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Soil Biology & Biochemistry 41 (2009) 1466–1474

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Soil Biology & Biochemistry

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Stand-scale spatial patterns of soil microbial biomass in natural cold-temperatebeech forests along an elevation gradient

Xin Zhao, Quan Wang*, Yoshitaka KakubariInstitute of Silviculture, Shizuoka University, Ohya 836, Shizuoka 422-8529, Japan

a r t i c l e i n f o

Article history:Received 17 October 2008Received in revised form24 March 2009Accepted 31 March 2009Available online 18 April 2009

Keywords:Soil microbeBiomassSpatial heterogeneityGeostatisticsFagus crenataNaeba

* Corresponding author. Tel.: þ81 54 2383683; faxE-mail address: wangquan@agr.shizuoka.ac.jp (Q.

0038-0717/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.soilbio.2009.03.028

a b s t r a c t

This study focuses on spatial heterogeneity in the soil microbial biomass (SMB) of typical climax beech(Fagus crenata) at the stand scale in forest ecosystems of the cold-temperate mountain zones of Japan.Three beech-dominated sites were selected along an altitudinal gradient and grid sampling was used tocollect soil samples at each site. The highest average SMB density was observed at the site 1500 m a.s.l.(44.9 gC m�2), the lowest was recorded at the site 700 m a.s.l. (18.9 gC m�2); the average SMB density atthe 550 m site (36.5 gC m�2) was close to the overall median of all three sites. Geostatistics, which isspecifically designed to take spatial autocorrelation into account, was then used to analyze the datacollected. All sites generally exhibited stand-scale spatial autocorrelation at a lag distance of 10–18 m inaddition to the small-scale spatial dependence noted at <3.5 m at the 550 m site. Correlation analysiswith an emphasis on spatial dependency showed SMB to be significantly correlated with bulk density atthe 550 and 1500 m sites, dissolved organic carbon (DOC) at the 700 and 1500 m sites, and nitrogen (N)at the 550 and 700 m sites. However, no soil parameter showed a significant correlation with SMB atevery site, and some variables were also differently correlated (negative or positive) with SMB atdifferent sites. This suggests that the factors controlling the spatial distribution of SMB are very complexand responsive to local in situ conditions. SMB regression models were generated from both the ordinaryleast-squares (OLS) and generalized least-squares (GLS) models. GLS performance was only superior toOLS when cross-variograms were accurately fitted. Geostatistics is preferable, however, since thesetechniques take the spatial non-stationarity of samples into account. In addition, the sampling numbersfor given minimum detectable differences (MDDs) are provided for each site for future SMB monitoring.

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1. Introduction

Soil microbial biomass (SMB) refers to the total mass of micro-organisms within a given soil (Brookes, 1995). It is a well-knownand important driver of soil decomposition and nutrient biogeo-chemical cycling processes, such as mineralization and immobili-zation (Tessier et al., 1998; Stockdale and Brookes, 2006). SMB alsoappears to show sensitivity and responsiveness to environmentalchanges, and it has long been suggested that it is a more reliableindicator of environmental change than total soil organic matter(Powlson and Jenkinson, 1976). Numerous studies have foundrelationships between SMB and various soil properties, such as soiltemperature (Grisi et al., 1998), moisture (Ross, 1990), organicmatter content (Lipson et al., 2000) and texture (Kaiser et al., 1992).Moreover, SMB responses to local soil properties are considered to

: þ81 54 2384841.Wang).

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be very rapid. SMB, therefore, exhibits complex spatial heteroge-neity, since soil properties show strong spatial variation over shortdistances (Trangmar et al., 1985), e.g. at the centimeter scale(Brockman and Murray, 1997).

