Scaling in Biology -

One of 'the' central problems facing biology is to mechanistically link how pattern and process scale from genes to ecosystems. Because evolutionary and ecological processes can opperate on vastly differing scales there has long been need for a framework by which to quantitatively scale across the hierrarchy of life.

Underlying this research is a long-standing collaboration with James H. Brown and Geoffry B. West, a physicist from the Santa Fe Institute and Los Alamos National Labs. Our work has resulted in a general model for the origin of allometric scaling laws in biology. In short the model is based on fractal geometry and the physics of hydrodynamics and provides unified explanation for the structure and function of biological resource distribution networks. It stems from the observation that biological phenomena are ultimately limited by the rate at which energy and other essential resources can be supplied to maintain structure and sustain function.


The General Model

Our proposed theoretical framework for scaling in biology is based on the assumption that biological rates and times are ultimately limited by the rates at which limited energy and materials can be supplied to cells through a hierarchical branching network. It further assumes that the distribution system has three attributes: i) it is space-filling (i.e., it reaches all parts of the organism); ii) it minimizes the energy required for distribution; and iii) it has size-invariant terminal units (e.g., capillaries or terminal xylem).

The figure is from M. Neumann et al. from the University of Vienna, it is an example of resource distribution networks in organisms created using fractal geometry.

From these assumptions we have derived a quantitative model for the geometry and physics of the entire distribution system. The model predicts: i) a fractal-like branching network with scaling laws governing the sizes of the branches; ii) whole-organism metabolic rate scales as the body mass raised to the 3/4 power; and iii) many other anatomical and physiological characteristics of mammalian cardiovascular and respiratory systems (West et al. 1997). This model, which claims to solve the longstanding problem of quarter-power scaling in biology, has elicited considerable attention, both from biologists who work on related problems and from the press: both scientific publications (commentaries or articles in Science, Nature, The Scientist, BioScience, and Trends in Ecology and Evolution, and an upcoming one in The New Scientist) and the news media (feature articles in the New York Times, Washington Post, and Dallas Morning Star).


Aspects on my work on allometry was recently featured in the New York Times Science Times and in the New Scientist . Further, several recent papers have been featured as news and views pieces in both Science, Nature, and PNAS (click here - Damuth_Review, Whittaker_Review, DamuthII_Review, Zens and Webb Review).


Toward a General Theory for Biological Scaling

This is an exciting time in the lab. The global network of people interested in scaling is growing. Current research is utilizing the 1997 model as a basis by which to build a more detailed quantitative framework for predicting how the scaling of physiological rates and times influence ecological and evolutionary patterns and processes. In particular extensions of the general model has led to an allometric model for structure and function in vascular plants. Extensions of this plant model is the basis for further more explicit models extending physiological, anatomical, and self-similar attributes with many macroscopic patterns in plants and plant assemblages. Excitingly, we are using our scaling framework to mechanistically link physiological variation within and between plants to the flux of energy and CO2 from diverse ecological systems.