Testing sagebrush allometric relationships across three fire chronosequences in Wyoming, USA

ARTICLE IN PRESS Journal of Arid Environments Journal of Arid Environments 72 (2008) 285–301 www.elsevier.com/locate/jaridenv

Testing sagebrush allometric relationships across three fire chronosequences in Wyoming, USA M.B. Clearya,, E. Pendalla,b, B.E. Ewersa,b a

Department of Botany, University of Wyoming, 1000 E. University Ave. Dept. 3165, Laramie, WY 82071, USA b Program in Ecology, University of Wyoming, USA Received 20 November 2006; received in revised form 23 July 2007; accepted 23 July 2007 Available online 4 September 2007

Abstract Aboveground and coarse root allometric relationships were tested across three mountain big sagebrush (Artemisia tridentata var. vaseyana (Rydb.) chronosequences at three stages of recovery from fire (establishment, expansion, and mature) in Wyoming, USA. Big sagebrush shrubs dominate North American rangelands and are critical components of habitat for threatened species such as sage grouse. There were no differences in regression relationships estimating biomass over space and time, which reduces the need to destructively sample sagebrush for local studies and supports regional carbon modeling and biomass estimates. Crown volume (CV) explained the most variability (R240.75) in aboveground biomass, and crown area (CA) explained the most variability for coarse roots (R240.87). Analyses supported both the 14 and 23 power universal scaling rules between leaf and stem biomass, but did not support global models of seed plant reproductive part biomass. This study provides compelling evidence that simple field measurements may be used to estimate biomass over large regions and that universal scaling rules are valid for semiarid shrubs. r 2007 Elsevier Ltd. All rights reserved. Keywords: Aboveground biomass; Artemisia tridentate; Plant allometry; Root biomass; Universal scaling

1. Introduction Applied allometric biomass estimates are integral for parameterizing models that improve predictive understanding of energy and nutrient flows and determine how ecosystems influence global carbon cycling (Na´var et al., 2002; Whittaker and Woodwell, 1968). Biomass estimates are also useful for making informed land management decisions including assessment of fuel loads (Perryman and Olson, 2000; Wambolt et al., 2001), forage quantity and quality (Murray and Jacobson, 1982; Rittenhouse and Sneva, 1977), habitat for threatened species (Frisina and Wambolt, 2004), shrub invasion (Lett et al., 2004), and growth of competitive shrub species (Vora, 1988). Coarse root allometric relationships are rare and especially important for improving estimates of ecosystem carbon pools. Biomass measurements are also useful for comparing individual species to global, theoretical allometric relationships to test the limits of universal scaling theory in Corresponding author. Tel.: +1 307 742 2003; fax: +1 307 766 2851.

E-mail addresses: [email protected] (M.B. Cleary), [email protected] (E. Pendall), [email protected] (B.E. Ewers). 0140-1963/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaridenv.2007.07.013

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ecology (Robinson, 2004) and to address inherent variability in data resulting in the lack of statistical difference between the 14 and 23 power scaling rules (Banavar et al., 2002). Applied allometry is useful for estimating standing biomass from relatively simple measurements at local scales. It reduces the need for destructive sampling at each local site if the relationships are consistent across large spatial scales. Most applied allometric equations for estimating aboveground biomass of shrubs use crown volume in single- or multiple-variable analyses (Huenneke et al., 2001; Murray and Jacobson, 1982; Uresk et al., 1977; Vora, 1988). Theoretical allometric relationships like the 14 and 23 power models explain resource allocation from cellular to ecosystem scales (Enquist et al., 2003; Martı´ nez and Lo´pez-Portillo, 2003; Zens and Webb, 2002). The 14 power model is based on metabolic constraints of cell size and the fractal nature of biological metabolic pathways (Enquist and West, 1999; West et al., 2001). The 23 scaling rule is based on the Euclidean surface area rule (Heusner, 1982; West and Brown, 2005). Big sagebrush dominates up to 1.1  106 km2 of North American rangelands (Beetle, 1960; Frisina and Wambolt, 2004; Perryman and Olson, 2000). It is an aromatic shrub with persistent as well as ephemeral spring leaves and does not resprout after fire disturbance (Beetle, 1960; Knight, 1994). It has medicinal uses (Moore, 1989), an important cover for threatened species including sage grouse, black-tailed prairie dogs, and pygmy rabbits (Frisina and Wambolt, 2004; Knight, 1994; Wambolt et al., 2001), used as winter forage by several ungulate species (Knight, 1994), and sometimes considered a hindrance to domestic livestock grazing (Frisina and Wambolt, 2004; Knight, 1994). Sagebrush ecosystems that burn may be threatened by the invasion of the annual grass Bromus tectorum (cheat grass) that increases fire frequency and disrupts recovery from fire (Baker, 2006). Time-since-fire chronosequences are useful for studying big sagebrush (Artemisia tridentata Nutt.) shrubs through their lifespans because fire is a disturbance initiating secondary succession of shrublands (Perryman and Olson, 2000; Wright and Bailey, 1982) and because it provides a baseline to monitor changes due to altered fire regimes. Because there are good fire records, replicated chronosequences of big sagebrush within the same region can be found and used to test the validity of big sagebrush allometry over space and time (Yanai et al., 2000). Past work describing allometric relationships for estimating big sagebrush biomass (Harniss and Murray, 1976; Rittenhouse and Sneva, 1977; Uresk et al., 1977; Vora, 1988) has not considered roots or explicitly tested for changes by region, life stages, or size. In addition, there are no publications to our knowledge comparing big sagebrush to universal scaling models. This study used chronosequences to describe three growth stages (establishment, expansion, and mature) of mountain big sagebrush (A. tridentata var. vaseyana (Rydb.)) growth at three locations in Wyoming, USA to: 1. determine if applied allometric relationships change between growth stages and across space, 2. compare global 14 and 23 power universal scaling rules to allometric measurements, and 3. estimate changes in standing biomass per ground area between growth stages.