SMB spatial variation must be characterized before the complexrelationships between SMB and soil environmental parameters canbe understood. Understanding how variability and patterns changeat different observational scales, and how the scales at which theseobserved patterns and their underlying mechanisms relate to eachanother, is a central problem in ecology and environmental science(Brockman and Murray, 1997). Indeed, these issues are highlycritical when developing predictive capabilities (Brockman andMurray, 1997), and therefore we require a quantitative knowledgeof how these factors influence each other if we are to understand,and ultimately predict and model, the resultant soil processes. Boththe variability and mean of each process are important properties,and therefore the evaluation of spatial and temporal variability cancontribute to the identification of key driving factors involved in thecontrol of soil microbial processes. Hence, the quantification and

Fig. 1. Location of study sites in the Naeba beech forests.

X. Zhao et al. / Soil Biology & Biochemistry 41 (2009) 1466–1474 1467

identification of these factors may be a potentially useful tool whenexamining relationships between soil variables (Perie et al., 2006),and such knowledge will also be instructive when designing fieldsampling methods.

In the past, three main sampling methods have been used:random, stratified and grid sampling. Statistical approaches arethen applied to the data collected in order to deal with spatialvariability. The relatively simple approach of random samplingalways provides a single measure of central tendency (mean ormedian) and variability (standard deviation or variance) for anygiven parameter. In contrast, stratified sampling designs are oftencoupled with analysis of variance (ANOVA), which provides anincreased awareness of spatial heterogeneity and greater statisticalrigor (Brockman and Murray, 1997). However, soil properties arespatially dependent over certain lengths/scales, and thus they oftenviolate the spatial stationarity assumptions of ANOVA, renderingthe analysis invalid. Accordingly, the importance of consideringspatial autocorrelation in geographical ecology has been addressedin a number of recent papers (e.g. Diniz-Filho et al., 2003; Lichsteinet al., 2002; Legendre et al., 2002). Lennon (2000) has also calledattention to problems caused by spatial autocorrelation, such as thepossibility of generating widespread ‘red herrings’ in the inter-pretation of ecological mechanisms and the well-know inflation ofType I errors. Consequently, Lennon (2000) argued that virtually allgeographical studies need to be reanalyzed with spatial autocor-relation taken into account.

An alternative method of analysis is geostatistics, which evalu-ates the degree of spatial dependence in a property withoutassuming sample independence. Geostatistics also provides a set ofstatistical tools for incorporating the spatial coordinates of soilobservations into data analyses. This allows the description andmodeling of spatial patterns, predictions for unsampled locationsby kriging or co-kriging, and the assessment of uncertaintiesattached to those predications (Goovaerts, 1998). Until the late1980s, geostatistics was essentially considered to be a method fordescribing spatial patterns using semivariograms and for predictingthe values of soil attributes at unsampled locations by kriging.However, it has recently been developed to tackle advanced prob-lems, such as the stochastic simulation of the spatial distributionsof soil properties and the modeling of spatiotemporal processes(Goovaerts, 1999).

The use of geostatistics in soil microbe spatial variation studieshas been evaluated previously (e.g. Webster and Boag, 1992), but itsapplication is still at a very early stage (Brockman and Murray,1997). Spatial heterogeneity manifests at many scales: micro-scale(centimeters), plot and stand scale (meters), landscape scale(kilometers), and even the regional scale. However, smaller scalesources of variability may become obscured by greater distances asthe scale increases, and thus the probability distribution of soilproperties at smaller scales may not apply at larger scales (Brejdaet al., 2000). Two main issues in current spatial heterogeneitystudies include: (1) spatial scaling with the special necessity ofunderstanding soil microbial dynamics at different scales; (2)sampling resolutions and techniques in studying microbialdynamics. These are fundamental to developing sampling proce-dures that produce fine-scale estimates of belowground functionsthat may as well facilitate development of regional scale models topredict the consequences of global climate change (Morris andBoerner, 1999).

