A Global Relationship Between the Heterotrophic and Autotrophic Components of Soil Respiration?

中国科技论文在线 http://www.paper.edu.cn Global Change Biology (2004) 10, 1756–1766, doi: 10.1111/j.1365-2486.2004.00816.x

A global relationship between the heterotrophic and autotrophic components of soil respiration?

BEN BOND-LAMBERTY*, CHUANKUAN WANG*w and S T I T H T . G O W E R * *Department of Forest Ecology and Management, University of Wisconsin-Madison, 1630 Linden Drive, Madison, WI 53706, USA wEcology Program, Northeast Forestry University, Harbin 150040, China

Abstract

Soil surface CO2 flux (RS) is overwhelmingly the product of respiration by roots (autotrophic respiration, RA) and soil organisms (heterotrophic respiration, RH). Many studies have attempted to partition RS into these two components, with highly variable results. This study analyzes published data encompassing 54 forest sites and shows that 2 RA and RH are each strongly (R 40.8) correlated to annual RS across a wide range of forest ecosystems. Monte Carlo simulation showed that these correlations were significantly stronger than any correlation introduced as an artefact of measurement method. Biome type, measurement method, mean annual temperature, soil drainage, and leaf habit were not significant. For sites with available data, there was a significant 2 (R 5 0.56) correlation between total detritus input and RH, while RA was unrelated to net primary production. We discuss why RA and RH might be related to each other on large scales, as both ultimately depend on forest carbon balance and photosynthate supply. Limited data suggest that these or similar relationships have broad applicability in other ecosystem types. Site-specific measurements are always more desirable than the application of inferred broad relationships, but belowground measurements are difficult

and expensive, while measuring RS is straightforward and commonly done. Thus the relationships presented here provide a useful method that can help constrain estimates of terrestrial carbon budgets. Keywords: autotrophic respiration, carbon cycling, heterotrophic respiration, Monte Carlo simulation,

root respiration, soil CO2 ﬂux Received 14 October 2003; revised version received 3 February 2004 and accepted 12 March 2004

into its heterotrophic and autotrophic source ﬂuxes Introduction (Singh & Gupta, 1977; Hanson et al., 2000). Such a The processes controlling the sources and dynamics of partitioning constitutes a gross simpliﬁcation of the

soil surface CO2 ﬂux (RS) remain poorly understood. sources of RS – and as such is probably unable to This ﬂux is the second largest in the global carbon cycle, capture processes controlling turnover of the large

contributing 20–40% of atmospheric CO2 annual input pools with slow turnover that ultimately control carbon (Raich & Schlesinger, 1992) with marked temporal storage and net ecosystem production – but is none- variation (Savage & Davidson, 2001, Raich et al., theless a highly useful one.

2002). At smaller scales, RS comprises a large percen- The partitioning of RS is an important issue in forest tage of ecosystem respiration (Lavigne et al., 1997; Law ecosystem ecology, carbon cycling, plant physiology, et al., 1999, Janssens et al., 2001), the variability of which soil science, and global climate change modelling. Root can determine forest carbon balance (Goulden et al., and microbial respiration may respond differently to

1998; Valentini et al., 2000). RS is overwhelmingly the temperature (Boone et al., 1998; Pregitzer et al., 2000; product of respiration by roots (autotrophic respiration, Epron et al., 2001), implying different ﬂux behaviours at

RA) and soil decomposers (heterotrophic respiration, a variety of time scales and in different plant species RH), and there have been many efforts to partition it (Kuzyakov & Domanski, 2000). This is important because the balance between soil organic matter decay

Correspondence: Ben Bond-Lamberty, tel. 1 1 608 262 6369, and CO2 fertilization effects may drive future changes fax 1 1 608 262 9922, e-mail: [email protected] in the global carbon cycle (Jenkinson, 1991; Melillo et al.,

