Scaling the depths: below‐ground allocation in plants, forests and biomes

Abstract

West, Brown & Enquist’s (1997, 1999) allometric scaling theory (hereafter, WBE) is based on a biophysical model of resource transport in branched networks in an ‘ideal’ organism. WBE derives equations that predict how biological attributes ( B , e.g. metabolic rate, rates of resource use, even morphological features) scale with body mass ( M ), i.e. B ∝ M α , where α is a scaling exponent. Many such exponents are predicted by WBE to be simple multiples of 1 / 4 . These predictions have largely been confirmed by statistical comparisons with extensive data sets. WBE is explanatory in the sense of ‘makes comprehensible’ as well as ‘accounts for most of the variation in the data’. This is remarkable, given the huge morphological and physiological diversity that exists among organisms. WBE deliberately ignores specific details and concentrates on general principles. It is clearly not intended to explain the detailed form or function of particular species. Just as the Gas Laws of classical physics account for the average behaviour of large populations of ‘ideal’ molecules but not of individual molecules, WBE deals with the gross patterns seen when many taxa, habitats or body sizes are compared. Choose a particular species at random and the probability is that its features will deviate from the WBE ‘ideal’. Nevertheless, if WBE is largely correct, most individuals presumably conform, on average, to the principles on which it is based. That presumption has yet to be verified. Until it is, doubts will remain about whether WBE provides unique insights into how nature works or is just one of many theories that can make similar predictions but from different starting points (e.g. Makarieva, Gorshkov & Li 2003). Other challenges to WBE’s theoretical or statistical bases have been made (e.g. Dodd, Rothman & Weitz 2001; Kozlowski, Konarzewski & Gawelczyk 2003; White & Seymour 2003). It is simply worth noting here that other scaling exponents (e.g. 2 / 3 ) that explain the data statistically do not yet have the theoretical justification of WBE’s 1 / 4 -power exponents. WBE’s parameters usually have clear structural or functional identities. This contrasts with the para-meters of the polynomial equations used in standard growth analysis. Comparisons between data and WBE can be discussed on the basis of general biophysical, physiological or morphological principles, and not just in terms of statistical goodness-of-fit (West, Brown & Enquist 2001). WBE also offers a way to predict general ecological patterns using some fairly basic and widespread information – stem diameter, plant height, species number, etc. (Enquist & Niklas 2001). For functional ecologists this must increase the rigour with which we can interrogate the natural world, even if WBE eventually comes to be regarded as one of several (and not necessarily the most fundamental) models that fulfil this need. One test of whether WBE is useful is if it can shed new light on important ecological questions. Here I explore how mass allocation patterns in vegetation can be analysed using WBE. Enquist & Niklas (2002) developed the original WBE model to explain general allocation patterns in plants. My analysis shows that despite its strengths, the current WBE model is insufficient to explain these patterns across all size scales; the alternative conclusion is that WBE suggests that the below-ground carbon (C) stocks of vegetation could be much larger than the current estimates based on biomass inventories. Enquist & Niklas (2002) derived an equation relating the above-ground mass of vegetation ( M A , comprising leaves and stems) to that below-ground ( M R ). The equation is (using Enquist & Niklas’ notation):