The stand scale is emphasized in the current study, since it is themost appropriate scale for studying the impacts of human activities(e.g. silviculture) on forest ecosystem functions including soil bio-logical processes (Barg and Edmonds, 1999; Perie et al., 2006).Indeed, other studies have placed a similar focus on this scale (e.g.Perie et al., 2006), but few have examined cold-temperate beech

forest ecosystems. The objectives of this study were: (1) to under-stand SMB spatial heterogeneity at the stand scale (range of meters)in cold-temperate deciduous forest ecosystems; (2) to examinespatial cross-correlations between SMB and environmental prop-erties, and (3) to present optimal sampling strategies for studyingspatial heterogeneity in SMB. The study was conducted in threebeech forest ecosystems along an altitudinal gradient within thecold-temperate climate zone of Japan. A 30� 30 m plot was estab-lished in each forest stand, the grid sampling method was applied toeach pixel at a resolution of 5 m, and geostatistics was used to assessthe spatial heterogeneity of SMB.

2. Materials and methods

2.1. Site description

This study was conducted at three permanent sites located atdifferent altitudes on the northern slope of Naeba Mountain, Japan(36�510N, 138�400E), where natural Japanese beech (Fagus crenata)forests grow at altitudes between 550 and 1500 m a.s.l. Ecologicalresearch in this region, sponsored by the International BiologicalProgram (IBP), can be traced back to the 1970s (Kakubari, 1977).Along the northern slope of Kagura Peak, more than 15 plots havesince been set up, where stand biomass, leaf area index (LAI) andother structural stand parameters have been continuously moni-tored for over 35 years now (see Fig. 1 for the established and studysites of IBP project). In this study, three sites at 550 m, 700 m and1500 m respectively have been selected and their details have beenpresented in Table 1. The 550 m site is located on the river terrace ofa deep-valley, 10 m above the current river level, while the 700 mand 1500 m sites are both on the south-facing of the mountainslope (Table 1).

The bedrock in the study area is predominantly basalt, on whichmoderately moist brown forest soils have developed. The upperlayer of the canopy mainly consists of F. crenata. Other species arealso occasionally present, such as Quercus mongolica var. grosse-serrata, Magnolia obovata and Acanthopanax sciadophylloides at the550 m and 700 m sites, and Betula grossa and Betula ermanii at the1500 m site. In addition, the prevalence of evergreen bamboo (Sasakurilensis) increases with elevation to >90% cover in the 1500 mzone.

The region is situated along the coast of the Japan Sea, and itsclimate is characterized by a high precipitation, ca. 2000 mm yr�1,much of which falls as snow in the winter, leading to a snow depthof 3–4 m. The deep winter snow accumulations remain until early

Table 1Descriptions of plots used in the study.

Plot 550 700 1500

Altitude (m) 550 700 1500Latitude 36�53033.2400 36�55010.600 36�50043.9500

Longitude 138�45046.9000 138�4608.800 138�43049.2500

Area (m2) 2400 1800 1000Azimuth (�) 0 N34W N40EInclination (�) 0 10 8Stand age (yr) 260 200 300Dominant species Fagus crenataDBH (cm) 37.1 36.9 17.6Mean tree height (m) 34 30 22Stand density (trees ha�1) 246 361 450Basal area (m2 ha�1) 36.3 52.4 30.4Percentage of main species (%) 97.5 82 98.6

X. Zhao et al. / Soil Biology & Biochemistry 41 (2009) 1466–14741468

May at the 550 m and 700 m sites, whereas snowmelt occurs inearly June at the 1500 m site. Beech leaves begin to flush in lateApril to early May at the 550 m and 700 m sites, and autumn leafcoloring starts in late October. In contrast, leaf flush at the 1500 msite occurs between late May and early June, whereas autumn leafcoloring begins in early October. The typical mean annual airtemperatures are 10.0, 9.3 and 5.6 �C at the 550 m, 700 m and1500 m sites, respectively.