2. Methods 2.1. Chronosequence selection and site descriptions Three mountain big sagebrush chronosequences were selected in Wyoming, USA, and called the Ed Young (ED), Glades (GL), and Sierra Madre (SM) locations (Ewers and Pendall, 2007). To select locations, state factors described by Jenny (1941) were used and included time, plant composition, climate, relief, and parent material. All possible ages (years since burn; ysb) were included to provide 2 or 3 ages at each location. The ages were grouped into three stages of post-fire growth: establishment (3–4 ysb), expansion (18–27 ysb), and mature (37–60 ysb). Dominance of the mountain (vaseyana) variety of big sagebrush was verified using methods described by Frisina and Wambolt (2004), and other plant constituents of the sagebrush systems were similar across the locations (Ewers and Pendall, 2007). Cheat grass was not present at any of the locations. For all locations, mean annual temperature was 6.2–7.2 1C and mean annual precipitation was 259–341 mm, 50% of which occurred in April, May, and June (Ewers and Pendall, 2007). Climate was assumed to be

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relatively constant across the growth stages because sagebrush shrubs have relatively short lifespans (30–60 year fire interval, Harniss and Murray, 1973). To minimize differences in soil, all locations were in the flattest areas (o1% slope, Ewers and Pendall, 2007). 2.2. Predictor and response variables for estimating biomass Allometric equations were tested by destructively harvesting a total of 37 sagebrush shrubs from the three locations. For each growth stage (establishment, expansion, and mature) at each location (ED, GL, and SM) at least one small, one medium, and one large plant was harvested. The GL location’s establishment stage had few shrubs, so only small and medium plants were collected. At the SM location live coarse roots to 0.25 m deep for 3 shrubs each were excavated from the expansion and mature stages (6 shrubs total). Prior to harvest, sagebrush canopy (length, width, and height) and stem (length and width) dimensions were measured to calculate three predictor values: stem basal area (BA), crown area (CA), and crown volume (CV, Table 1). Elliptical area ¼ pab (Eq. (1)) was used to calculate crown area, and ellipsoid volume ¼ 43pab (Eq. (2)) was used to calculate crown volume, where a and b are radii. Elliptical formulae best approximates the shape of mountain big sagebrush and provides the most flexibility for multiple canopy dimensions (Vora, 1988). The two widest stem and canopy widths perpendicular to each other and parallel to the ground were measured and used to calculate BA and CA, respectively, using Eq. (1) (Rittenhouse and Sneva, 1977; Vora, 1988). For multistem shrubs, stem BA for each stem were summed to calculate total BA. The CA width measurements with height measured perpendicular to the ground at the highest foliage were used to calculate CV using Eq. (2) (Murray and Jacobson, 1982). Aboveground biomass was separated into five response variables: leaves, inflorescences (including raceme stems), new stem growth (annual apical extension not including radial increment of woody biomass), wood o1 cm diameter, and wood 41 cm diameter (Table 1). Biomass was dried to constant mass for 48 h at 60 1C before weighing. Leaves, inflorescences, and stems in the bottom of bags in which we transported the plants from the field to the laboratory were quantitatively subsampled. Coarse roots (42 mm diameter) were separated from soil using a 2 mm sieve. Material remaining on the sieve was floated in water to wash soil from the roots and dried at 60 1C for 48 h. Once dry, live roots were picked out and separated into diameter size classes: 2–5 mm, 45–10 mm, and 410 mm (Table 1). Root samples were ground to pass a fine mesh and placed in a muffle furnace at 550 1C for 8 h to calculate ash-corrected weights (Cronan, 2003).

Table 1 Four predictor variables and 10 response variables for 3 growth stages (establishment, expansion, and mature), at 3 chronosequence locations (ED, GL, and SM), and for all growth stages and locations combined were used to determine mountain big sagebrush biomass allometric relationships Predictor variables (X)

Response variables (Y)

CV ¼ crown volume (m3) CA ¼ crown area (m2) BA ¼ basal area (cm2) CVBA ¼ crown volumebasal area

Aboveground shrub biomass (g) Total Leaves Inflorescences New stem growth Wood o1 cm diameter Wood 41 cm diameter Belowground coarse roots (g) (Sierra Madre only) Total 2–5 mm diameter 45–10 mm diameter 410 mm diameter

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2.3. Allometric relationships for estimating biomass Sigma Plot 9.01 (Systat, 2004) was used to plot all 400+ combinations of predictor and response variables using both direct power functions, y ¼ bxa (Eq. (3); Gayon, 2000; Huxley, 1936; Perryman and Olson, 2000), and natural log (ln) transformed linear fits, ln(y) ¼ a ln(x)+b (Eq. (2), Vacher, 1999), for each growth stage and location, and all growth stages and locations combined (Table 1). Statistical reports in Sigma Plot provided regression slope (a) and intercept (b) parameters with their standard errors (SE), adjusted coefficient of variation (adj. R2), standard error of the estimate (SEE), and residuals for the regressions. Residuals were plotted and ranked either hetero- or homoskedastic. Regressions that had the best fit for estimating biomass were determined using four steps to streamline the process: Step 1: Regressed all possible combinations of: 4 predictors, 10 responses, 3 growth stages, 3 locations, all growth stages and locations combined, and 2 types of fits (Table 1). Step 2a: Discarded regressions with adj. R2p0.75 or heteroskedastic residuals. Step 2b: For the remaining ln-linear regression equations, a correction factor (CF) was calculated using the method described by Sprugel (1983), where CF ¼ exp (SEE2/2) (Eq. (5)). The CF was applied after estimates were backtransformed to correct for logarithmic transformation errors (Beauchamp and Olson, 1973; BondLamberty et al., 2002; Northup et al., 2005). Step 3: Determined the most robust fit (power or ln-linear) and predictor (BA, CA, CV, or CV*BA) combination for all growth stages and locations combined, each growth stage, and each location. The choice was based on adj. R2, degree of homoskedasticity of residual plots, and standard estimate of the error (SEE). Step 4: Determined significant differences between the chosen fit/predictor combinations for each growth stage, location, and all the growth stages and locations combined equations. To compare both a and b parameters simultaneously ANOVA analysis could not be used because regression equations were not replicates. Instead, equations with 95% confidence intervals (C.I.) were plotted and considered not significantly different if the 95% C.I. overlapped. 2.4. Global allometric relationships Sagebrush component biomass was compared to that described for other species globally by creating a subset of data including mass of leaves (ML), mass of stems (MS ¼ new stem growth+wood o1 cm+wood 41 cm), and mass of inflorescences (MI). Globally, leaf mass scales as the 34 power of stem or root mass (Enquist and Niklas, 2002; Enquist et al., 2003) and reproductive parts scale to the 0.657 power of stems and to the 0.861 power of leaves in seed plants (Niklas and Enquist, 2003). Sagebrush data was transformed using log10 and reduced major axis (RMA) regressions were used to normalize unequal variance in the data and for consistency when comparing to Enquist and Niklas (2002) and Niklas and Enquist (2003). PAST software (Hammer et al., 2001) was used to compare MS vs. ML, MS vs. MI, and ML vs. MI. Sagebrush and global relationships were not different when the global relationship was within the 95% CI of the sagebrush relationship. Biomass plant1 of the response variable (ML or MI) was estimated using aRMA values of the sagebrush and global relationships separately as a second test of significance. 2.5. Applied allometric biomass estimates Shrub total biomass and biomass for each component were estimated on an areal basis at the SM location in 2004. This site was used because additional, concurrent studies of ecosystem carbon and water fluxes were being conducted. For each growth stage all live sagebrush shrubs growing in 12 circular plots (13 m2 diameter) were measured. Plots were randomly located at least 5 m apart. CV was determined using the same method as for measuring the predictor variables, except canopy pieces were measured separately when there was a X30 cm gap between areas of foliage (Rittenhouse and Sneva, 1977). The calculated CA or CV values were used in the allometric equations to estimate total and component biomasses. Biomass estimates were summed for each plot and then divided by plot area to calculate areal biomass. We estimated upper and lower bounds by adding and subtracting the standard errors of a and b, respectively.

