A general model for allometric covariation in botanical form and function

*Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ 85721;
^‡Sante Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501; and
^§Department of Systems Biology, Harvard Medical School, Boston, MA 02115

Edited by Karl J. Niklas, Cornell University, Ithaca, NY, and accepted by the Editorial Board June 14, 2007 (received for review March 11, 2007)

Abstract

The West, Brown, and Enquist (WBE) theory for the origin of allometric scaling laws is centered on the idea that the geometry of the vascular network governs how a suite of organismal traits covary with each other and, ultimately, how they scale with organism size. This core assumption has been combined with other secondary assumptions based on physiological constraints, such as minimizing the scaling of transport and biomechanical costs while maximally filling a volume. Together, these assumptions give predictions for specific “quarter-power” scaling exponents in biology. Here we provide a strong test of the core assumption of WBE by examining how well it holds when the secondary assumptions have been relaxed. Our relaxed version of WBE predicts that allometric exponents are highly constrained and covary according to specific quantitative functions. To test this core prediction, we assembled several botanical data sets with measures of the allometry of morphological traits. A wide variety of plant taxa appear to obey the predictions of the model. Our results (i) underscore the importance of network geometry in governing the variability and central tendency of biological exponents, (ii) support the hypothesis that selection has primarily acted to minimize the scaling of hydrodynamic resistance, and (iii) suggest that additional selection pressures for alternative branching geometries govern much of the observed covariation in biological scaling exponents. Understanding how selection shapes hierarchical branching networks provides a general framework for understanding the origin and covariation of many allometric traits within a complex integrated phenotype.

Footnotes

^†To whom correspondence should be sent at the present address:
Department of Biology, Georgia Institute of Technology, Atlanta, GA 85721.
E-mail: cprice6{at}mail.gatech.edu
Author contributions: C.A.P. and B.J.E. designed research; C.A.P. and V.M.S. performed research; C.A.P., B.J.E., and V.M.S. analyzed data; and C.A.P., B.J.E., and V.M.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. K.J.N. is a guest editor invited by the Editorial Board.
This article contains supporting information online at www.pnas.org/cgi/content/full/0702242104/DC1.
Abbreviation:

WBE,

West, Brown, and Enquist theory.