2.2. Field sampling

Special consideration is required when designing field samplingmethods for geostatistical analyses that focus on the spatial char-acterization of SMB. Olea (1984) demonstrated that grid samplingprovide the most efficient method of sampling for spatial vari-ability over random, stratified and clustered sampling techniques.The number of samples needed to be taken for proper variogramanalysis can be a problem, especially for microbiological variableswhich are very expensive to analyze. The common practice fordesigning sampling grids and transects is ensuring that at least 30sample pairs are available for each lag in the variogram (Journeland Huijbregts, 1978), which can be attained with fewer than 25data points arranged on a 2-D square grid (Brockman and Murray,1997). Hence a 5� 5 mesh could produce the minimum requiredsamples for spatial analysis. Here in this study, a 6� 6 mesh wasapplied to each stand, about one third over the required minimumsample.

A soil core of up to 50 cm depth (and sometimes even 80 cm)was collected from the center of each pixel using a specialized soilsampler (Geo-Environment Technology Research Center, Japan).When a tree was located in the center of the pixel sampling wasconducted within 1 m of the center. Once collected, the coreswere immediately stored in ice-boxes prior to transportation tothe lab. An auger was used to collect another set of soil samplesfor the analysis of soil physical properties; these samples weretaken close to the pixel center at 10 cm depth intervals (up to30 cm). In situ soil moisture and soil hardness measurementswere also taken from each 10 cm interval with a TDR and Hard-ness Meter, respectively. In addition, simple soil profiles of up to30 cm depth were prepared for recording the depth of the Ahorizon.

The litter in each pixel was sampled within a 25� 25 cm frame,with the thicknesses of the L (slightly decomposed), F (moderatelydecomposed) and H (highly decomposed) layers measured beforecollection. All coarse woody debris was removed from the samplesprior to analysis, and litter sample dry weights were recorded in thelaboratory.

2.3. Lab analysis

The mass of L and F layers was air-dried and weighed prior tocalculating bulk densities relative to the respective sampling area.Soil bulk density for each 10 cm layer was calculated from the massof the oven-dry soil (105 �C) and core volume (100 cm3). The oven-dry soil samples were further passed through 2 mm sieve toremove stone and roots, and later combined with other sets of soilsamples to calculate stone and root density for each 10 cm layer.

The soil cores were divided into 10 cm deep subsamples, andthen sieved through a 2 mm mesh to remove stones and roots. Thesieved subsamples were then split again for use in soil C/N and SMBanalyses. The SMB samples were stored in freezers at �20 �C, or atleast below 4 �C, until analysis.

Soil organic carbon (SOC) and total nitrogen of the soil sampleswere analyzed by SUMIGRAPH TC/N Analyzer (Sumigraph NC-900,SCAS, Osaka, Japan). pH was also measured using a pHTestr 30(EUTECH Instruments Pte. Ltd) after mixing the soil samples with2.5 times their weight of water (Edit Committee of Soil Environ-mental Analysis, 1997).

Soil microbial biomass was determined using chloroformfumigation–extraction method (Vance et al., 1987). For CFEmethod, 10 g dry weight equivalent fresh soil samples (10 daysincubation at 25 �C) were placed in 50 ml beakers and kept ina vacuum desiccator containing a 100 ml beaker with 25 mlalcohol-free chloroform. Another desiccator was maintainedwithout chloroform and both kept for 24 h at 25 �C in the dark. Thefumigated samples were then evacuated with a vacuum pumpuntil the chloroform had completely evaporated. Extractions werethen performed on the fumigated and unfumigated samples byadding 40 ml 0.5 M K2SO4 to each sample, shaking them for30 min, and finally filtering the extract through a Whatman No. 42filter paper. Organic C in the extractants was analyzed usinga Shimadzu TOC-VCSH total organic C analyzer (Shimadzu Corpo-ration, Japan). Soil microbial biomass C was determined from thedifference between extractable organic C in fumigated and unfu-migated samples using an Ec factor of 2.04 (Research Association ofSoil Microbes, 1997). In addition, the total organic C outputs ofunfumigated samples were used as dissolved organic carbon(K2SO4 retrieved DOC, referred to as DOC hereafter).