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2.6. Data analysis and statistical methods General linearized models (GLM) with Tukey’s comparisons were used to test for differences between growth stages and locations for predictor variables, response variables, and biomass estimates. Levene’s test was used to determine equality of variance prior to using the GLM. When a dataset did not pass Levene’s test the data was natural log transformed and tested again, and if transformed data did not pass the analysis was terminated. Student’s t-test (p40.05) was used to test for differences between sagebrush and global biomass estimates (Minitab, 2004). 3. Results 3.1. Changes in predictor and response variables between growth stages Mountain big sagebrush shrub dimensions (BA, CA, and CV) and aboveground biomass were largest at the GL location and tended to increase between growth stages (Table 2). Crown dimensions at the SM location, however, decreased between the expansion and mature stages. Proportions of ephemeral (leaves, new stem Table 2 Means (with standard errors) for three predictor and ten response variables measured for three mountain big sagebrush fire chronosequences. Predictor variables were calculated using elliptical formulas (Eqs. (1) and (2)1,2). Coarse roots were collected to 25 cm soil depth at the SM location only Chronosequence locations

Growth stage n Predictor variables Basal area (cm2 plant–1) Crown area (m2 plant–1) Crown volume (m3 plant–1)

Ed Young (ED)

Glades (GL)

Sierra Madre (SM)

Expansion Mature

Establishment Expansion Mature

Establishment Expansion

3 14.0 (4.45) 0.382 (0.161) 0.187 (0.097)

3 34.6 (18.8) 0.476 (0.201) 0.220 (0.117)

2

3

3.23 (2.71) 0.075 (0.063) 0.035 (0.031)

3

41.8 (22.1) 1.08 (0.736) 0.845 (0.639)

3

9 9.27a (5.17) 0.579 (0.290) 0.275 (0.145)

81.4 0.24 (38.9) (0.109) 1.46 0.008 (0.453) (0.006) 1.28 0.001 (0.468) (0.001)

Aboveground response variables (g plant–1) Total 518.7 825.3 (259.2) (530.1) Leaves 66.8 61.0 (23.7) (29.4) Inflorescences 63.2 16.4 (35.4) (8.62) New stem 21 8.5 Growth (11) (0.5) Wood o1 cm diameter 250.8 314.0 (118.0) (183.9) Wood 41 cm diameter 116.5 425.4 (74.06) (311.0)

111.6 (94.09) 19.7 (12.5) 37.3 (35.7) 7.4 (4.8) 40.50 (34.37) 6.800 (6.800)

2522 (1554) 282 (194) 410 (210) 79 (40) 808.2 (493.4) 943.7 (625.3)

6092 (2232) 188 (109) 382 (167) 27 (9.8) 2605 (1143) 2890 (1273)

5 (3.678) 2.50 (1.89) 0 0 1.2 (1.0) 1.200 (0.8511) 0.0000 (0.0000)

Belowground response variables (g plant–1)a Total nc nc 2–5 mm diameter nc nc 45–10 mm diameter nc nc 410 mm diameter nc nc R:S nc nc

nc nc nc nc nc

nc nc nc nc nc

nc nc nc nc nc

nc nc nc nc nc

527.1 (172.1) 73.6 (22.9) 50.4 (20.8) 24 (8.6) 248.4 (84.08) 130.6 (52.45)

Note: m is the meters, n the sample number, nc the not collected, R:S the coarse root to woody shoot ratio. a Basal area n ¼ 6, expansion stage n ¼ 3, and mature stage n ¼ 5.

62.9 (44.5) 4.6 (1.8) 5.4 (4.2) 52.9 (46.1) 0.32 (0.17)

Mature 11 14.3a (6.48) 0.343 (0.120) 0.160 (0.063) 748.3 (322.1) 45.5 (18.3) 13.9 (7.26) 10 (3.7) 289.2 (107.2) 389.6 (192.2) 31.0 (21.3) 7.0 (4.5) 7.7 (4.0) 16.4 (13.0) 0.32 (0.07)

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a

Cb

% Ephemeral % Total Wood 80 % Biomass Plant -1

b

Aboveground Biomass

Aa

Coarse Root Biomass Diameter Classes %2-5 mm %>5-10 mm %>10 mm

Bb

60 Ba Ab

40

20

Ca na hm

ent

lis tab

Es

sion

n

a Exp

Ma

t

ure

ent

hm

lis tab

Es Growth Stages

on

nsi

a Exp

e

tur

Ma

Fig. 1. Proportions of (a) total aboveground biomass in ephemeral parts or wood and (b) total coarse root biomass in three root size classes of mountain big sagebrush. Error bars are standard errors and sample sizes are in Table 2. Letters indicate significant differences (po0.05); small letters compare ephemeral to wood within growth stage and capital letters compare ephemeral or wood between growth stages. Roots were not significantly different.

