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Sampling sites and sample preparationCulms of three- to four-year-old of Bambusa vulgaris Schrad. ex J.C., B. maculata Widjaja, and Gigantochloa atter (Hassk) Kurz ex Munro were collected from naturally bamboo forests at four sites in Lombok Island, Indonesia23. The culm age was estimated based on some morphological features (the presence of culm sheath, color, and sound created by tapping with fingers) checked by an experienced bamboo farmer. Figure 1 shows the map of sampling sites and climatic conditions of the sites. Ten individual culms in each species at each site were collected from different clumps and cut 20 cm above the ground (Fig. 2). A total of 120 culms (three species × four sites × 10 individual culms from 10 individual clumps) were collected in the present study (Fig. 2). To determine the longitudinal variations of the anatomical characteristics and mechanical properties, the internode section was collected at 2-m intervals from 2 to 8 m above the ground; a total of 480 internode sections. (120 culms × four heights) were obtained from three species (Fig. 2). The collection of bamboo culms was permitted by Indonesian Institute of Science (Reference no. B-206/SKIKH/KS.02.04/X/2020) and complied with relevant guidelines and regulations of Indonesian CITES Management Authority, Ministry of Environment and Forestry, Indonesia. In addition, the voucher specimen was deposited at the Herbarium Lesser Sunda, University of Mataram, Indonesia under the voucher number of DSR01, 02, and 03 (specimens were identified by Mr. Niechi Valentino). Table 1 shows the culm diameter at 1.3 m above the ground, total culm height, and mean value of culm thickness at four positions23.Figure 1Locations and climate conditions of sampling sites in the present study23. Note: Site I, Tempos (8°41′59″ S, 116°8′40″ E); Site II, Kabul (8°47′21″ S, 116°10′21″ E); Site III, Keruak (8°45′45″ S, 116°28′54″ E); Site IV, Genggelang (8°23′16″ S, 116°15′35″ E). *, mean annual precipitation. The value in the bracket is the mean annual temperature. Climate data were provided from Nusa Tenggara River Basin Management I, Indonesia. Mean monthly temperature and precipitation were calculated by averaging monthly values from 2016 to 2018. Bars indicate the mean values of precipitation. Circles indicate the mean values of temperature. The graph was originally created by R27 (version 4.0.3, https://www.R-project.org/).Full size imageFigure 2Photographs of the clumps in three bamboo species (a–c) and schematic diagrams of experimental procedures (d). Note: a, B. vulgaris; b, B. maculata; c, G. atter. The specimens of fiber area measurement and mechanical properties have the whole culm thickness (including the cortex and inner part of the culm) in the radial direction.Full size imageTable 1 Mean values and standard deviations of growth characteristics in three bamboo species at each site23.Full size tableAnatomical characteristicsThe internode sections were split into two parts: the strips (10 mm in the longitudinal direction) and the small blocks (10 [T] mm by 10 [L] mm by culm thickness in the radial direction) (Fig. 2). The strips and small blocks were the samples for measuring fiber length and fiber area, respectively. In the present study, the fiber area was defined as the sheaths area around the vascular bundles24.To determine the fiber length, small sticks (not including the cortex and the most inner part of the culm) were obtained from the strips with a razor blade (Fig. 2). Randomly selected sticks from each height position (without separation of collected positions of the samples within the radial direction of the culm in a height) were macerated with Schultze’s solution (100 mL of 35% nitric acid containing 6 g potassium chloride) at 70 °C for two hours. The length of 50 fibers was measured in each sample with a digital caliper (CD-15CX, Mitutoyo, Kawasaki, Japan) on a microprojector (V-12B, Nikon, Tokyo, Japan).To measure the fiber area, one block was taken at each height position on each individual