2.4. Geostatistics

Geostatistics focuses on the spatial patterns of data, providingtools for characterizing spatial distribution and estimation of vari-ables at unsampled locations. For SMB, the apparent controllingfactors of hydrogeological and geochemical processes do not varyrandomly but rather exhibit strong spatial continuity. Hence, givenappropriate sampling strategies, geostatistics handles uncertaintyrelated to spatial autocorrelation by building probabilistic modelsof spatial continuity in a given set of data.

Moran’s I coefficient and semi-variance were used to statisti-cally analyze spatial autocorrelation. Indeed, Moran’s I is the mostcommonly used index and it is statistically robust (Moran, 1950).Therefore, we used Moran’s I as the primary statistic whendescribing spatial structure, although semivariograms were alsoused.

A semivariogram is estimated by calculating half the averagesquared difference between all pairs of points separated by a givendistance. Mathematical functions must also be fitted to the resul-tant semivariograms if geostatistical methods are to be used topredict the value of a variable at an unsampled location. Severalmathematical functions are known to be appropriate for use invariogram modeling, including the linear, exponential, spherical

X. Zhao et al. / Soil Biology & Biochemistry 41 (2009) 1466–1474 1469

and Gaussian functions (Griffith and Layne, 1999). The equations forthe respective mathematical functions are as follows:

For the linear model:

gðhÞ ¼ C0 þ C½ðh=A0Þ� (1)

For the spherical model with range A0:

gðhÞ ¼ C0 þ Ch1:5ðh=A0Þ � 0:5ðh=A0Þ3

i; h � A0

gðhÞ ¼ C0 þ C; h � A0

(2)

For the exponential model with distance parameter b:

gðhÞ ¼ C0 þ C½1� expð � h=bÞ� (3)

For the Gaussian model with distance parameter b:

gðhÞ ¼ C0 þ Ch1� exp

��h2=b2

�i(4)

where C0 is nugget variance (the y intercept of the model), whichindicates either variance exists at a shorter distance than fieldsampling intervals or measurement error; C is the asymptote ofsemi-variance g(h); the sum of C0 and C is called sill; A0 is calledrange, the distance over which spatial dependence is apparent(autocorrelation) for the direction examined. The best-fit modelsfor the semivariograms are selected based on the smallest set ofresidual sum of square (RSS) between model predictions of vari-ance for each lag distance and the measured values.

Spatial relationships between the environmental factors andSMB were examined using the cross-correlogram technique, whichis a geostatistical tool related to the semivariogram. Calculation ofa cross-correlogram involves calculating the correlation coefficientfor two variables between pairs of samples separated by some lagdistance, and then repeating the calculation for all lag distances ofinterest (cf. Goovaerts, 1998).

Spatial autocorrelation raises problems for classical statisticaltests, such as the ordinary least-squares (OLS) regression. This isdue to the violation of the independently distributed errorsassumption (Haining, 1990; Legendre, 1993), the underestimationof standard errors, and the inflation of Type I errors (Legendre,1993). In contrast, generalized least-squares (GLS) regressionexplicitly models the spatial component in residual terms, asdefined by a fitted semivariogram. Thus, the residuals containa strong spatial component that must be decomposed into spatiallystructured residuals and pure error terms using Cholesky decom-position (Haining, 2002). The resultant error vector, or noisecomponent (3), is given as:

3 ¼ L�1ðY � XbÞ (5)

where b is the vector of the estimated slopes and LLT¼ Cov, and Cov

is the covariance of the residuals. Cholesky decomposition of the

Table 2SMB summary statistics for each experimental site (0–30 cm depth).

