension of life.

The major accomplishment of this idea is that the plethora of scaling laws, that cover all life, all derive from the same set of principles. But the model goes much further and says not only are we constrained as we develop, but also as we evolve. What seems most amazing is that the very simple principles of the model not only can be applied to the mammalian cardiovascular system, but also to plants, insects and, possibly, all life.

So far, the collaborative research efforts of Brown, Enquist and West has resulted in several papers in Science, Nature, and other peer-reviewed journals, a book, Scaling in Biology (Oxford University Press), and a five-year $960,000 grant from the David and Lucille Packard Foundation. Mainstream press also took notice with feature articles in the New York Times, The Dallas Morning News, and New Scientist Magazine, among others.

Jim Brown was recognized by UNM with in 1999 with its highest recognition for research, the Annual Research Lecturer Award. and the National Science Foundation recently awarded the group a $2.5 million grant to collaborate with other researchers and organizations to look at how scaling relationships—which appear to occur in all taxa and environments—may offer clues to underlying mechanisms of biodiversity."We use the interplay of mathematical models and empirical measurements to elucidate the physical and biological principles that determine how life history, abundance, distribution, and species richness of organisms scale with body size, space, and time," said Brown.

This research and education program involves collaborations among physicists, mathematicians, geologists/hydrologists, ecologists and other biologists from seven institutions supplementing the existing accord between UNM, the Santa Fe Institute, and Los Alamos National Laboratory. Seven graduate students and eight postdocs are supported by the Packard and NSF grants.Recently given the Ecological Society of America's Robery H. MacArthur Award, Jim also visited England in December, 2002, to receive the Marsh Award for Ecology from the British Ecological Society, which recognizes outstanding achievements and contributions to the science of ecology.