culm (Fig. 2). The transverse sections of the blocks were polished with sandpaper sheet (#180, 3 M Japan, Tokyo, Japan), and then their images were captured using a microscope digital camera (DS-2210, Sato Shouji Inc., Kawasaki, Japan) attached to a stereo microscope (SZX12, Olympus, Tokyo, Japan). The fiber area was determined by ImageJ25 (version 1.53e). Binarized images were prepared by ImageJ to distinguish as clearly as possible between the vascular bundle and the background (Fig. 3). The darker area of binarized images in Fig. 3 was identified as fiber sheaths. The fiber area was calculated as follows:$$FAleft( % right) , = A_{fs} /A_{c} times {1}00$$
(1)
where FA = fiber area (%), Afs = the transverse-sectional area of fiber sheath in bamboo culm (mm2), and Ac = the transverse-sectional area of bamboo culm (mm2).Figure 3The photomicrographs of transverse section in B. vulgaris (a and d), B. maculata (b and e), and G. atter (c and f). Note: a, b and c, original image; d, e and f, binarized image processed by ImageJ25 (version 1.53e, https://imagej.nih.gov/ij/). The darker area in photomicrographs (d, e and f) is fiber sheath area.Full size imageMechanical propertiesThe following mechanical properties of culm were measured: bending properties (MOE and MOR), CS, and tensile properties (TM and TS). A total of 480 specimens (one specimen × four heights in an individual × ten individuals × three species × four sites) without node were obtained in each property (Fig. 2).The strips (10 [T] mm × 200 [L] mm × varied culm thickness in the radial direction) were prepared as the specimens for the static bending test (Fig. 2). The static bending test was conducted using a universal testing machine (MSC 5/500–2, Tokyo Testing Machine, Tokyo, Japan). A load was applied to the center of the specimen on the outer cortex surface with 180 mm span and 3 mm min−1 load speed. Due to larger thickness (exceeded 12.9 mm = 180 mm of span / 14) in the radial direction, the span / depth ratio in some specimens was less than 14, indicating that MOR in some specimens might be underestimated due to the occurrence of the shearing strength26. Of 480 specimens, the large culm thickness exceeded 12.9 mm was total 19 specimens from B. vulgaris species collected at 2 m height position from different sites (Site I = four specimens, Site II = six specimens, Site III = four specimens, and Site IV = five specimens). However, all these 19 specimens were broken at the tension side of the specimens during static bending test, which was the normal breaking forms of bending specimens with span / depth ratio less than 14.The load and deflection were recorded with a personal computer, and then MOE and MOR were calculated by the following formulae:$$MOE , left( {GPa} right) , = Delta Pl^{3} / , 4Delta Ybh^{3} , times 10^{ – 3}$$
(2)
$$MOR , left( {MPa} right) , = , 3Pl/ , 2bh^{2}$$
(3)
where ΔP = difference between upper and lower proportional limit within the range of elasticity (N), l = length of the span (mm), ∆Y = deflection due to ∆P (mm), b = width of the specimen (mm), h = height of the specimen (mm), and P = maximum load (N).The compressive test specimen (10 [T] mm × 20 [L] mm × culm thickness in the radial direction) was also prepared (Fig. 2). The test was conducted using a universal testing machine (RTF-2350, A&D, Tokyo, Japan) with a load speed of 0.3 mm min−1. The compressive strength parallel to grain (CS) was calculated by the following formula:$${text{CS }}left( {{text{MPa}}} right) , = P/A_{0}$$
(4)
where P = maximum load (N), and A0 = the cross-sectional area of the specimen (mm2).The tensile tests were conducted using bone-shaped specimens (Fig. 2). The specimen length was 230 (L) mm with a 20 (T) mm width of the specimen grip. The cross-sectional area of the specimen was 2 mm in the tangential direction by culm thickness in the radial direction. A strain gage type extensometer (SG25-10A, A&D, Tokyo, Japan) was used to detect the elongation in the test specimen. The specimen grip sections were attached to small boards (75 mm in length × 40 mm in width × 5 mm in thickness) and then were clamped between the metal grip of a universal testing machine (RTC-2410, A&D, Tokyo, Japan). The tensile load was applied at 1 mm min−1. The tensile strength (TS) and Young’s modulus (TM) were calculated by the following formulae:$${text{TS }}left( {{text{MPa}}} right) , = P/A_{0}$$