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SOIL AUTOTROPHIC AND HETEROTROPHIC CO2 FLUX 1757

2002), as the global soil organic matter pool contains limitations of estimating RA and RH from measure- twice the C of the atmosphere (Post et al., 1982). Plant ments of annual RS. This paper focuses primarily on fine roots play important roles in terrestrial carbon and forest RS because forests comprise 50% of the global nutrient cycling (Hendricks et al., 1993), and accurate land surface, with an even greater share of terrestrial measurements of RS and RA can help constrain NPP (Melillo et al., 1993), and more data on RS and RC estimates of carbon allocation to these roots (Nadelhof- have been published for forests than for any other fer & Raich, 1992). In addition, while measurements of ecosystem type (Hanson et al., 2000). net primary production (NPP) subsume RA losses, knowledge of heterotrophic fluxes is required to Methods calculate net ecosystem production and permit comparison of process- and biomass-based estimates with We collected studies in the scientific literature that net ecosystem exchange derived from eddy covariance estimated autotrophic and heterotrophic sources of RS. techniques. Thus the contribution of each RS compo- We used only studies that (i) partitioned RS into its nent must be known to understand the effects of global heterotrophic and autotrophic component fluxes, or change on net exchange of CO2 between terrestrial otherwise calculated RC, and (ii) reported annual (not ecosystems and the atmosphere. simply growing season) RS flux for one or more field Belowground measurements are difficult to perform, study sites. If a study did not report annual RS but was and values of 10–90% for the root contribution (RC, performed at an intensively studied site for which these defined here as RA/RS)toRS have been reported for data were available (e.g., the BOREAS NSA tower site both forest and nonforest ecosystems (Hanson et al., in Manitoba, Canada), the study was included. Data

2000). Much of this variability may be caused by from a study of RS and RC for a boreal black spruce problems associated with different methods used to (Picea mariana (Mill.) BSP) chronosequence (Bond- estimate RC, rather than any underlying variability Lamberty, 2004 (in press)) were included; annual RS between ecosystems, species, or developmental stages has been published for these sites (Wang et al., 2002). (Ho¨gberg et al., 2001), as the complexity, cost, and We focused on undisturbed forests or tree plantations disturbance associated with experimental treatments and thus excluded several studies (Edwards & Ross- complicate field and laboratory measurements (Kuzya- Todd, 1983; Gordon, 1987; Toland & Zak, 1994) kov & Domanski, 2000). Another difficulty is that comparing recent clearcuts to intact forests, all of which microbial respiration is influenced by root exudates reported essentially no root contribution to RS (i.e., (Kuzyakov, 2002). Here we follow many previous RC 5 0% for intact forest). This is improbable, and we studies in using the terms ‘root respiration’ and believe that the high disturbance associated with such ‘autotrophic respiration’ interchangeably, as there is clearcuts justified excluding these studies. In addition, no standard practice to include rhizospheric respiration the RA values reported by Ryan et al. (1997) for the in microbial soil respiration or in autotrophic root BOREAS NSA research site exceeded reported RS at this respiration (Hanson et al., 2000); a clean separation of site, and were significantly different from a number of the two sources may not be possible, or even realistic. other studies using similar techniques at the same site We acknowledge that there are heterotrophic contribu- (Steele et al., 1997; Dioumaeva et al., 2002). These data tions to ‘root’ or ‘autotrophic’ respiration, e.g., the respi- were thus excluded; we did not exclude data from other ration in the rhizosphere of symbiotic mycorrhizal fungi sites reported by Ryan et al. (1997) using the same and other microorganisms (Kelting et al., 1998), but in a techniques (but doing so would not have significantly meta-analysis such as this study, there was no practical changed our results). Finally, one study (Thierron & way to correct for this. Thus, we simply used RA or RH Laudelout, 1996) with extremely high reported values values reported by authors, making no attempt to for RS and RC was excluded after model fitting, as an correct for varying definitions of ‘root respiration.’ outlier test (Chatterjee & Price, 1991) using it and the