growth, and inflorescences) and total wood (o1 cm and 41 cm diameter) biomass to total biomass were different at all growth stages (po0.002), and changed between growth stages regardless of location (po0.002; Fig. 1). Proportion of ephemeral components to total ephemeral biomass did not change between growth stages; leaf biomass was 5774% (p ¼ 0.214), inflorescence biomass was 2574% (p ¼ 0.224), and new stem growth was 1772% (p ¼ 0.386). The proportion of o1 cm diameter wood to total wood remained constant between growth stages (3975%; p40.055). At the SM location, the only one where roots were collected, the coarse root: woody shoot ratios remained constant (0.3270.17; p ¼ 0.669). Coarse roots in the 2–5 and 45–10 mm size classes increased by 30–35% and 410 mm diameter root biomass decreased (50%) between the expansion and mature stages, but none of the changes were significant (p ¼ 0.703, 0.721, and 0.371, respectively). 3.2. Applied allometric equations Allometric equations for aboveground biomass did not differ by growth stage, location, or combined growth stages and location (within 95% C.I.; Fig. 2; Table 3). The one exception was wood 41 cm diameter in the expansion stage that was overestimated (outside the 95% C.I.) by the combined equation. Inflorescences and new stem growth were the only aboveground response variables not having relationships for all of the fit/ predictor combinations tested. Log-transformed CV using a linear fit explained the most variability for total aboveground, leaf, new stem growth, and wood o1 cm diameter biomass. The non-transformed interaction CVBA using a direct power function explained the most variability for inflorescence and wood 41 cm diameter biomass. All aboveground component equations are provided in Appendix A. Total root biomass and roots 410 mm diameter had significant relationships in expansion and mature growth stages (Table 3). However, roots 2–5 mm and 45–10 mm diameter were only correlated to prediction variables for the mature stage and these two classes were not used in further analyses (Appendix B). Allometric regression equations of total and 410 mm diameter roots did not differ (within 95% C.I.) by growth stage, location, or combined growth stage and location. Non-transformed CA using a direct power fit explained the most variability for total coarse roots and coarse roots 410 mm diameter. All belowground component equations are provided in Appendix B.

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Locations

ln Total Aboveground Biomass (g)

8

291

Growth Stages

a

b

c

d

6 4 2 0 6

ln Leaf Biomass (g)

4

2 ED GL SM 95% C.I. All Locations

0

-10

-8

-6

-4

-2

0

Establishment Expansion Mature 95% C.I. All Stages 10-

8-

6-

4-

-2

0

ln Crown Volume (m3) Fig. 2. Examples of allometric relationships between ln crown volume (ln CV) vs. ln total aboveground biomass (a) and (b) or vs. ln leaf biomass (c) and (d) demonstrating the methodology used to determine significant difference between regression equations. Sample sizes are listed in Table 2.

Table 3 Regression equations using all growth stages and locations combined

Total Aboveground Leaves Inflorescences New stem growth Wood o1 cm Wood 41 cma Total Belowground Roots 410 mm

d.f.

Fit

Predictor

a (SE)

36 36 36 36 36 36 7 7

L L P L L P P P

CV CV CVBA CV CV CVBA CA CA

0.8539 0.6144 0.5611 0.5679 0.9192 0.6271 0.6080 0.9754

(0.0414) (0.0399) (0.0786) (0.0525) (0.0504) (0.0504) (0.1469) (0.1583)

b (SE)

SEE

CF

adj. R2

7.889 (0.1611) 5.129 (0.1552) 30.81 (12.60) 3.668 (0.2046) 7.174 (0.1961) 127.6 (34.12) 83.34 (11.68) 53.45 (8.181)

0.6533 0.6294 94.17 0.8295 0.7952 307.6 20.42 11.46

1.238 1.502 na 1.502 1.372 na na na

0.92 0.87 0.77 0.76 0.90 0.92 0.87 0.95

a The expansion stage equation was significantly different from all the growth stages and locations combined equation. Parameters for the expansion stage were: a(SE) ¼ 0.6108 (0.0469), b(SE) ¼ 91.87 (21.46), SEE ¼ 96.69, R2 adj. ¼ 0.97, po0.0001.Note: d.f. is the degrees of freedom, L the ln-linear function (Eq. (4)), P the power function (Eq. (3)), CV the ellipsoidal crown volume (Eq. (2)), CA the elliptical crown area (Eq. (1)), BA the elliptical basal area (Eq. (1)), a the slope parameter, b the intercept parameter, SE the standard error, SEE the standard error of the estimate, CF the correction factor (Eq. (5)), adj. R2 the adjusted coefficient of determination, na the not applicable.

3.3. Global relationships The observed sagebrush aRMA value equaled 23 power and was not different (within 95% C.I. and biomass estimates not different, p ¼ 0.881) from the 34 power global relationship describing mass of stems (MS) vs. mass of leaves (ML; Fig. 3). Although steeper, the observed sagebrush aRMA value was not different (within 95% C.I. and biomass estimates not different) than the global value describing mass of stems (MS) vs. mass of

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Global:

αRMA = 0.750

kg leaves plant-1 = 0.078 (0.018) Sagebrush:

αRMA = 0.673(0.041),

βRMA = -1.01(0.057), r2 = 0.93, p < 0.000 kg leaves plant-1 = 0.075 (0.016)

log10 Leaf Biomass (ML)

0

-1

-2

-3

Sagebrush Global Sagebrush 95% C.I.