(5)
$${text{TM }}left( {{text{GPa}}} right) , = Delta Pl/A_{0} Delta l times {1}0^{{ – 3}}$$
(6)
where P = maximum load (N), A0 = the cross-sectional area of the specimen (mm2), ∆P = difference between upper and lower proportional limit within the range of elasticity (N), l = gauge length (mm), and ∆l = elongation of the original gauge length (mm).The moisture content and air-dry density of each specimen were measured after each mechanical testing by the oven-dry method. The moisture content and air-dry density of the specimen at testing were listed in Table S1.Statistical analysisThe statistical analyses were conducted using R software (version 4.0.3)27. To evaluate the longitudinal variations of the measured properties in each species, the y-intercept, linear, and nonlinear mixed-effects models with each measured property value as a responsible variable, the height position as a fixed effect, and site and individual culm as random effects were developed by the “lmer” function in “lme4” packages28 and the “nlme” function in the “nlme” package29. The following four full models were developed and compared:Model I (y-intercept model):$$Y_{ijk} = alpha_{{1}} + Site_{{{1}k}} + Culm_{{{1}jk}} + e_{ijk}$$
(7)
Model II (linear model):$$Y_{ijk} = , (beta_{0} + Site_{0k} + Culm_{0jk} )X_{ijk} + beta_{{1}} + Site_{{{1}k}} + Culm_{{{1}jk}} + e_{ijk}$$
(8)
Model III (logarithmic model):$$Y_{ijk} = , (gamma_{0} + Site_{0k} + Culm_{0jk} ){text{ ln }}left( {X_{ijk} } right) + gamma_{{1}} + Site_{{{1}k}} + Culm_{{{1}jk}} + e_{ijk}$$
(9)
Model IV (quadratic model):$$begin{gathered} Y_{ijk} = , (zeta_{0} + Site_{0k} + Culm_{0jk} )X_{ijk}^{{2}} + , (zeta_{{1}} + Site_{{{1}k}} + Culm_{{{1}jk}} )X_{ijk} hfill \ + zeta_{{2}} + Site_{{{2}k}} + Culm_{{{2}jk}} + e_{ijk} hfill \ end{gathered}$$
(10)

where Yijk is measured property at the ith height position from the jth individual culm within the kth site, Xijk is the ith height position from the jth individual culm within the kth site, α1, β0, β1, γ0, γ1, ζ0, ζ1, and ζ2 are the fixed effects, Site0k, Site1k, and Site2k are the random effect at the site level, Culm0jk, Culm1jk, and Culm2jk are the random effects at the individual culm level, and eijk is residual. Total 36 derived models (three y-intercept models, 15 linear models, nine logarithmic models, and nine quadratic models) were developed. The model selection was conducted using the Akaike information criterion30. The model with the minimum AIC value was regarded as the most parsimonious model among developed models. In addition, the differences in AIC (ΔAIC) ≤ 2 indicate no significant differences between models, and a simpler model with fewer parameters is preferred31. To evaluate the longitudinal variation, estimated values of each property was calculated at 0.1 m interval from 2.0 to 8.0 m above the ground using fixed-effect parameters of the selected models. Mean value and standard deviation were obtained from the estimated values from 2.0 to 8.0 m in each property. In addition, the coefficient of variation was also calculated from the mean value and standard deviation. The longitudinal variation patterns were classified into four types (Types A to D) based on the model selection (Fig. 4). Although model II to IV was selected, longitudinal variation with the coefficient of variation less than 3.0% was regarded as stable (Type A in Fig. 4).Figure 4Classification of longitudinal variation of bamboo culm property. Note: Lines or curves indicate formulae with fixed-effect parameters in the selected mixed-effect model for explaining longitudinal variation (Tables 3, 4, 5). Coefficient of variation calculated from mean values and standard deviation from 2 to 8 m above the ground estimated by fixed-effect parameters values less than 3.0% is regard as stable variation (Type A), even in selected model is Model II to IV.Full size imageGeographic variations in each bamboo property were estimated by evaluating the variance component of sites and culms as random effects by using the intercept-only linear mixed-effects model. The full model is described as follows:$$Y_{ijk} = mu + Site_{k} + Culm_{jk} + e_{ijk}$$