This paper examines published estimates of RS and reduced data set was highly signiﬁcant (Y* 5 817, RC, the annual root contribution to RS, and discusses YPRED 5 191, SE(YPRED) 5 105, T53 5 5.96, Bonferroni- relationships between RS and its two major source adjusted Po0.001). We did not exclude studies based ﬂuxes, RA and RH. This is equivalent to testing the on measurement method (e.g., low readings possibly hypothesis that there is a global correlation between the associated with alkali absorbents) (Raich & Nadelhof-

RA and RH components of RS. We discuss the biological fer, 1989). and statistical underpinnings of such a relationship, Thirty-one boreal, cold temperate, warm temperate, show why these variables are signiﬁcantly more and tropical forest studies were used for the ﬁnal correlated than can be explained simply as an artefact analyses, with data from 54 total sites, 47 of them being of measurement method, and outline the uses and unique (Table 1). Techniques used to separate RA from r 2004 Blackwell Publishing Ltd, Global Change Biology, 10, 1756–1766 中国科技论文在线 http://www.paper.edu.cn

1758 B. BOND-LAMBERTY et al.

Table 1 Studies used in the analysis presented here, with values reported for total soil surface CO2 ﬂux (RS), its autotrophic (RA) 2 1 and heterotrophic (RH) subcomponents (all in g Cm yr , and/or root contribution to RS (RC, equal to RA/RS)

Study Method Location Habit Soil Age RS RA RH RC (%)

Boreal Bond-Lamberty et al. Excl Thompson, MB, Canada – D 3 262 255 (2004) Excl Thompson, MB, Canada – W 3 85 76 Excl Thompson, MB, Canada D/E D 6 85 76 Excl Thompson, MB, Canada D/E W 6 551 385 Excl Thompson, MB, Canada D/E D 12 425 285 Excl Thompson, MB, Canada D/E W 12 540 394 Excl Thompson, MB, Canada D/E D 20 551 385 Excl Thompson, MB, Canada D/E W 20 550 375 Excl Thompson, MB, Canada D/E D 37 484 378 Excl Thompson, MB, Canada D/E W 37 491 425 Excl Thompson, MB, Canada E D 71 540 394 Excl Thompson, MB, Canada E W 71 311 285 Excl Thompson, MB, Canada E D 151 375 329 Excl Thompson, MB, Canada E W 151 330 293 w Dioumaeva et al. (2002) Extr Thompson, MB, Canada E D 150 330* 50 w Extr Thompson, MB, Canada E W 150 327* 30 Ho¨gberg et al. (2001) Comp A˚ heden, Sweden E D 50 275z 54 Malhi et al. (1999) Subtr Prince Albert, SK, Canada E D 115 143 449 O’Connell et al. (2003) Excl Prince Albert, SK, Canada E D 118 564 440 Excl Prince Albert, SK, Canada E W 118 319 264 Russell & Voroney (1998) Subtr Prince Albert, SK, Canada D D 70 905 60 Ryan et al. (1997) Extr Prince Albert, SK, Canada D D 67 905§ 314 Extr Prince Albert, SK, Canada E D 115 564} 192 Extr Prince Albert, SK, Canada E D 65 338k 151 Wide´n & Majdi (2001) Extr Uppsala, Sweden E D 34 98** 29 Extr Uppsala, Sweden E D 50 149** 33 Cold temperate Arneth et al. (1998) Subtr Christchurch, New Zealand E D 8 950 640 310 Bowden et al. (1993) Excl Harvard Forest, USA D D 80 371 33 w Buchmann (2000) Excl Fichtelgebirge, Germany E D 47 710 210 500 30 Gaudinski et al. (2000) Isot Harvard Forest, USA D D 70 840 490 Haynes & Gower (1995) Excl Boulder Junction, WI, USA E D 30 858 496 Irvine & Law (2002) Extr Sisters, OR, USA E D 14 512 52 Extr Sisters, OR, USA E D 50–250 511 46 Kutsch et al. (2001) Extr Kiel, Germany D W 45 1754 1234 Phillipson et al. (1975) Sub Oxford, UK D D 150 122 5 Tate et al. (1993) Extr Maruia, New Zealand D D ? 650 23 Warm temperate ww Andrews et al. (1999) Isot Duke Forest, NC, USA E D 15 956 30 Edwards & Harris (1977) Extr Oak Ridge, TN, USA D D 50 1065 373 35 Epron et al. (1999) Excl Moselle, France D D 30 660 264 40 Epron et al. (2001) Subtr Moselle, France D D 30 660 52 Ewel et al. (1987) Excl Bradford County, FL, USA E D 9 850 51 Excl Bradford County, FL, USA E D 29 1300 62 Maier & Kress (2000) Extr Laurinburg, NC, USA E D 11 1263 663 600 Malhi et al. (1999) Subtr Oak Ridge, TN, USA D D 55 395 359 Nakane et al. (1983) Comp Hiroshima, Japan E D 80 1299 774 Nakane et al. (1986) Comp Hiroshima, Japan E D 80 1255 676 Ohashi et al. (2000) Comp Kyushu, Japan E D 10 618 49 w Pulliam (1993) Extr Ogeechee River, GA, USA D W ? 881 554 w Extr Ogeechee River, GA, USA D W ? 902 543 (continued)