-3

-2 -1 log10 Stem Biomass (MS)

Fig. 3. Log10-mass of stems (MS) vs. log10-mass of leaves (ML) of sagebrush compared with global (Enquist and Niklas, 2002). Leaf biomass estimates from sagebrush and global regression parameters were not different (p ¼ 0.881, n ¼ 37). Standard errors are in parentheses.

inflorescences (MI; Fig. 4a). The observed sagebrush aRMA value was different (outside 95% C.I. and biomass estimates different) than the global value describing mass of leaves (ML) vs. mass of inflorescences (MI) using all growth stages and locations combined (Fig. 4b). When each growth stage and location was regressed separately for ML vs. MI, the global lines fell within the 95% C.I. of the observed lines and the biomass estimates were not different for the establishment stage (p ¼ 0.330), expansion stage (p ¼ 0.073), or GL location (p ¼ 0.446). 3.4. Biomass estimates, shrub size and density at Sierra Madre Big sagebrush size, density, and standing biomass estimates (g m2) increased, and ranges of biomass estimates did not overlap between growth stages (Fig. 5; Table 4). Proportions of estimated ephemeral (leaves, new stem growth, and inflorescences) and total wood (o1 cm and 41 cm diameter) biomass to total estimated biomass on an areal basis (g m2) were different from each other at all growth stages (po0.01; Fig. 6). Ephemeral parts comprised a higher proportion of total biomass (p ¼ 0.01) at the establishment stage. Proportions of ephemeral and woody biomass were not different between expansion and mature stages (p ¼ 0.498). Proportion of leaves to total ephemeral biomass did not change between growth stages (p40.06) and mean percentage of leaves was 7371%. Proportion of new stem growth was higher at the establishment stage (2671%) than at the expansion (2072%, p ¼ 0.007) and mature (2070.0%, p ¼ 0.003) stages. Inflorescence proportions were lowest at the establishment stage (0.270.0%) and highest at the expansion stage (9.773%), but we did not test significance because Levene’s test for equal variance was not passed even after transforming the data. The proportion of o1 cm diameter wood to total wood was higher at the establishment stage (7372%) than at the expansion (6273%, p ¼ 0.004) and mature (6071%, p ¼ 0.0003)

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Global: αRMA = 0.861

kg inflorescences plant-1 = 0.069 (0.013) Sagebrush: αRMA = 1.53(0.201),

kg inflorescences plant-1 = 1.41 (0.288) Sagebrush: αRMA = 2.17(0.250),

293

βRMA = -1.03(0.333), r2 = 0.78, p < 0.000

βRMA = -1.14(0.155), r2 = 0.71, p < 0.013 kg inflorescences plant-1 = 0.182 (0.077)

kg inflorescences plant-1 = 0.261 (0.159)

b

a log10 Inflorescence Biomass (MI)

0

-1

-2

-3 Sagebrush Global Sagebrush 95% C.I.

-4

-2

-1 0 log10 Stem Biomass (MS)

1

-2.0

1.5-1.0 -0.5 log10 Leaf Biomass (ML)

0.0

Fig. 4. Sagebrush and global (Niklas and Enquist, 2003) relationships comparing log10-mass of inflorescence (MI) vs. (a) log10-mass of stem (MS) and (b) log10-mass of leaves (ML). MI sagebrush and global estimates were not different (p ¼ 0.160) when related to MS, but were different when related to ML (p ¼ 0.001). Standard errors are in parentheses and sample size was 29.

Leaves

700

Inflorescences New Stem Growth Wood <1 cm Wood >1 cm Total Aboveground Total Coarse Roots

600

Estimated Biomass (gm-2)

500

400

300

200

100

0 0

10 20 30 Growth Stage (Years Since Burn)

40

Fig. 5. Estimated mountain big sagebrush biomass (g m2) at four growth stages at the SM location using regression equations listed in Table 3 and calculated for Table 4. Error bars are standard errors.

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Table 4 Mountain big sagebrush (a) mean shrub size and density, and (b) biomass estimates (g m2 of dry mass) using measurements from the SM location YSB in 2004

n

Size (SE) m3

N

Density (SE) shrubs ha1

(a) Mean size and density 1

3

12

192.0 (100.3)

5 19 38

10 141 591

3.613  105 (2.178  105) 0.0056 (0.0101) 0.0339 (0.0035) 0.0377 (0.0035)

12 12 12

640.0 (228.3) 9024 (2498) 38,820 (3129)

YSB in 2004

Estimate (SE)

Lower bound (SE) (a-SE and b-SE)

Upper bound (SE) (a+SE and b+SE)

Absolute range (g m2)

0.0124 (0.0085) 2.025 (1.650) 110.1 (31.34) 617.9 (64.16)

0.0075 (0.0022) 2.028 (0.5855) 134.9 (38.93) 697.2 (201.3)

0.0053–0.0209 0.3756–2.614 78.76–173.8 553.7–898.5

0.0082 (0.0051) 0.4244 (0.3012) 13.92 (3.807) 94.91 (7.047)

0.0105 (0.0065) 0.4376 (0.3000) 12.92 (3.526) 91.36 (6.288)

0.0064 (0.0018) 0.4140 (0.1195) 15.07 (4.351) 98.94 (28.56)

0.0046–0.0170 0.2945–0.7376 9.391–19.42 85.07–127.5

0.0000 (0.0000) 0.0075 (0.0073) 3.244 (1.405) 8.699 (2.816)

0.0000 (0.0000) 0.0162 (0.0156) 3.208 (1.176) 10.84 (2.340)

0.0000 (0.0000) 0.0033 (0.0010) 3.315 (0.9571) 7.649 (2.208)

0.0030 (0.0019) 0.1223 (0.0834) 3.548 (0.9684) 25.24 (1.715)

0.0042 (0.0025) 0.1286 (0.0834) 3.242 (0.8866) 24.13 (1.479)

0.0022 (0.0001) 0.1176 (0.0339) 3.919 (1.131) 26.57 (7.669)

0.0021–0.0067 0.0837–0.212 2.356–5.050 22.65–34.24

Wood o1 cm (g) 1 5 19 38

0.0027 (0.0020) 0.8557 (0.7349) 60.27 (17.85) 304.3 (36.95)

0.0037 (0.0026) 0.8512 (0.7142) 53.08 (15.41) 281.7 (31.83)

0.0020 (0.0006) 0.8646 (0.2496) 68.68 (19.83) 329.9 (95.24)

0.0014–0.0063 0.1370–1.114 37.67–88.51 249.9–425.1

Wood 41 cm (g m2)a 1 5 19 38

0.0008 (0.0006) 0.5119 (0.4580) 46.58 (14.46) 211.6 (29.80)

0.0039 (0.0027) 0.8422 (0.7028) 51.16 (14.80) 274.5 (30.52)

0.0002 (5.153  105) 0.3202 (0.0924) 43.31 (12.50) 168.0 (48.51)

0.0001–0.0066 0.2278–1.545 30.81–19.96 119.5–305.0

Total belowground (g m2) 1 0.0029 (0.0018) 5 0.1436 (0.1014) 19 4.632 (1.266) 38 31.77 (2.331)