(11)
where Yijk is the bamboo property at the ith height position of the jth individual culm within kth site, μ is the model intercept or grand mean, Sitek is the random effect of the kth site, Culmjk is random effect of jth individual culm within kth site, and eijk is the residual. The contribution of each level of variation was calculated as a percentage of the total random variation in the best model32,33. More

Biodiversity on Earth is threatened by land-use changes, overexploitation of resources, pollution, biological invasions, and current and projected climate change. Understanding how species will respond to these stressors is difficult, in part because stressors don’t occur in isolation, and because responses can trickle through ecological networks due to interactions among species. More

Our approach uses hypothetical 30 cm fixed depth samples taken at three successive time points (t0, t1, and t2) with prescribed changes in SOC (1.4% to 1.6%) and BD (1.5–1.1 g cm−3) over these time points (Table 1). The 30 cm soil depth is the common international standard for sampling and analysis required for SOC stock assessment and adhered to by carbon accounting and market organizations6,18. The changes we adopted (a 27% decrease in BD and a 14% increase in SOC) while relatively large, are consistent with those reported in the literature. For example, Reganold and Palmer reported a 25% decrease in BD (1.2–0.9 g cm−3) in neighboring farms with differing management practices23, and Syswerda et al. observed a 17% increase in SOC concentration (10.4–12.2 g C kg soil−1) when converting from a conventionally to organically managed row crop rotation21.Table 1 Hypothetical changes in bulk density (BD) and soil organic carbon (SOC) concentration in 30 cm fixed depth samples at time points t0, t1 and t2 along with calculated values of SOC stock and total soil mass and mineral soil mass.Full size tableIn Table 1, the total soil mass, mineral soil mass, and the SOC stock of the fixed depth samples were calculated by equations as described in the introduction from our prescribed changes in BD and SOC values.ScenariosWe compared hypothetical ESM correction scenarios with our 30 cm fixed depth sample at each time point (Table 2, Figs. 2, 3).Table 2 Hypothetical ESM scenarios showing variation with depth for bulk density (BD) and soil organic carbon (SOC) at each sampling time point, along with the sample depth intervals investigated.Full size tableFigure 2Flow chart of the definition, sampling, and SOC stock correction for a theoretical data set at time points t0, t1, and t2 for scenarios s1 with linear distributions of BD and SOC and s2 with a linear increase in BD and exponential decrease in SOC with depth. Scenario s2 is sampled at (a) 10 cm, (b) 15 cm, and (c) 30 cm intervals.Full size imageFigure 3Scenarios (S1 and S2), showing (a) bulk density variation (BD, g cm−3), and (b) soil organic carbon (SOC, %) variation by depth (0–30 cm) at each time point (t0, t1, and t2). For scenario 2, the single 30 cm depth interval was used (2c). See Table 1 and 2 for details.Full size imageScenario 1We carried out the ESM correction on a 30 cm sample and assumed that the sample was homogenous throughout the profile, with constant SOC and BD values at each time point.To correct for the error in SOC stock estimation when using fixed depth soil sampling, we used  Eqs.2a, 2b and 2c that consider changes in BD28,35. The adjusted soil depth resulting from the change in BD is calculated as:$${mathrm{M}}_{mathrm{n}}= {mathrm{M}}_{mathrm{i}}$$
(2a)
$${mathrm{D}}_{mathrm{a}}*{mathrm{BD}}_{mathrm{n}}*left(1-mathrm{k}*{mathrm{SOC}}_{mathrm{n}}right)={mathrm{D}}_{mathrm{i}}*{mathrm{BD}}_{mathrm{i}}*left(1-mathrm{k}*{mathrm{SOC}}_{mathrm{i}}right)$$