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SOIL AUTOTROPHIC AND HETEROTROPHIC CO2 FLUX 1759

Table 1 (Contd.)

Study Method Location Habit Soil Age RS RA RH RC (%)

Rey et al. (2002) Excl Roccarespampani, Italy D D 40 1097 45 Ryan et al. (1996) Extr Canberra, Australia E D 20 987 274 28 Tropical Malhi et al. (1999) Subtr Manaus, Brazil E D ? 1650 680 970 Trumbore et al. (1995) Isot Paragominas, Brazil E D ? 2400 1510 Lamade et al. (1996) Extr Ouidah, Benin E D 20 1610 1127 Excluded data Edwards & Ross-Todd (1983) Comp Oak Ridge, TN, USA D D 50–120 92 121–154 Gordon (1987) Comp Bonanza Creek, AK, USA D D 133 1075 1433 Ryan et al. (1997) Extr Thompson, Canada E D 150 330* 382 Thierron & Laudelout (1996) Extr Chimay, Belgium D D ? 1909 90 Toland & Zak (1994) Comp Manistee Forest, MI, USA D D ? 487 467 Comp Manistee Forest, MI, USA D D ? 469 474

Biome, method (exclusion (Excl), extraction (Extr), isotope (Isot), comparison (Comp), subtraction (Subtr)), location, leaf habit (deciduous or evergreen), soil (dry or wet), and forest age are given.

*Annual soil respiration (RS) from Wang et al. (2002). w Fine roots only. zUnpublished data. § Annual soil respiration (RS) from Russell & Voroney (1998). } Annual soil respiration (RS) from O’Connell et al. (2003). k Annual soil respiration (RS) from Striegl & Wickland (1998). **Estimated from ﬁgure. ww Calculated from Andrews & Schlesinger (2001).

RH included site comparison (e.g., comparing RS at simulations to determine if the observed relationships intact stands and recent burns, or physiological between RS, RA, and RH were simply due to the manipulation of root photosynthate supply in treat- correlation introduced by measurement, or signiﬁed an ment plots), root exclusion (e.g., trenched plots), root underlying correlation between RA and RH themselves. extraction (measuring respiration of either roots or pure Fifty random, independent RA and RH values were 2 soil), stable or radioactive isotope labelling, and mass generated using statistical distributions (w7 and nega- balance (subtraction using other components of the tive exponential with l 5 4, respectively) that approxi- carbon cycle). We examined the relationships between mated the distribution of these values in the real data

