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 Systems Biology
Mixedpower scaling of wholeplant respiration from seedlings to giant trees

Edited by James Hemphill Brown, University of New Mexico, Albuquerque, NM, and approved November 13, 2009 (received for review March 16, 2009)
Abstract
The scaling of respiratory metabolism with body mass is one of the most pervasive phenomena in biology. Using a single allometric equation to characterize empirical scaling relationships and to evaluate alternative hypotheses about mechanisms has been controversial. We developed a method to directly measure respiration of 271 whole plants, spanning nine orders of magnitude in body mass, from small seedlings to large trees, and from tropical to boreal ecosystems. Our measurements include the roots, which have often been ignored. Rather than a single powerlaw relationship, our data are fit by a biphasic, mixedpower function. The allometric exponent varies continuously from 1 in the smallest plants to 3/4 in larger saplings and trees. Therefore, our findings support the recent findings of Reich et al. [Reich PB, Tjoelker MG, Machado JL, Oleksyn J (2006) Universal scaling of respiratory metabolism, size, and nitrogen in plants. Nature 439:457–461] and West, Brown, and Enquist [West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122 126.]. The transition from linear to 3/4power scaling may indicate fundamental physical and physiological constraints on the allocation of plant biomass between photosynthetic and nonphotosynthetic organs over the course of ontogenetic plant growth.
From the smallest seedlings to giant trees, the masses of vascular plants span 12 orders of magnitude in mass (1). The growth rates of most plants, which are generally presented in terms of net assimilation rates of CO_{2}, are believed to be controlled by respiration (2, 3). Furthermore, many of the CO_{2}budget models of plant growth and carbon dynamics in terrestrial ecosystems are based on wholeplant respiration rates in relation to plant size (2, 4–7). Thus far, however, there have been few studies of wholeplant respiration over the entire range of plant size from tiny seedlings to large trees. The purpose of the present study was to quantify the allometric scaling of metabolism by directly measuring wholeplant respiration over a representative range of sizes.
For the past century, the scaling of metabolic rate with body size has usually been described using an allometric equation, or simple power function, for the form (8 ⇓ ⇓ ⇓ ⇓ ⇓ ⇓ ⇓ ⇓–17)
where Y is the respiratory metabolic rate (μmol s^{−1}), F is a constant (μmol s^{−1} kg^{f}), M is the body mass (kg), and f is the scaling exponent. The exponent f has been controversial, and various values have been reported based on studies of both animals and plants (15). Recently, it was suggested that f = 1 for relatively small plants, based on data for a 10^{6}fold range of body mass (16), including measurements using a wholeplant chamber (18, 19). If f = 1, this means that wholeplant respiration scales isometrically with body mass, which may be reasonable in the case of herbaceous plants and small trees because nearly all of their cells, even those in the stems, should be active in respiration. However, it was suggested that f = 3/4 based originally on empirical studies of animal metabolism (8). This idea is consistent with the mechanistic models of resource distribution in vascular systems (10, 11), including the pipe model (20, 21) and models based on spacefilling, hierarchical, fractallike networks of branching tubes.
A recent study showed sample sizes, measurement errors, and statistical analytical methods influence the allometric scaling exponents estimated by metadata syntheses (22). Most data on wholeplant respiration have been acquired using indirect methods of estimation, limited to small plants, or focused on a narrow range of body sizes (2, 5, 15, 16, 18, 19, 23⇓⇓–26). Furthermore, most studies of plant metabolic scaling have been based on the aboveground parts and have ignored respiration of the roots, which is very difficult to measure (23). Furthermore, the flow of dissolved CO_{2} in the sap brings into question the accuracy of estimating wholetree respiration based on measuring small portions of large trees using the standard clampon chambers that are commercially available (16, 27⇓⇓–30).
Given the methodological difficulties inherent in wholeplant physiological studies, it is not surprising that there have thus far been no empirical measurements of complete wholeplant respiration, including roots, that have a reasonable sample size and encompass a wide range of plant sizes (2, 22, 26, 31–34). Accurate and efficient methods using wholeplant chambers to measure respiration rates have recently been developed (5, 18, 19, 24⇓–26) and can be applied to assess metabolic scaling (Fig. 1). To determine the metabolic scaling of whole plants, including roots, across ontogenetic stages and species, we measured CO_{2} fluxes in a large number of sample plants from tropical to boreal ecosystems (22). These data allow the most comprehensive analysis of scaling of wholeplant metabolic rate undertaken to date.
Results
Using the wholeplant chamber (Fig. 1; detailed description in SI Methods ), we measured the respiration of 271 naturally grown whole plants spanning nine orders of magnitude in body mass, from 10^{−6} to 10^{4} kg. The plants comprised 64 species from biomes from Siberia to Southeast Asia (Table 1). The diameter, height, and age of the sample plants ranged from ca. 0.05–72 cm, 1–2,900 cm, and 1 week to 240 years of age, respectively.