(2b)
$${mathrm{D}}_{mathrm{a}}={mathrm{D}}_{mathrm{i}}*frac{{mathrm{BD}}_{mathrm{i}}}{{mathrm{BD}}_{mathrm{n}}}*frac{1-mathrm{k}*{mathrm{SOC}}_{mathrm{i}}}{1-mathrm{k}*{mathrm{SOC}}_{mathrm{n}}}$$
(2c)
where Mi = Initial mineral soil mass per area (left[frac{M}{{L}^{2}}right]) , Mn = New mineral soil mass per area (left[frac{M}{{L}^{2}}right]) , Da = Adjusted soil surface depth (left[Lright]) , BDi = Initial bulk density (left[frac{M}{{L}^{3}}right]) , BDn = New bulk density (left[frac{M}{{L}^{3}}right]) , SOCi = Initial SOC as a decimal percent (left[frac{M}{M}right]) , SOCn = New SOC as a decimal percent (left[frac{M}{M}right]) , Di = Initial depth (left[Lright]).To conform with Eq. (2a), an increase in SOC over time results in a displacement of some soil mineral mass from the sample, whereas a decrease in SOC over time requires some soil mineral mass to be replaced34. Multiplying the BD by the mineral fraction of the soil (left(1-mathrm{k}*{mathrm{SOC}}right)) for each time point allowed us to compare equivalent mineral mass28. The effect of a change in SOC on mineral mass is small, with a 1% change in SOC equating to approximately a 2% change in apparent depth. This adjustment relates SOC per unit of mineral mass of the fine fraction ( 2 mm)20. The corrected apparent depth can then be used to calculate the corrected SOC stock of a single layer, fixed depth sample (Eq. 3).$$SO{C}_{stock}={D}_{a}*BD*SOC$$
(3)
Scenario 2In ESM correction scenarios 2a, 2b, and 2c, we imposed variable, dynamic BD and SOC values with depth over time (Table 2, Figs. 2, 3). To investigate these profiles, we determined the SOC and BD values throughout the soil depth by separating the soil into one (1) cm depth increments (i.e., 0–1 cm, 1–2 cm, etc.). We refer to this calculated incremental profile as the scenario 2 baseline. We assumed that our prescribed SOC concentration varied with depth following an exponential decay. To represent this decay, we simulated the global average distribution of SOC concentration with depth on crop land36, following the distribution from Hobley and Wilson37 (Eq. 4),$$SOCleft(dright)=SO{C}_{infty }+left(SO{C}_{o}-SO{C}_{infty }right)times {e}^{-dk}$$
(4)
where SOC (d) is the SOC concentration at depth (d), ({SOC}_{infty }) is the infinity SOC concentration, SOC0 is the SOC concentration at the soil surface, and k is the decay rate. We solved for the decay rate, initial SOC0, and infinity ({SOC}_{infty }) to fit the global average distribution for the 30 cm profile36 and then scaled the SOC concentration to our 30 cm fixed depth sample’s average SOC (1.4%) at t0 (Fig. 3).In scenarios 2a, 2b, and 2c, the BD increased linearly with depth38,39. At the initial time point (t0), we varied the BD values by ± 10% of the BD average over the 30 cm depth, such that for example, BD at t0 (profile average of 1.5 g cm−3) was 1.35 g cm−3 and 1.65 g cm−3 for the upper (0–1 cm) and lower (29–30 cm) depth increment, respectively. For each sequential time point, as the average BD decreased, the soil expanded. To determine the expansion, the depth of the initial sample (e.g., at t0) that filled the 30 cm depth in the subsequent sample (e.g., at t1) was calculated as the initial depth multiplied by the ratio of the average initial BD over the average new BD (e.g., 1.5/1.3 = 1.15 for t0/t1).The linear increase in BD with depth of each following time point maintained the average BD of scenario 1. We then varied the new BD by ± the percent change in the average BD between the time periods (see annotated scripts “main.R” and “functions.R” in Supplementary Material 1 for the development of the theoretical dataset). We then divided each initial BD increment (using soil mass for every 1 cm depth increment) by the new BD in the expanded increment (using soil mass for every  > 1 cm depth increment) to determine the expanded depth of each increment. The SOC value at the initial time represented the same, now expanded, ( > 1 cm) increments, as SOC is a ratio of mass. We