RS and its components RA and RH for these studies. In set. RS was computed as RA 1 RH, and statistical addition, studied systems were categorized by biome, RA RS and RH RS models, with forms (logarithmic leaf habit, method of RS partitioning, soil drainage, transformation, etc.) identical to those discussed below latitude, mean annual temperature, and precipitation; for the real data, were fit to the simulated data. these were treated as fixed effects during model Adjusted R2 values were recorded for each model. This significance testing. When available, ancillary site data process was repeated 10 000 times, and the resulting R2 (aboveground detritus production, NPP, and below- distributions compared with those obtained from the ground fine root production) were tested for their real data. Tukey’s test for nonadditivity was used to test effects on RS partitioning. for curvature of residual plots. SAS version 8.1 (SAS No study discussed here provided independent field Institute Inc., 2001) was used for all statistical tests. measurements of RA and RH – rather, most measure RS and either R or R , computing the complementary A H Results and discussion term by subtraction. ‘Exclusion’ and ‘comparison’ techniques introduce additional correlation, as the Global relationships between RS, RA, and RH reported subcomponent flux (typically RH) is computed not as an independent measurement but as the Soil heterotrophic respiration was significantly and difference between two RS values. This means that positively correlated to RS across all studies (Fig. 1). some inherent correlation exists in the data set Biome type, measurement method, mean annual discussed here (see Appendix for a simplified treatment temperature, latitude, precipitation, soil drainage, and of the statistical issues involved). We used Monte Carlo leaf habit had no significant (a 5 0.05) effect on this r 2004 Blackwell Publishing Ltd, Global Change Biology, 10, 1756–1766 中国科技论文在线 http://www.paper.edu.cn

1760 B. BOND-LAMBERTY et al. relationship. The model implies that RH approaches was necessary to ensure homogeneous variance, and zero with RS; this makes biological sense, as some thus, the model is approximately linear except at low RS heterotrophic respiration occurs in the soil if RS40. The values. Mathematically, this implies that RC increases relationship between RS and RA (Fig. 2a) was slightly asymptotically with RS (Fig. 2b), although we note that stronger than that of the RH RS relationship. None of a ‘change-point’ model (Chappell, 1989) would also ﬁt the secondary effects listed above explained any addi- the data well (implying a constant RC above some tional variation in the model. Square-root transforma- break point in the data). The model predicts RC values tion of both the dependent and independent variables of 30–50% for RS values reported for most terrestrial systems (Raich & Schlesinger, 1992), a range consistent with mean RC values generally reported (Hanson et al.,

2000). The RA RS and RH RS relationships shown in Figs 1 and 2 imply that RA and RH are themselves correlated at the global scale (since by deﬁnition

RA 1 RH 5 RS); several lines of evidence can be adduced in support of this hypothesis.

Statistical support for RA–RH correlation The results of the Monte Carlo simulations (Fig. 3) show that the correlations discussed above are much stronger than what could be expected simply as a result of the Fig. 1 Relationship between annual soil respiration (RS) and its measurement methods used to estimate RA and RH (i.e., heterotrophic (RH) component, by study biome. A logarithmic transformation was necessary for residual homogeneity. For the the fact that no study measures RA and RH indepen- 2 2 53 sites examined, ln (RH) 5 1.22 1 0.73 ln(RS), R 5 0.81, Po0.001. dently in the field). The RH RS relationship R value Dotted lines show model 95% confidence intervals; inset graph of 0.81 was significantly (T9999 5305.96, Po0.001) shows model residuals (y-axis) vs. predicted values (x-axis). higher than the R2 distribution for the simulated data

in which RA and RH were uncorrelated; similarly, the 2 RA RS R value of 0.87 was signiﬁcantly higher than its corresponding simulated distribution (T9999 5 268.97, Po0.001). Thus the correlations shown in

Fig. 3 Results of Monte Carlo simulation in which random,

uncorrelated autotrophic (RA) and heterotrophic (RH)CO2 ﬂux data were generated (50 values each, N 5 10 000), from the same

