## Abstract

A general allometric model has been derived to predict intraspecific and interspecific scaling relationships among seed plant leaf, stem, and root biomass. Analysis of a large compendium of standing organ biomass sampled across a broad sampling of taxa inhabiting diverse ecological habitats supports the relations predicted by the model and defines the boundary conditions for above- and below-ground biomass partitioning. These canonical biomass relations are insensitive to phyletic affiliation (conifers versus angiosperms) and variation in averaged local environmental conditions. The model thus identifies and defines the limits that have guided the diversification of seed plant biomass allocation strategies.

Despite its importance to ecology, global climate research, and evolutionary and ecological theory, the general principles underlying how plant metabolic production is allocated to above- and below-ground biomass remain unclear (1–6). Indeed, there are few large data sets with which to evaluate patterns of standing biomass within and across the broad spectrum of vascular plant species (2, 7). The resulting uncertainty severely limits the accuracy of models for many ecologically and evolutionarily important phenomena across taxonomically diverse communities (8–11). Thus, although quantitative assessments of biomass allocation patterns are central to biology, theoretical or empirical assessments of these patterns remain contentious (2, 8, 10, 11).

Nonetheless, the scaling relations among standing leaf, stem, and root (below-ground) biomass (*M*
_{L},*M*
_{S}, and *M*
_{R}, respectively) can be derived analytically by first noting that the amount of resource used per individual plant, *R˙*
_{0}, approximates metabolic demand and gross photosynthesis (*B*) (12–14). Because *B* is predicted to scale proportionally to total *M*
_{L}(*R˙*
_{0} ∝ *B* ∝*M*
_{L}), theory predicts that the surface areas over which resources are exchanged with the environment (e.g., leaf surface area, which correlates with *M*
_{L}) are proportional to the 3/4 power of the total plant biomass (*M*
_{T}) (12–14). Thus, *B* ∝*M*
_{L} ∝ *M*
_{T}
^{3/4}and *M*
_{L} ∝*D*
_{S}
^{2}, where *D*
_{S}is stem diameter. Empirical studies confirm that plant metabolic rate scales as the 3/4 power of *M*
_{T} (which equals the sum of *M*
_{L}, *M*
_{S}, and*M*
_{R}) and that metabolic rates scale isometrically with respect to *M*
_{L} (7, 12,13, 15). Here, we extend this theory (16) on the basis of three assumptions: (i) Stem and root bulk tissue densities are approximately constant during ontogeny (13), (ii) the effective hydraulic cross-sectional areas of stems and roots are equivalent (owing to the conservation of water mass flowing through a plant) (17, 18), and (iii) stem length scales roughly isometrically with respect to root length (*L*
_{R}). If valid, these three basic assumptions corroborate the predictions that standing *M*
_{L}will scale as the 3/4 power of *M*
_{S} and as the 3/4 power of *M*
_{R} and that standing*M*
_{S} and *M*
_{R} will scale isometrically with respect to each other (*M*
_{L} ∝*M*
_{S}
^{3/4} ∝*M*
_{R}
^{3/4} and *M*
_{S}∝ *M*
_{R}). It also follows that above-ground biomass (*M*
_{A}) will scale in a nearly isometric manner with respect to *M*
_{R} (i.e.,*M*
_{L} + *M*
_{S} ∝*M*
_{R}) across and within clades and different habitats.

These predictions were tested against data gathered from a variety of sources for standing *M*
_{L},*M*
_{S}, and *M*
_{R} per plant across monocot, dicot, and conifer species differing by ∼nine orders of magnitude in total body mass (19–21) [see supplemental data (22)]. Regression analyses (21) of these data show that all observed scaling exponents (α_{RMA}) comply remarkably well with those predicted by the model (Table 1). For example,*M*
_{L} scales across species as the 1.99 power [95% confidence interval (CI) = 1.90 ≤ α_{RMA}≤ 2.07] of *D*
_{S} (Fig. 1) and does not differ significantly between angiosperm and conifer species (Table 1). Likewise, comparisons between angiosperm and conifer species reveal no statistically significant variation in the scaling exponents for standing *M*
_{L}, *M*
_{S}, and*M*
_{R}, whereas the relation between*M*
_{A} and *M*
_{R} is nearly isometric for mature individuals, as predicted (i.e.,*M*
_{A} = 3.88*M*
_{R}
^{1.02}) (Fig. 2). Within the larger size ranges, statistical outliers are remarkably absent from all bivariant plots even when data from arborescent palm species, which lack a branched growth habit, are included (Figs. 1 and 2). However, our theory predicts a nonlinear log-log relation between *M*
_{A} and*M*
_{R} for plants less than 1 year old (16). This is not evident in our data for juvenile plants (i.e., less than 1 year old), which are best approximated by a linear log-log curve (Fig. 2). We attribute the departure of these data from theoretical expectations to the influence of nutrients provided by endosperm or megagametophyte tissues on the biomass partitioning pattern attending seedling establishment. Such a “maternal resource compartment” is expected to favor *M*
_{R} as opposed to *M*
_{A} (specifically leaf) accumulation.

