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First published online April 13, 2009; doi:10.3732/ajb.0800380 American Journal of Botany 96: 877-884 (2009) © 2009 Botanical Society of America, Inc.

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Scaling relations for a functionally two-dimensional plant: Chamaesyce setiloba (Euphorbiaceae)¹

² Department of Biology, University of New Mexico, Albuquerque, New Mexico 87131 USA ³ The Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501 USA

ABSTRACT

Many characteristics of plants and animals scale with body size as described by allometric equations of the form Y = βM, where Y is an attribute of the organism, β is a coefficient that varies with attribute, M is a measure of organism size, and is another constant, the scaling exponent. In current models, the frequently observed quarter-power scaling exponents are hypothesized to be due to fractal-like structures. However, not all plants or animals conform to the assumptions of these models. Therefore, they might be expected to have different scaling relations. We studied one such plant, Chamaesyce setiloba, a prostrate annual herb that grows to functionally fill a two-dimensional space. Number of leaves scaled slightly less than isometrically with total aboveground plant mass ( 0.9) and substantially less than isometrically with dry total stem mass ( = 0.82), showing reduced allocation to leaf as opposed to stem tissue with increasing plant size. Additionally, scalings of the lengths and radii of parent and daughter branches differed from those predicted for three-dimensional trees and shrubs. Unlike plants with typical three-dimensional architectures, C. setiloba has distinctive scaling relations associated with its particular prostrate herbaceous growth form.

Key Words: Chamaesyce setiloba • Euphorbiaceae • leaves • metabolic rate • scaling • two-dimensional

Received for publication 11 November 2008. Accepted for publication 20 January 2009.

FOOTNOTES

¹ The authors thank D. Marshall’s laboratory for use of space and equipment, H. Simpson and N. Abrahamson for helpful advice, M. Moses and J. Nekola for valuable discussions, A. Pesci for pictures and data collecting, three anonymous reviewers for helpful comments, and J. Stewart, S. McCoy-Hayes, M. Barnes, and M. Donovan for support and kindness. This research was funded by the NSF through Grant No. PHY 0202180, Grant No. 0353791, and a Biocomplexity Grant: DEB-0083422.

⁴ Author for correspondence (e-mail: jhbrown{at}unm.edu)

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