0.0110 (0.0065) 0.2532 (0.1554) 5.525 (1.520) 42.87 (2.364)

(b) Biomass estimates Total Aboveground (g m2) 1 0.0097 (0.0067) 5 2.023 (1.685) 19 121.7 (35.14) 38 655.4 (72.43) Leaves (g m2) 1 5 19 38 Inflorescences (g m2)a 1 5 19 38 New stem growth (g m2) 1 5 19 38

0.0007 (0.0002) 0.0864 (0.0249) 4.068 (1.174) 24.19 (6.984)

0.0000 (0.0000) 0.0023–0.0318 2.032–4.272 5.441–13.18

0.0005–0.0175 0.1113–0.4086 2.894–7.045 17.21–45.23

Note: YSB is the years since burn, n the sample size, a the slope parameter, b the intercept parameter, SE the standard error. a BA was not measured at SM, so CV was used with the following parameters: Parameters for inflorescences: a ¼ 196.7(44.11), b ¼ 1.683(0.3263), SEE ¼ 91.67, adj. R2 ¼ 0.74. Parameters for Wood 41 cm diameter: a ¼ 1585(187.6), b ¼ 1.027(0.1690), SEE ¼ 555.3, and adj. R2 ¼ 0.71.

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% Ephemeral % Total Wood

Bb

Bb

80

295

% Estimated Biomass m-2

Aa 60 Ab Ba

40

Ba 20

ent

hm

lis tab

Es

ion

ans

Exp

e

tur

Ma

Growth Stages

Fig. 6. Proportions of estimated ephemeral parts or wood to total aboveground biomass of mountain big sagebrush on an areal basis changed between growth stages. Error bars are standard errors. Sample size for establishment was 9 and for expansion and mature was 12. Letters indicate significant differences (po0.05); small letters compare ephemeral to wood within age class and capital letters compare ephemeral or wood between growth stages.

stages. Coarse root biomass increased (po0.001) and there were no estimates for roots by size classes because there were no combined relationships for 2–5 and 45–10 mm diameter classes. 4. Discussion There were no significant differences among applied allometric relationships across time or space for aboveground and coarse root biomass for mountain big sagebrush. This validates the use of a single regression equation to model mountain big sagebrush biomass and reduces need for future destructive sampling at local sites. The composition of ephemeral and woody parts shifted between growth stages, which validated using the chronosequence method for allometric studies. There were no differences between the local sagebrush and global relationships for mass of stems (MS) vs. mass of leaves (ML), suggesting sagebrush physiology is similar to other plant species. Areal biomass estimates (using CV for aboveground and CA for coarse root biomass) produced distinct ranges for each growth stage. This result indicates that allometric equations will provide reliable estimates of mountain big sagebrush biomass at the landscape level. The equations should be useful in developing regional carbon models or assisting in land management planning for sagebrush at the landscape scale. 4.1. Applied allometric equations A single subspecies of big sagebrush (vaseyana) was explicitly tested for changes in allometric relationships between growth stages and across space, which was not done in previous big sagebrush allometric studies (Harniss and Murray, 1976; Rittenhouse and Sneva, 1977; Uresk et al., 1977; Vora, 1988). Vora (1988) collected plants of varying size, but did not test regression relationships across the different sizes. Only two studies specified big sagebrush variety; Harniss and Murray (1976) included both basin (tridentata) and mountain (vaseyana) varieties and Rittenhouse and Sneva (1977) focused on the Wyoming (wyomingensis) variety. All of these studies found significant biomass estimation relationships using crown volume or a combination of the components of crown volume (i.e. widths or circumference, and height).

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Regression of aboveground measurements to coarse root biomass for big sagebrush is unique to this study. Elliptical CA was the preferred predictor variable for big sagebrush coarse roots in WY (Table 3). Because crown dimensions explain coarse root variability satisfactorily for mountain big sagebrush, crown dimensions are preferable over stem measurements because they are more efficient to collect and they also estimate aboveground biomass. 4.2. Global relationships The allometric relationship between mass of stems (MS) and mass of leaves (ML) for mountain big sagebrush (aRMA ¼ 0.67) was not different from the 34 power universal scaling law for seed plants predicated by Enquist and Niklas (2002, Fig. 3). This result strengthened the argument for the 34 power relationship between MS and ML and suggested sagebrush shrubs conform to the basic metabolic principles behind the rule. The basic principles state that gross photosynthesis must scale proportionately to leaf biomass and leaf biomass surface area must be proportional to total biomass (Enquist and Niklas, 2002). The results also supported the theory of 23 power scaling (Heusner, 1982; West and Brown, 2005) and the argument of Banavar et al. (2002) that the exponents 0.75 and 0.67 are not statistically different. Mass of big sagebrush reproductive parts (MI) did not scale well to ML and MS as reported by Niklas and Enquist (2003, Fig. 4). The results for MI were not conclusive possibly due to the difficulties of defining and measuring MI. Niklas and Enquist (2003) included multiple definitions of MI including total flower, seed, and fruit biomass, but our definition included florets and stems. A definition other than the one used in this study (e.g. seeds only or florets without stems) may fit the globally expected models. Annual production of sagebrush inflorescences are controlled by several environmental mechanisms including soil water and nutrient availability (Bates et al., 2005; Evans et al., 1991; Miller et al., 1991), which also suggests allometric measurements may not provide reliable estimates of inflorescence biomass regardless of how they are defined. 4.3. Aboveground biomass measurements and estimates Mountain big sagebrush biomass per plant increased between growth stages (except at SM, Table 2) and switched from primarily ephemeral parts to wood as shrubs aged. Despite this shift there were no differences in regression relationships between growth stages; and single regression relationships for each component described biomass regardless of shrub size (Fig. 2). This result was due to finding non-linear relationships (Table 3) that encompassed the changing proportions with shrub size (Figs. 1, 6). The proportion of leaves+inflorescences for mature mountain big sagebrush in Wyoming (25+3%) was very similar to that reported for mature Wyoming big sagebrush in WA (22%, Uresk et al., 1977). This suggests similar allometric relationships may hold across large regions and over subspecies of big sagebrush because the relationships are based on size, and is therefore independent of changes in shrub age, subspecies, and site quality. The regression equations estimated biomass ranges that did not overlap among growth stages, indicating the relationships were useful in describing temporal differences on an areal basis (Table 4). This result will be valuable for modeling biomass and carbon changes across landscapes temporally and in response to disturbance. Sagebrush biomass estimates were within the range of semiarid shrublands worldwide (53–1740 g m2; Huenneke et al., 2001; Siebert et al., 2004; Sternberg and Shoshany, 2001; Uresk et al., 1977), suggesting the allometric equations and biomass estimates were reasonable. 4.4. Coarse root measurements and estimates Changes in coarse root biomass between the expansion and mature stages were not significant because small, medium, and large plants were included in the analysis and small plants never had coarse roots. The samples, therefore, inherently encompassed large variability due to the collection method. The coarse root: woody shoot ratio, however, did not change between the growth stages (Table 2), which suggests there is a relationship between above- and belowground biomass that validates using allometric relationships for total and 410 mm diameter roots. Estimated biomass on an areal basis increased between the stages due to the

