LETTER Nitrogen/phosphorus leaf stoichiometry and the scaling of plant growth Karl J. Niklas, 1 * Thomas Owens, 1 Peter B. Reich 2 and Edward D. Cobb 1 1 Department of Plant Biology, Cornell University, Ithaca, NY 14853, USA 2 Department of Forest Resources, University of Minnesota, St Paul, MN 55108, USA *Correspondence: E-mail: kjn2@cornell.edu Abstract We adopted previous N : P stoichiometric models for zooplankton relative growth to predict the relative growth rates of the leaves l L of vascular plants assuming that annual leaf growth in dry mass is dictated by how leaf nitrogen N L is allocated to leaf proteins and how leaf phosphorus P L is allocated to rRNA. This model is simplified provided that N L scales as some power function of P L across the leaves of different species. This approach successfully predicted the l L of 131 species of vascular plants based on the observation that, across these species, N L scaled, on average, as the 3/4 power of P L , i.e. N L µ P 3=4 L . When juxtaposed with prior allometric theory and observations, our findings suggest that a transformation in N : P stoichiometry occurs when the plant body undergoes a transition from primary to secondary growth. Keywords Plant allometry, plant size, protein-rRNA models, scaling laws. Ecology Letters (2005) 8: 636–642 INTRODUCTION Dobberfuhl (1999; see Sterner & Elser 2002; Vrede et al. 2004) first proposed a general model that attempts to predict the relative growth rates of all manner of organisms based on how total body nitrogen N T is allocated to protein construction. Noting that some portion of total body phosphorus P T must be allocated to rRNA to maintain any specific quantity of protein, this model conceptually relates relative growth rates to N : P stoichiometry by envisioning proteins as the ÔoverheadÕ that must be produced to achieve growth and rRNA as the protein-output ÔmachineryÕ that must be maintained to recycle this overhead. As noted by Dobberfuhl and others (e.g. A ˚ gren 2004), assuming a constant chemical composition, relative growth l can be mathematically expressed in terms of carbon C, nitrogen N, or phosphorus P content and rate of change by the formula l ¼ 1 C dC dt   ¼ 1 N dN dt   ¼ 1 P dP dt   : ð1Þ For any one of these essential substances, designated here by X, this formula takes the general form l ¼ 1 X dX dt   ¼ ln X 2 X 1    t 2  t 1 ð Þ 1 ð2Þ where X 2 is the cell (tissue or organismal) concentration of X at time t ¼ 2 and X 1 is the concentration of X at time t ¼ 1 (see Hunt 1990). If the expression X is thought of in terms of protein synthesis, Dobberfuhl’s (1999) model expresses relative growth as l ¼ ln f N N T þ k s r e Ff P P T m r   f N N T 2 4 3 5  t 1 ; ð3Þ where f N is the decimal fraction of N T invested in proteins, k s is the protein synthesis rate per ribosome, r e is the protein retention efficiency, F is the decimal fraction of total RNA allocated to rRNA, f P is the decimal fraction of P T invested in RNA, and m r is average ribosome mass. Using estimates or published numerical values of the variables required by this model, various authors have used eqn 3 (or its variants) to predict the relative growth rates of different unicellular plants and animals (e.g. Nielsen et al. 1996; Klausmeier et al. 2004; Vrede et al. 2004). This approach has been remarkably successful despite the numerous assumptions and simplifications underlying eqn 3, e.g. the assumption that N and P allocation patterns are ontogenetically invariant, the requirement that balanced growth has been achieved, and the supposition that resources are not limiting. With these caveats in mind, we note that eqn 3 can be integrated into prior work showing that, across a broad spectrum of vascular plant species, annual growth in dry mass per individual G T scales isometrically with respect to Ecology Letters, (2005) 8: 636–642 doi: 10.1111/j.1461-0248.2005.00759.x Ó2005 Blackwell Publishing Ltd/CNRS