Site Mean Median Minimum Maximum

(SMB: gC m�2)

550 m 36.5 35.7 10.1 71.1700 m 18.9 18.4 3.6 46.81500 m 44.9 43.3 24.9 89.5

covariance among the residuals will then allow the L matrix to beobtained. In GLS, this error term then becomes a function of themodel used to fit the semivariogram, and the effectiveness of GLS-based models, in terms of autocorrelation, can be judged by theabsence of spatial structures in the error term.

The model performance criteria were based on the AkaikeInformation Criterion (AIC), r2, and the F-test. Generally, lower AICscorrespond to closer approximations to reality, and therefore thebest model is the one with the lowest AIC. Differences in AIC values�3 are also generally considered to denote a ‘remarkable’ differencebetween models (Fotheringham et al., 2002). In addition, anapproximate likelihood ratio test based on the F-test can be used tocompare the relative performance of the models to replicateobserved data (Fotheringham et al., 2002).

The geostatistics used was mainly derived using the free soft-ware SAM (Spatial Analysis in Macroecology, Rangel et al., 2006,http://purl.oclc.org/sam/).

3. Results

3.1. Descriptive statistics

The three research sites were selected along an altitudinalgradient, representing different components of the northern slopeof Naeba Mountain’s typical landscape. Summary statistics for theSMB measurements (up to the depth of 30 cm) are provided inTable 2. The average SMB densities at the three sites varied between18.9 and 44.9 gC m�2, a difference of almost 2.5 times, whereas thecoefficient of variance (CV) for the densities ranged from 34% to49%. The largest average SMB density was observed at the highelevation site (1500 m site, 44.9 gC m�2), while the lowest wasrecorded at the 700 m site (18.9 gC m�2). Average SMB density atthe 550 m site was close to the overall median, being nearly 20%lower than the largest recorded value from the sites. ANOVArevealed that significant difference existed among different sites(P< 0.000). In contrast, average SOC showed a much more limitedrange across the three sites (3.9–4.5 kg m�2). Frequency distribu-tions for the average SMB measurements (up to 30 cm depth) fromeach site are given in Fig. 2.

3.2. Spatial patterns (kriging)

The spatial patterns of SMB density at each site are presented inFig. 3. The plot coordinates relate to relative scales, with the centerof the lower left corner corresponding to the pixel number 31 andset to (0, 0); pixel number 1 is located at the upper left corner and36 is at the bottom right corner. The highest SMB densities at the550 m site were recorded in the lower left area of the quadrat,which generally corresponded with the spatial distribution of SOC.Large SMB values were also apparent in the upper right area of the700 m site. Similarly, high SMB densities were recorded in theupper right corner of the 1500 m site.

Spatial patterns were also examined for the following environ-mental parameters: SOC, SMB/SOC, DOC, nitrogen, C/N, pH, bulkdensity, soil water content (SWC), root density, stone content, LF

Standard Deviation Kurtosis Skewness CV (%)

14.1 0.5 0.4 399.2 2.3 1.1 49

15.4 1.6 1.1 34

Fig. 2. Frequency distributions of average SMB measurements from up to 30 cm depthat the three experimental sites.

X. Zhao et al. / Soil Biology & Biochemistry 41 (2009) 1466–14741470

(slightly to moderately decomposed) layer density, L layer density, Flayer density, and A horizon depth. These were then used in theregression analyses.

3.3. Spatial autocorrelation

The Moran’s I and semi-variance results for different distancesacross each site are provided in Table 3; SMB semivariograms areshown in Fig. 4. A significant spatial autocorrelation was observedin the SMB of the 550 m site at small lag distances (<3.54 m,P¼ 0.002). A statistically significant spatial autocorrelation(P< 0.05) was also observed in the 1500 m site at a lag distance of10.6 m. There were no statistically significant autocorrelations(P< 0.05) at the 700 m site for any of the lag distances examined(<30 m).