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increase in shrub density. There were no relationships for the 2–5 and 45–10 mm diameter size classes possibly due to inadequate sample size, higher coarse root turnover than aboveground wood turnover, or the root sampling method used. Research comparing the method used in this study to the soil saturation (Bolte et al., 2004; Olson et al., 2003) or dry skeleton excavation (Litton et al., 2003; Swamy et al., 2004) methods with larger sample sizes may improve regression relationships for big sagebrush.

5. Conclusions This was the first study to quantify and test aboveground allometric relationships of woody plants across replicated chronosequences, compare mountain big sagebrush to the global 14 and 23 power rules, and test coarse root allometric relationships across plant size and age. There were no significant differences in allometric relationships across growth stages for mountain big sagebrush in Wyoming, which is significant for carbon (C) modeling and land-use management because data from this study support the validity of large-scale biomass and C estimates. Mountain big sagebrush followed global allometric scaling for plants, but could not differentiate between 23 and 34 relationships between leaf and stem biomass. We suggest future research (1) determine if our approach would be useful across broader regions and for other subspecies of big sagebrush, (2) develop models to consider impacts of environmental events influencing inflorescence production, and (3) quantify additional coarse root biomass to develop more robust relationships between root biomass and shrub canopy architecture.

Acknowledgements This project was supported by the National Research Initiative of the USDA Cooperative State Research, Education and Extension Service, Grant number #2003-35101-13652 and a Graduate Student Fellowship from the Wyoming Space Grant Consortium. Partial funding was also provided by the Agricultural Experiment Station Competitive Grants program, project #WYO-401-06. We thank L. Schwendenmann, S. Adelman, J. Adelman, I. Abernethy, B. Cline, R. Harp, and D. Sackett for assistance with data collection and processing. We thank C. Newberry, G. Soehn, B. Budd, K. Brauneis and J. Ward from the BLM for assistance in locating appropriate field sites. We thank D. Stratton and S. Scott for access to their grazing allotments and private lands for this research. Many thanks also to the anonymous reviewers who provided excellent feedback and suggestions that improved the manuscript.

Appendix A All aboveground component equations are provided in Table A.1.

Appendix B All belowground component equations are provided in Table B.1.

df

Fit

Predictor

a (SE)

b (SE)

SEE

CF

adj. R2

p

L

CV

0.8539 (0.0414)

7.889 (0.1611)

0.6533

1.238

0.92

o0.0001

L L L

CV CV CV

0.7985 (0.0529) 0.7923 (0.0681) 0.8999 (0.0967)

7.395 (0.3659) 7.634 (0.2113) 8.138 (0.3016)

0.2850 0.5632 0.8209

1.041 1.172 1.401

0.98 0.91 0.85

0.0006 o0.0001 o0.0001

Locations ED GL SM

5 7 22

L L L

CV CV CV

1.0485 (0.0884) 0.9688 (0.0503) 0.8082 (0.0590)

8.123 (0.1856) 8.299 (0.1234) 7.668 (0.2714)

0.1827 0.2899 0.7761

1.017 1.043 1.351

0.97 0.98 0.89

0.0003 o0.0001 o0.0001

36

L

CV

0.6144 (0.0399)

5.129 (0.1552)

0.6294

1.502

0.87

o0.0001

4 14 15

L L L

CV CV CV

0.6226 (0.0746) 0.5691 (0.0521) 0.6720 (0.0859)

5.315 (0.5167) 5.330 (0.1616) 4.972 (0.2681)

0.4024 0.4307 0.7296

1.084 1.097 1.305

0.94 0.89 0.80

0.0036 o0.0001 o0.0001

Locations EDa GLb SM

5 7 22

L L L

CV CV CV

0.7749 (0.1086) 0.6004 (0.1149) 0.5995 (0.0543)

5.441 (0.2281) 5.235 (0.2822) 5.030 (0.2497)

0.2246 0.6628 0.7139

1.025 1.246 1.290

0.91 0.79 0.85

0.0020 0.0020 o0.0001

(c) Inflorescence biomass (g) 36 Allc Growth stage Establishment 4 Expansion 14 Mature 15

P

CVBA

0.5611 (0.0786)

30.81 (12.60)

94.17

n/a

0.77

o0.0001

nf P P

nf CVBA CVBA

nf 0.4969 (0.0800) 0.7048 (0.1044)

nf 61.02 (23.39) 11.66 (6.7353)

nf 86.99 64.94

nf n/a n/a

nf 0.85 0.91

nf o0.0001 o0.0001

Locations ED GLd SM

nf P nf

nf CVBA nf

nf 0.3623 (0.0967) nf

nf 94.45 (47.11) nf

nf 121.0 nf

nf n/a nf

nf 0.84 nf

nf

L

CV

0.5679 (0.0525)

3.668 (0.2046)

0.8295

1.502

0.76

o0.0001

L L L

CV CV CV

0.6174 (0.0924) 0.6168 (0.0754) 0.6464 (0.0783)

4.360 (0.6398) 4.228 (0.2341) 3.230 (0.2444)

0.4983 0.6240 0.6653

1.132 1.215 1.248

0.92 0.82 0.82

0.0068 o0.0001 o0.0001

5 7 22

(d) New stem growth biomass (g) Alle 36 Growth stage Establishment 4 Expansion 14 Mature 15

0.0009 nf

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(b) Leaf biomass (g) All Growth stage Establishment Expansion Mature