Fig. 2 (a) Relationship between annual soil respiration (RS) and distributions as the real data. Statistical models, of identical form its autotrophic (RA) component, by study method. For the 54 to those used for the real data, were fitted to describe the 0:5 0:5 2 sites examined, RA ¼7:97 þ 0:93RS , R 5 0.87, Po0.001. relationship between RA, RH, and total soil surface CO2 flux (RS, Dotted lines show model 95% confidence intervals; inset graph calculated as RA 1 RH). Histograms show distribution of 2 2 shows model residuals. (b) Root contribution (RC) to RS. For the adjusted R values for these models. Arrows indicate R values 2 53 sites examined, RC 5 0.66 1 0.16 ln(RS), R 5 0.38, Po0.001. observed in actual data.

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SOIL AUTOTROPHIC AND HETEROTROPHIC CO2 FLUX 1761

Figs 1 and 2 cannot be explained simply as an artefact of measurement. This ‘extra’ correlation is expected if

RA and RH are themselves correlated (see Appendix), and supports the biological arguments for RA–RH correlation outlined below.

Biological support for RA–RH correlation There is a strong conceptual basis for the empirical correlation between RA and RH reported here, based on the detritus production and root exudates of terrestrial vegetation. At large scales, plant production and soil Fig. 4 Relationship between total detritus input (aboveground respiration are certainly linked processes: RS is corre- detritus 1 fine root net primary production) and heterotrophic lated with litterfall (Raich & Nadelhoffer, 1989), NPP, soil respiration (RH). For the 37 sites examined, RH 5 mean annual temperature, and mean annual precipita- 2 253.49 1 0.61 Detritus, R 5 0.56, Po0.001. Inset graph shows tion (Raich & Schlesinger, 1992). In addition, total model residuals. ecosystem respiration and gross primary production are correlated (Landsberg & Gower, 1997; Waring et al., (Landsberg & Gower, 1997). This idea is also testable 1998; Janssens et al., 2001). using these data. There was a significant and positive At smaller scales, many studies and reviews have relationship between total detritus input (assumed to explored the coupling of photosynthate supply and be equal to fine root NPP plus aboveground litterfall) root respiration (Szaniawski & Kielkiewicz, 1982; van and RH (Fig. 4). This is consistent with the global der Warf et al., 1994; Sprugel et al., 1995; Lambers et al., relationship between RS and aboveground litterfall 1996; Heilmeier et al., 1997; Lambers et al., 1998; Reich (Raich & Nadelhoffer, 1989), and assumes that annual et al., 1998; Ekbald & Ho¨gberg, 2001), generally con- soil C changes are small compared with the annual C cluding that a strong correlation exists between the two, fluxes into and out of the soil. Compared with the tight because of the links between tissue chemistry and coupling of photosynthesis and RA, there will be a metabolism, plant potential and relative growth rate, greater time lag between C fixation in photosynthesis and stand dynamics. Many other biotic and abiotic and release in decomposition via RS. Schimel et al. factors affect root respiration, including temperature, (1994) and Janssens et al. (2001) discussed these issues nutrient supply, and water (Amthor, 1994; Sprugel et al., in the context of European forests. 1995), but the availability of photosynthate C remains We conclude that there are a priori reasons to suspect the primary and fundamental limitation (Lambers et al., a global correlation between forest RA and RH, although 1998; Singh et al., 2003). The link between production any perturbation or aberration in climate (Braswell and RA is testable in these data: in the subset of studies et al., 1997) may cause short-term departures from the (N 5 17) that reported above- and belowground NPP, general relationship. After disturbance, forest ecosys-