used a linear decay rate that was twice that of the percent change in BD between time points to maintain an average BD that was consistent with scenario 1. To model the subsequent fixed depth sample, the BD and SOC concentration values of this expanded soil profile were then interpolated back to the 30 × 1 cm increments of the scenario 2 baseline depth. This calculation preserved the prescribed average BD of the new time point by only expanding the initial SOC concentration.We adjusted the SOC concentration of the next time point to maintain the average SOC concentrations of the 30 cm fixed depth sample, (see annotated scripts “main.R” and “functions.R” in Supplementary Material 1). Because the BD changed between time points and because the SOC stock in the 30 cm fixed depth sample was known, we determined the change in SOC stock between time points by subtracting the average SOC stock in the prior sample from the new sample. We then weighted this change across the 30 cm profile using the distribution of the global soil SOC in the top 30 cm to simulate SOC stratification with reduced tillage or agricultural intensification40. We then multiplied this change by the BD to convert back to SOC concentration and added the delta ((Delta )) SOC value to the prior sample. A worked example is shown in Supplementary Material 2 “Correction Example”.At each time point we split the soil profile at 10 cm and 15 cm depth intervals to create samples for scenarios 2a (3 soil intervals) and 2b (2 soil intervals), respectively. Note that scenario 2c is mathematically equivalent to scenario 1—with only one sample depth interval (30 cm) the sample contains no data on varying SOC or BD. The samples for 2a and 2b were generated by summing the total mass per area and SOC stock values from the scenario 2 baseline to produce single sample values of total soil mass per area and SOC concentration values per depth interval (as would be determined in a laboratory) and calculating BD and mineral mass.In scenario 2, any required additional mineral mass and the associated SOC values were ‘placed’ at the base of the sample to represent a soil profile that had expanded below the fixed 30 cm depth. To account for this, we calculated the increase in adjusted sample depth and accumulated additional soil mineral mass with the lowest sample depth interval of each split sample (Eqs. 5 and 6).$$mathrm{Delta D}={D}_{a}-{D}_{i}$$
(5)
$$SO{C}_{stock}={(D}_{1}*B{D}_{1}*SO{C}_{1}+dots + {(D}_{j}+Delta D)*B{D}_{j}*SO{C}_{j}))*10^2 (mathrm{g}/mathrm{cm}^{2})/(mathrm{Mg}/mathrm{ha})$$
(6)
where (mathrm{ Delta D}) is the apparent change in depth needed to generate the same mineral mass of the initial sample and the subscript j is the number of sample depth intervals from 1 to j.Varying BD linearly with depth introduces additional complexity in the calculation of the apparent depth. Each sample depth interval may expand (or contract in cases not explored here) at differing rates. Here, the over or under sampling of soil mineral mass is no longer constant with depth and the correction for apparent depth (Da) is estimated with linear interpolation using the BD of each sampling depth interval (i.e., 10 cm, 15 cm, or 30 cm). To do so, we calculated the mineral mass in each depth interval, determined their difference between the initial sample time point and new sample time point, and converted the change in mineral mass to a depth, where:$${mathrm{D}}_{mathrm{a}}={mathrm{D}}_{mathrm{i}}+frac{left(mathrm{sum}left({mathrm{D}}_{mathrm{ij}}*{mathrm{BD}}_{mathrm{ij}}*(1-mathrm{k}*{mathrm{soc}}_{mathrm{ij}}right))- mathrm{sum}left({mathrm{D}}_{mathrm{nj}}*{mathrm{BD}}_{mathrm{nj}}*(1-mathrm{k}*{mathrm{soc}}_{nmathrm{j}})right)right)}{{mathrm{BD}}_{{mathrm{nj}}_{mathrm{bottom}}}*1-mathrm{k}*{mathrm{soc}}_{n{mathrm{j}}_{mathrm{bottom}}}}$$
(7)
where jbottom is the lowest sample depth interval, and other terms are as previous. Using Eqs. (5), (6), and (7), with variable BD and SOC values, SOC stock can be corrected using samples split into the 10 cm and 15 cm sampling depth intervals. More