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(a) Total aboveground biomass (g) All 36 Growth stage Establishment 4 Expansion 14 Mature 15

298

Table A.1 Mountain big sagebrush aboveground biomass regression equations for all growth stages and locations combined, growth stages only, and locations only to estimate (a) total aboveground, (b) leaf, (c) inflorescence, (d) new stem growth, (e) wood o1 cm diameter, and (f) wood 41 cm diameter biomass

Locations ED GL SMf

5 7 22

nf nf L

nf nf CV

nf nf 0.5751 (0.0686)

nf nf 3.639 (0.3155)

nf nf 0.9020

nf nf 1.502

nf nf 0.76

nf nf o0.0001

CV

0.9192 (0.0504)

7.174 (0.1961)

0.7952

1.372

0.90

o0.0001

CV CV CV

0.9139 (0.0292) 1.019 (0.0877) 0.7666 (0.0963)

6.837 (0.2019) 7.135 (0.2722) 7.115 (0.3006)

0.1572 0.7255 0.8180

1.012 1.301 1.397

1.0 0.91 0.81

o0.0001 o0.0001 o0.0001

Locations ED GL SM

L L L

CV CV CV

1.057 (0.0616) 0.9676 (0.0859) 0.9089 (0.0748)

7.314 (0.1294) 7.288 (0.2110) 7.1516 (0.344)

0.1274 0.4955 0.8696

1.008 1.131 1.460

0.98 0.95 0.98

o0.0001 o0.0001 o0.0001

5 7 22

P

CVBA

0.6271 (0.0504)

127.6 (34.12)

307.6

na

0.92

o0.0001

na P P

na CVBA CVBA

na 0.6108 (0.0469) 0.5789 (0.0383)

na 91.87 (21.46) 186.6 (38.24)

na 96.69 245.1

na na na

na 0.97 0.98

na o0.0001 o0.0001

Locations ED GLh SM

P P P

CVBA CVBA CVBA

1.022 (0.0752) 0.6206 (0.1384) 1.366 (0.2002)

31.35 (7.852) 131.6 (99.39) 19.53 (12.09)

35.32 562.2 116.1

na na na na

0.99 0.90 0.91

o0.0001 0.0002 o0.0001

a

5 7 22

The power fit had a slightly higher adj. R2 (0.96), but the linear fit was chosen for comparison. CA had a slightly higher adj. R2 (0.80), but CV was chosen for comparison. c CV parameters used for estimates: a(SE) ¼ 196.7(44.12), b(SE) ¼ 1.683 (0.3263), adj. R2 ¼ 0.74, and SEE ¼ 91.67. d CA had a slightly higher adj. R2 (0.90), but CV*BA was chosen for comparison. e CA had adj. R2 ¼ 0.76, but a slightly higher SEE (0.8426). f CA had an adj. R2 ¼ 0.77 and a slightly lower SEE (0.8715), so CV was chosen for comparison. g CV parameters used for estimates: a(SE) ¼ 1585(187.6), b(SE) ¼ 1.027(0.1690), adj. R2 ¼ 0.71, and SEE ¼ 555.3. h Significantly overestimated by the all growth stages and locations combined equation.Note: df is the degrees of freedom, L the ln-linear function (Eq. (4)), P the power function (Eq. (3)), CV the ellipsoidal crown volume (Eq. (2)), CA the elliptical crown area (Eq. (1)), BA the elliptical basal area (Eq. (1)), a the slope parameter, b the intercept parameter, SE the standard error, SEE the standard error of the estimate, CF the correction factor (Eq. (5)), adj. R2 the adjusted coefficient of determination, p the p-value (a ¼ 0.05), na the not applicable, and nf the no fit. b

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(f) Wood 41 cm diameter (g) 36 Allg Growth stage Establishment 4 Expansionh 14 Mature 15

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(e) Wood o1 cm diameter biomass (g) All 36 L Growth stage Establishment 4 L Expansion 14 L Mature 15 L

299

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Table B.1 Mountain big sagebrush coarse root biomass regression equations for all growth stages combined and growth stages only for estimating (a) total, (b) 2–5 mm diameter, (c) 5–10 mm diameter, and (d) 410 mm diameter biomass from the SM location Predictor

a (SE)

b (SE)

SEE

CF

adj. R2

CA CA CA

0.6080 (0.1469) 0.9225 (0.0445) 1.082 (0.5063)

83.34 (11.68) 57.74 (2.601) 124.0 (15.71)

20.42 2.414 13.60

na na na

0.87 1.0 0.92

(b) Coarse roots 2– 5 mm diameter (g) Growth stage All 7 nf nf Expansion 2 nf nf Mature 4 P CA

nf nf 0.9053 (0.3904)

nf nf 25.97 (3.799)

nf nf 3.410

na na na

nf nf 0.88

nf nf 0.0113

(c) Coarse roots 45– 10 mm diameter (g) Growth stage All 7 nf nf Expansion 2 nf nf Mature 4 P CA

nf nf 0.6350 (0.2443)

nf nf 23.66 (4.387)

nf nf 4.095

na na na

nf nf 0.78

nf nf 0.0285

(d) Coarse roots 410 mm Growth stage All 7 Expansion 2 4 Maturea

0.9754 (0.1583) 1.512 (0.0005) 0.6350 (0.2443)

11.46 0.0101 4.095

na na na

0.95 1.0 0.79

o0.0001 o0.0001 0.0285

df

Fit

(a) Total coarse root biomass (g) Growth stage All 7 P Expansion 2 P Mature 4 P

p

0.0004 0.0141 0.0065

diameter (g) P P P

CA CA CA

53.45 (8.181) 30.32 (0.0146) 23.66 (4.387)

a CV had better adj. R2 (0.95) and SEE (6.705), but CA was chosen for comparison. Note: df is the degrees of freedom, L the ln-linear function (Eq. (4)), P the power function (Eq. (3)), CV the ellipsoidal crown volume (Eq. (2)), CA the elliptical crown area (Eq. (1)), BA the elliptical basal area (Eq. (1)), a the slope parameter, b the intercept parameter, SE the standard error, SEE the standard error of the estimate, CF the correction factor (Eq. (5)), adj. R2 the adjusted coefficient of determination, p the p-value (a ¼ 0.05), na the not applicable, and nf the no fit.

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