RA was not related to aboveground (P 5 0.986), below- tems will have lower RC, due to a drop in RA and ground (P 5 0.803), or total (P 5 0.085) NPP. A number environmental changes – for example, rising tempera- of factors could account for this poor NPP–RA relation- ture and soil moisture (O’Neill et al., 2002) – in the soil ship. NPP is inﬂuenced by numerous abiotic factors, substrate that raise RH. In contrast, high medium- and and can exhibit large year-to-year variation (Fang et al., long-term RS must be sustained by increased produc- 2001; Knapp & Smith, 2001). There are also difﬁculties tivity (Janssens et al., 2001). This productivity feeds into and variability associated with NPP measurement RA (directly) and RH (indirectly), providing a strong methods (Clark et al., 2001). conceptual basis for the RA RS and RH RS relation- Soil RH is also linked to photosynthate supply and ships presented here. NPP. Soil microorganisms are often considered C-limited, and NPP and microbial biomass C have been Effect of other variables on R , R , and R shown to be related on large scales (Zak et al., 1994). S A H

The largest RH source is from the decay of young Studies in warmer climates had higher RC (F1, 51 5 organic matter (Melillo et al., 1982; Parton et al., 1987; 26.94, Po0.001; data not shown), but mean annual Bowden et al., 1993; Schimel et al., 1994; Gaudinski et al., temperature was not significant in the RA RS or 2000) (i.e., new above- and belowground litter inputs RH RS relationships. This is consistent with recent into the soil that are linked to photosynthate supply), studies suggesting that other factors – seasonality, photo- since fine litter comprises a significant fraction of NPP synthesis, and belowground allocation patterns – may r 2004 Blackwell Publishing Ltd, Global Change Biology, 10, 1756–1766 中国科技论文在线 http://www.paper.edu.cn

1762 B. BOND-LAMBERTY et al. be as important as soil temperature in controlling RA (Fitter et al., 1998; Rey et al., 2002; Singh et al., 2003). Thus we agree with the conclusion of Singh et al. (2003) that while soil respiration may be modelled at a single site using soil temperature, general or larger-scale models should incorporate aboveground photosynthesis and plant allocation patterns.

Measurement method was not signiﬁcant (F4, 46 5 2.16; P 5 0.088) in the relationships shown in Figs 1 and 2. Based on the data in Fig. 2, we note that (i) isotope studies report relatively low RC values; and (ii) the results of root exclusion studies (primarily trenched plots) are not signiﬁcantly different from studies based Fig. 5 Relationship between autotrophic (RA) and heterotrophic (R ) soil respiration for published studies in agriculture, on other measurement methods, despite the frequent H forest, prairie, and tundra systems. criticism of the disturbance effects associated with this method. The single study (Ho¨gberg et al., 2001) that manipulated root photosynthate supply by tree gird- selected using the same criteria as described above.) ling, a new technique, reported a relatively high RC. The high-disturbance agriculture systems exhibit high

This variety of measurement methods reduces concerns RH relative to RA, as would be expected given the low about autocorrelation of the underlying data, and the biomass and short duration of agricultural root systems validity of the resulting models. (Raich & Tufekcioglu, 2000). Prairie studies appear no different than forest studies, while the two tundra

studies (both at Barrow, Alaska) have high RA relative Limitations of the RA RS and RH RS models to RH; it would be unsurprising if plant roots supply a We emphasize that the relationships shown in Figs 1 high percentage of RS in such undeveloped, nutrient- and 2 may not provide accurate estimates of the RS poor soils (Nakatsubo et al., 1998). Finally, we note the partitioning between RH and RA in a specific location, increased variability of the data in Fig. 5. This is due to particularly for aggrading or recently disturbed forests; the measurement issue discussed above – the fact that their use in this way is strongly discouraged. For no study measures RA and RH independently increases example, extremely large RH fluxes (the ‘carbon flush’) the variability of the ‘computed’ flux relative to the have been measured in newly clearcut stands (Gordon, measured one (see Appendix). Future studies that