Four types of variogram models were fitted for the semi-vari-ances of each site, and the model with the smallest RSS wasselected as the best-fit model. The results for SMB density at eachsite were as follows:

The 550 m site: the best-fit was provided by a spherical model,where C0¼ 44,700, C0þ C¼ 176,200, and A0¼ 46.01 (r2¼ 0.949;RSS¼ 1.88Eþ08).The 700 m site: the best-fit was provided by an exponentialmodel, where C0¼ 640, C0þ C¼ 9110, and A0¼ 2.15 (r2¼ 0.057;RSS¼ 3,503,953).The 1500 m site: the best-fit was provided by a linear model,where C0¼ 20,867.97, C0þ C¼ 20,867.92, and A0¼ 26.18(r2¼ 0.939; RSS¼ 4.09Eþ08).

Fig. 3. Spatial patterns of SMB at each experimental s

3.4. Correlation analysis

The relationships between SMB and the measured environ-mental parameters were examined with ordinary correlationanalysis, the results of which are presented in Table 4.

The correlation results for the 550 m site showed bulk density tohave the highest coefficient with SMB (r¼�0.54, P< 0.001), fol-lowed by N, C/N, SWC, SOC and stone content (r¼ 0.51,�0.49,�0.46,0.44 and 0.44, respectively, all at P< 0.01). Bulk density was theparameter that showed the highest correlation with SMB at the1500 m site (r¼ 0.52, P< 0.01), followed by DOC (r¼ 0.48, P< 0.05).However, there was no relationship between bulk density and SMBat the 700 m site, with only DOC, N and SOC exhibiting significantcorrelations (r¼ 0.51, 0.48 and 0.47, respectively, all at P< 0.01).

However, the above analyses do not take spatial autocorrelationinto account and therefore the degrees of freedom are over-estimated, leading to confidence intervals that are much narrowerthan they should be. Indeed, the data is not independent of spatialstructure and therefore this may confound the analysis, resulting inweakly correlated variables being associated with significantcoefficients (Rangel et al., 2006), as well as an increase in Type Ierrors and results that are not robust. Consequently, the aboveresults should be interpreted with caution.

Further analyses were then performed with spatial autocorre-lation taken into account. All of the previous correlations from the550 m site remained significant, albeit with different degrees offreedom and therefore lower F values and significance levels. Forexample, the corrected degrees of freedom from the SMB and bulkdensity correlation in the 550 m site dropped from 32 to 12.444, sothe F value and the corresponding P value dropped from 13.281 to5.008 and <0.001 to <0.05, respectively. Conversely, the degrees offreedom barely changed for the SMB and bulk density correlation atthe 1500 m site, and hence the P< 0.01 significance level wasmaintained. At the 700 m site, the significance levels for the SMBcorrelations with DOC and N also dropped from P< 0.01 to P< 0.05after the corrections.

The cross-correlograms and cross-variograms for the highestcorrelations from each site (SMB–bulk density for the 550 m and1500 m sites, and SMB–DOC for the 700 m site) are given in Fig. 5.There was a clear suggestion of negative spatial autocorrelation atshort distances (<10 m) in the cross-correlogram for SMB–bulkdensity at the 550 m site, with a peak in the positive autocorrela-tion at about 20 m. In addition, the Gaussian model provided thebest-fit cross-variogram for SMB–bulk density at the 550 m site(r2¼ 0.990). A similar pattern was observed in the cross-correlo-gram for SMB–bulk density at the 1500 m site, although here the

ite, extrapolated by kriging at a resolution of 1 m.

Table 3Moran’s I and semi-variance of SMB for each experimental site.