At first, we tried to fit the relationship between the respiration rate and the wholeplant mass using a simplepower function on loglog coordinates. We found that f = 0.838 (n = 254, 95% CI of f = 0.820–0.855, r = 0.99, P < 0.001, ln F = −0.889) for the aboveground parts and f = 0.844 (n = 183, 95% CI of f = 0.824–0.863, r = 0.99, P < 0.001, ln F = −0.972) based on reduced major axis (RMA) regression of the log transformed version of Eq. 1. These values are significantly different from the exponents of f = 1 and 3/4 reported in previous studies (2, 8–17). Using ordinary least squares (OLS) rather than RMA regression did not change the pattern (Table 2).
Inspection of the data reveals a convex upward trend and a gradual change in the slope on loglog coordinates. Because there appears to be a systematic change in the value of f, a simplepower function fails to adequately express the relationship between wholeplant respiration and mass across the wide range of body masses that we investigated (Fig. 2).
For a mathematical description of this empirical metabolic scaling, we suggest a mixedpower function, which captures the transition between two simplepower functions, as follows (37): where G (μmol s^{−1} kg^{g}) and H (μmol s^{−1} kg^{h}) are coefficients, and g and h are exponents. As M varies, Eq. 2 maps onto two asymptotic relationships as follows: We used Akaike’s information criterion (AIC) (38 ⇓–40) to compare the mixedpower function of Eq. 2, the simplepower function of Eq. 1, and a quadratic equation (Table 2). The mixedpower function gave the best fit (the AIC value of 366.33 for Eq. 2 was the less than 372.12 for Eq. 1 and 369.18 for the quadratic function). For aboveground respiration, the AIC value of 555.72 for Eq. 2 was similar to the 555.31 for the quadratic function and less than the 560.18 for Eq. 1. Therefore, we recommend the mixedpower function as the best model for the metabolic scaling of plants.
As shown in Fig. 2 and Table 2, Eq. 2 reflected real trends in both wholeplant and aboveground respiration as a function of plant size well. The slope S that maps ln Y to ln M can be derived as a function of M by differentiating ln Y with respect to ln M in Eq. 2: Therefore, S is defined as the weighted mean of h and g given the values of Y _{1} and Y _{2}, respectively. As M increases, Y _{1}/(Y _{1} + Y _{2}) and Y _{2}/(Y _{1} + Y _{2}) change from 0.0 to 1.0 and from 1.0 to 0.0, respectively. The effect of the second term on the first term gradually decreases, and ultimately the slope S converged on h. Thus, Eq. 5 describes a biphasic relationship with two asymptotes, depending on individual mass.
The change in slope is shown in Fig. 3. The value of S changed gradually over the range of M (≈10^{−6} to 10^{4} kg), from ≈1.03 to 0.78 in the aboveground parts and from 1.21 to 0.81 in the whole plants. So, for both the aboveground parts and for whole plants, the allometric exponent was close to 1 only for the smallest masses (17) and rapidly converged to a value h = 0.780 ± 0.037 indistinguishable from 3/4 (8, 10, 11) for the aboveground parts, and to a value h = 0.805 ± 0.018, slightly >3/4, for the whole plants (SEM data in Table 2). In summary, we have integrated the two simplepower functions into Eq. 2, and they give two asymptotic slopes of 1 and 3/4 (8, 10, 11, 16) as individual plant mass increases.
Let point P on loglog coordinates denote the intersection between the straight lines representing Eq. 3 and Eq. 4. Also, let point Q be the intersection between the vertical line through P and the curve expressing Eq. 2 on the same coordinates. Then, the slope of a straight line touching this curve at the point Q is (g + h)/2. This is because Y _{1} is equal to Y _{2} at the intersection point P, where the M value is (H/G)^{[1/(g−h)]}. The value of M at the intersection point P, Y _{1} = Y _{2}, was calculated to be 1.054 × 10^{−4} kg and 3.429 × 10^{−5} kg for aboveground and wholeplant respiration, respectively. Therefore, as shown in Fig. 3, the exponent is close to 1 in only the very smallest plants (M < 1g) converges to 3/4 when M ≈ 0.1 kg (results qualitatively similar but quantitatively somewhat different from ref. 35). The precise transition is likely determined by physicochemical constraints (15) and may be reflect adaptation to various environments.
Discussion
Enquist et al. (35) and Hedin (36) also pointed out the possibility of an ontogenetic shift in the scaling wholeplant respiration over a wide range of body size. An ontogenetic shift from isometric (f = 1) to negatively allometric (f < 1) scaling has also been reported in animals with distinct larval and adult stages (15).