1987; Toland & Zak, 1994) that far exceed these models’ independently measure each component flux of RS will estimates. Even in stable forests, a variety of biotic and help quantify and constrain this source of variability. abiotic factors can affect respiration, particularly over the relatively short time period of measurement; the Conclusion resulting variability means that at low RS values, the confidence limits on RA and RH span the entire RS range The excellent fits and homoscedastic residual distribu- (Figs 1 and 2). Site-specific measurements are always tions of these models suggest that they have broad more desirable than the application of broad relation- applicability, at least in conditions encountered in the ships inferred across stands, ecosystems, and biomes data used in this study: forest systems that have not (Gower et al., 1996). But such measurements are not al- experienced recent disturbance. In such systems, the ways possible, while annual RS is straightforward to esti- relationships in Figs 1 and 2 will help constrain mate using chamber and/or eddy covariance techniques. terrestrial carbon budgets, in particular estimates of Do the relationships presented here hold for non- total root carbon allocation and net ecosystem produc- forested ecosystems? The fundamental constraint of tion. These RH RS and RA RS relationships may photosynthate supply remains the same. Figure 5 need adjusting as more data become available. In contrasts the relationship between RA and RH for the particular, few studies have quantified RC in poorly forest studies cited above with studies in agriculture drained ecosystems (Silvola et al., 1996), and there is a

(Monteith et al., 1964; Singh & Shekhar, 1986; Buya- clear need for more tropical (or other high RS) data – novsky et al., 1987; Paustian et al., 1990; Koizumi et al., the few values published (Trumbore et al., 1995; 1993), prairie (Kucera & Kirkham, 1971; Herman, 1977; Lamade et al., 1996; Malhi et al., 1999; Kutsch et al., 2 1 Buyanovsky et al., 1987; Hungate et al., 1997), and 2001) for very high (RS41500 g C m yr ) flux rates tundra (Billings et al., 1978; Chapin et al., 1980; are variable, and influential in the models presented Nakatsubo et al., 1998) ecosystems. (These studies were here. Such data will be essential to refine and test these

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1766 B. BOND-LAMBERTY et al. most studies RA and RH do not have independent To examine how the correlation between RS and one variances resulting from measurement, and raises the of its subcomponents changes if the two subcomponents problem of how much of the correlation between RS are themselves correlated, we distinguish two cases: and its subcomponents is due to this subtraction, and how much due to correlation between RA and RH Case 1: r 5 0. For simplicity, assume sA 5 sH 5 s. themselves. Here we examine the correlation between Then, using Eqn (A2),

RS and RH (proof is identical for RA); in the following s s s qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisH ffiffiffiffiffiffiffis 1ffiffiffi A, H, and S denote the standard deviation of RA, RH, CorrðRS; RHÞ¼ ¼ p ¼ p ; 2 2 2s2 2 and RS, respectively. sA þ sH

First note that i.e., even if there is no correlation between RA and RH, RS ¼ RA þ RH; RS and RH will be correlated.

CovðRS; RHÞ¼CovðRA þ RH; RHÞ¼VarðRHÞ Case 2: r 6¼ 0. Again assume sA 5 sH 5 s.

þ CovðRA; RHÞ: ðA1Þ pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis þ rs psffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1 þ rÞ 1 þffiffiffi r CorrðRS; RHÞ¼ ¼ ¼ p The correlation between RS and RH can be written as 2s2 þ 2rs2 2s2ð1 þ rÞ 2 CorrðRS; RHÞ

Thus any positive correlation between RA and RH CovðRS; RHÞ ¼ from the definition of correlation will increase the correlation between RS and its sSsH subcomponents. In the data set used in this paper, 2 s þ CovðRA; RHÞ 5 5 ¼ H by substitution of Eqn ðA1Þ r 0.55 and thus in theory Corr(RS, RH) Corr(RS, s s S H RA) 5 0.88 (in practice the values are 0.94 and 0.81, as s CorrðR ; R Þs s sA4sH for these data). ¼ H þ A H A H sS sSsH sH rsA sHqþffiffiffiffiffirsA ¼ þ ¼ where r ¼ CorrðRA; RHÞ sS sS 2 sS s þ rs ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiH A : ðA2Þ 2 2 sA þ sH þ 2rsAsH

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