The effect of plant size on the numerical values of scaling exponents was insignificant above the threshold of 1-year-old plants. When the data in the large size ranges were sorted into different size ranges, separate regression analyses failed to detect statistically significant differences in the scaling exponents for*M*
_{L}, *M*
_{S}, and*M*
_{R} relations. For example, regression of*M*
_{L} versus +3 < log_{10}
*M*
_{R} < –0.5 obtained a scaling exponent of 0.77 ± 0.02 (95% CI = 0.74 to 0.81,*r*
^{2} = 0.783, *n* = 337, *F* = 1208, *P* < 0.0001), whereas regression of *M*
_{L} versus –0.5 ≤ log_{10} *M*
_{R} < +3 obtained a scaling exponent of 0.79 ± 0.04 (95% CI = 0.68 to 0.89,*r*
^{2} = 0.539, *n* = 183, *F* = 211.3, *P* < 0.0001). Slight deviations were observed for allocation exponents involving*M*
_{R} (Table 1). This is likely due to increased error in sampling the smallest roots from large trees.

Compilations of intraspecific variation in*M*
_{A} and *M*
_{R} during ontogeny provide strong additional support for our theory. Across 61 species of woody tree and large shrub species, the average scaling exponent for*M*
_{L} versus basal stem diameter scales is 2.17 (95% CI = 2.01 to 2.32, mode = 2.06, *n* = 61). This numerical value is essentially indistinguishable from that predicted or observed within or across our data sets. Furthermore, as predicted, the average intraspecific exponent for the scaling of root and shoot biomass (*M*
_{A}) during ontogeny across 32 independent studies including 26 species of herbaceous and woody plant species is 0.98 (95% CI = 1.09 ≤ α_{RMA} ≤ 0.885). These exponents also agree with data reported for a limited number of studies treating individual species or individual community samples of comparable geographic scale (2), although it is evident from our theory that a maternal compartment can influence shoot-to-root ratios for especially small, juvenile plants.

The scaling exponents predicted by the model also appear to be insensitive to ecological factors known to influence local community composition, abundance, and average plant size. For example, whereas average *M*
_{T} per community is inversely proportional to the number of plants per ha, *M*
_{T}∝ *N*
^{−4/3} or *N* ∝*M*
_{T}
^{−3/4} in accordance with allometric theory (12), the scaling exponents for biomass allocation do not vary across diverse communities differing by over five orders of magnitude in average plant size (Fig. 3). Despite the residual variation in organ and *M*
_{T}attributable to plants grown under stressful conditions [e.g., drought, light deprivation, or elevated ultraviolet-B (UV-B levels)], statistical outliers are once again comparatively rare.

The ability to predict the absolute amounts of*M*
_{L}, *M*
_{S}, or*M*
_{R }at the level of both the individual plant or an entire community is limited, because significant variation exists in the numerical values of allometric “constants” across species. For example, although both angiosperm and gymnosperm*M*
_{L} scales as the 3/4 power of*M*
_{S} (Table 1), the corresponding allometric constants (β_{RMA }values = the *y*intercepts) significantly differ from each other (i.e., 0.13 ± 0.075 and 0.34 ± 0.074, respectively) (Table 1). Thus, for equivalent *M*
_{S}, conifers have, on average, 2.6 times more *M*
_{L} than do angiosperms. This observation resonates with the fact that conifers typically retain three cohorts of leaves that have less well-developed aerenchymatous mesophyll as compared with angiosperm leaves. Yet, even though conifer wood tends to be less dense than angiosperm wood, angiosperms and gymnosperms do not differ in the allometric relation between total*M*
_{R} and *M*
_{A} nor with the scaling of plant density and *M*
_{A} (Figs. 2 and 3).

Plant biologists have long held the opinion that much idiosyncratic and site-specific variation exists in biomass allocation both within and across plant taxa, especially during ontogeny (23). Taxon and site-specific variation in biomass allocation is well known in response to differential selection for adaptations to different environmental conditions (e.g., species adapted to arid and hot conditions tend to have reduced*M*
_{L} with respect to *M*
_{S} or*M*
_{R}) (23, 24). Nevertheless, when viewed across a large range of plant sizes, the about 10-fold variation in biomass allocation shown in Figs. 1 through 3 is slight as compared with the striking invariance observed (and predicted) for the scaling exponents of *M*
_{L},*M*
_{S}, and *M*
_{R} across an impressive ∼nine orders of magnitude of *M*
_{T}across diverse communities differing in latitude and elevation. Traditionally, this variation has been indexed by ratios (e.g., stem:leaf, root:shoot, etc.). However, ratios fail to capture the actual functional relations characterizing biomass allocation among organ types. In contrast, our model and empirical findings quantitatively define the numerical limits on plant allocation strategies, which incidentally accord well with the observation that*M*
_{A} and *M*
_{R} are not significantly correlated with site age, absolute latitude, elevation, or number of species within the community. Furthermore, expressing allocation in terms of functional allometric relation provides a baseline by which to assess residual variation. For example, residual variation in biomass allocation between roots and shoots is significantly, although very weakly, correlated with plant height (*P* < 0.0001, *r*
^{2} = 0.058, *n* = 271) and local productivity (*P* = 0.007, *r*
^{2} = 0.04, *n* = 178).

Our model provides strong bridges to more detailed biometric analyses of individual plants within and across communities (10, 25). Furthermore, in conjunction with the allometric relation predicted by a growing body of allometric theory (12–15, 26), a general allometric framework directly pertains to developing quantitative models for global climate as well as a variety of other important ecological and evolutionary phenomena including the approximate boundary conditions for difficult-to-measure *M*
_{R}(1–10). Also, by identifying fundamental biomass partitioning rules, the model helps to identify the biophysical constraints acting on allocation tradeoffs in plant biology that potentially extend into the fossil record when seed plants first evolved. Allometric theory therefore holds great promise as a powerful quantitative tool with which to predict past and present-day plant structure-function relation at the level of the individual, community, or entire ecosystem (26).

↵* To whom correspondence should be addressed. E-mail: benquist{at}u.arizona.edu