We can provide a biological rationale for this shift in scaling that is described by the mixedpower function and consistent with the morphological/physiological transition from tiny seedlings to giant trees (41, 42). During the earlier stages of ontogeny, a larger fraction of plant biomass is devoted to metabolically active leaf tissue, and a smaller fraction to vascular tissue for transport of water and nutrients. Furthermore, in small plants, such as small herbs and tree seedlings, the entire tissue of stems is metabolically active (43). We conclude that the nearisometric scaling of metabolic rate in herbs and juvenile trees is due to the large proportion of biomass that is metabolically active.
In comparison with small plants, most of the biomass of large trees is in the woody stems, which are much less metabolically active than the leaves and small branches. A large proportion of the trunk and large branches is typically composed of nonliving, metabolically inactive biomass, which serves a mechanical function, supporting the plant against the forces of gravity (11, 35) and wind. Plant respiration is ultimately limited by photosynthesis because plants can only respire compounds that have been fixed. Therefore, photosynthesis and respiration should be closely related to total leaf area (44 ⇓ ⇓–47), and the lessthanlinear scaling rate of metabolic plants might reflect a decreased leaftostem ratio with increasing plant size (48). Furthermore, the physiological and morphological changes in stems and leaves between juvenile and mature trees (41, 42) may also affect changes in wholeplant physiology. For all these reasons, with increasing plant size, the allometric exponent should decrease from 1 toward the canonical 3/4.
Conclusions
We conclude that interspecific metabolic scaling of vascular plants can be modeled using a mixedpower function. In Eq. 5, the slope of the mixedpower function is defined as the weighted mean of the slopes of the two asymptotes. Thus, the mixedpower function synthesizes the two previous models that feature slopes of 1 and 3/4 into a single synthetic model. Our proposed function implies a gradual ontogenetic transition in the scaling of metabolism from small seedlings to larger mature plants, a transition that is also seen across species in comparisons of herbaceous and woody plants. Our model can accommodate the variation in the scaling exponent that is observed over the 12 orders of magnitude variation in plant mass in our data. Thus, our function integrates the observed differences between small and large plants into a single statistical model that reflects allocation to photosynthetic and nonphotosynthetic organs during plant growth. Our approach may offer insights into the diversity of plant sizes in the context of physicochemical constraints consistent with the ecological traits of organisms (15).
Materials and Methods
Materials.
We examined 254 aboveground parts, 200 roots, and 183 whole plants to obtain measurements from 271 specimen plants of 64 species, sampled from tropical through boreal ecosystems of Eurasia, as shown in Table 1. At each site, we measured the respiration rates of fieldgrown plants.
Methods.
We measured wholeplant dark respiration rates during the growing season. We developed two kinds of respiration measurement methods, using a closedair circulation approach. One system was designed to acquire data using intact aboveground parts of standing trees (Fig. 1 A and B), and the other system was designed to monitor excised aboveground parts (Fig. 1 C–E) or excavated roots (Fig. 1F). As shown in SI Methods , there were no differences in respiration rates of the aboveground parts between the intact and excised materials at the same temperature (Fig. S1). To measure each giant tree, we divided the tree into portions and monitored the respiration of each portion to evaluate wholeplant respiration (see Fig. 1C). The masses of whole plants were measured directly using various balances that could accommodate seedlings to giant trees. Details are given in SI Methods .
Statistical Analysis.
1. To compare the scaling exponents from the present study with previous studies, a simplepower function of the form ln Y = ln F + fln M as shown in Eq. 1 was fitted to the data using both RMA and OLS regression.
2. To compare AIC among Eqs. 1 and 2 and a quadratic function, we analyzed all relationships using nonlinear least squares regressions (NLS) and OLS in Table 2. All analyses were performed using the R software package (49).
Acknowledgments
We thank K. Kikuzawa, K. Hozumi, J. H. Brown, and two anonymous reviewers for helpful comments and discussions regarding the manuscript, and the Forestry Technology Center of the Tohoku Regional Forest Office of the Japan Forestry Agency for field support. This research was partially supported by the Japan Ministry of Education, Culture, Sports, Science and Technology (MEXT) GrantinAid Scientific Research (B) 18380098 (FY20062008), the Japan Ministry of Environment Project B2 (FY19972000), and the Japan Forestry and Forest Products Research Institute Research Grant 200608 (FY19962010).
Footnotes
 ↵ ^{1}To whom correspondence should be addressed. Email: moris{at}ffpri.affrc.go.jp.

Author contributions: S.M. and K.Y. designed research; S.M., K.Y., A.I., S.G.P., O.V.M., A.H., A.T.M.R.H., R.S., A.O., M.K., T.M., T. Kajimoto, T. Koike, Y.M., T.T., O.A.Z., A.P.A., Y.A., M.G.A., T. Kawasaki, Y.C., and M.U. performed research; S.M. and T.U. contributed new reagents/analytic tools; S.M., A.H., A.O., and T.N. analyzed data; and S.M. and A.H. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0902554107/DCSupplemental.
Freely available online through the PNAS open access option.
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