Site Count Distance (m) Moran’s I Standard deviation P I (max) I/I (max) Semi-variance

550 98 3.5 0.244 0.09 0.002 0.542 0.449 13,63142 8.5 0.057 0.147 0.551 0.611 0.094 18,59870 10.6 0.083 0.109 0.299 0.485 0.17 17,52660 13.1 0.018 0.121 0.691 0.53 0.033 19,15953 15.4 �0.032 0.13 0.99 0.485 �0.066 20,93064 17.9 �0.249 0.117 0.062 0.465 �0.536 26,21352 20.6 �0.22 0.13 0.146 0.506 �0.434 24,09061 23.1 �0.188 0.118 0.181 0.548 �0.343 25,17061 30.2 �0.157 0.108 0.242 0.675 �0.233 26,200

700 70 3.5 0.03 0.099 0.487 0.453 0.067 860231 8.5 0.041 0.163 0.624 0.459 0.09 726452 10.6 <0.001 0.12 0.746 0.515 <0.001 825840 13.1 �0.271 0.141 0.099 0.602 �0.45 10,24435 15.4 �0.026 0.152 0.937 0.585 �0.045 11,10239 17.9 0.017 0.143 0.697 0.63 0.027 864245 21.2 �0.062 0.129 0.855 0.539 �0.115 10,90539 27.2 �0.078 0.129 0.76 0.449 �0.173 7333

1500 67 3.5 �0.206 0.101 0.105 0.317 �0.649 31,55626 8.5 �0.352 0.179 0.083 0.768 �0.458 32,25744 10.6 0.234 0.131 0.036 0.5 0.469 24,21517 12.7 0.134 0.225 0.436 1.043 0.128 30,68848 15.0 0.039 0.126 0.521 0.406 0.096 23,93732 17.9 �0.131 0.16 0.579 0.529 �0.247 20,20036 21.2 �0.042 0.146 0.997 0.391 �0.108 13,62130 27.2 0.055 0.148 0.511 0.338 0.164 8292

X. Zhao et al. / Soil Biology & Biochemistry 41 (2009) 1466–1474 1471

peak positive autocorrelation appeared around 30 m and the best-fit cross-variogram was provided by a linear type model. Incontrast, the cross-correlogram for SMB–DOC at the 700 m siteshowed a continuously decreasing pattern, and spatial autocorre-lation appeared to disappear at distances >20 m. However, none ofthe models provided a fitted cross-variogram for SMB–DOC at the700 m site.

3.5. Regressions

Regression analyses were initially carried out using the OLSmethod, and alternative autoregression models were applied ifstrong autocorrelations were found in the model residuals.

For each site, the SMB measurements were regressed against thefollowing environmental variables: SOC, DOC, pH, N, C/N, bulkdensity (BD), SWC, root density (RD), stone content (SC), L layerdensity (LL), F layer density (FL) and horizon A thickness (A). Thebest-fit models were then chosen from a total of 4095 candidatemodels based on AIC. The best-fit models for each site, along witha number of independent variables, are as follows:

Fig. 4. Semivariograms of SMB for each experimental site.

The 550 m site : SMB gC m�2

� �

¼ 1:969DOCþ 54:980N� 49:339BDþ 2:263RDþ 7:820�AIC ¼ 257:67; r2 ¼ 0:64; P < 0:000

�ð6Þ

The 700 m site : SMB�

gC m�2�

¼ 1:034DOC� 13:566pHþ 59:657�AIC ¼ 195:68; r2 ¼ 0:34; P < 0:007

�ð7Þ

The 1500 m site : SMB�

gC m�2�

¼ �0:797C=Nþ 134:733BDþ 1:048A� 23:556�AIC ¼ 197:457; r2 ¼ 0:59; P < 0:000

�ð8Þ

The residuals for the above models are shown in Fig. 6. Auto-correlation analyses were performed on the residuals from eachmodel. This showed that the residuals for the 550 m site weresignificant at 0.05 autocorrelation (P¼ 0.012) at ca. 10.6 m (Moran’sI¼ 0.241) and those from the 700 m site were significant at 0.039 at

Table 4Correlation analysis for SMB in relation to other environmental parameters at eachexperimental site (n¼ 34, 27, and 25 for the 550 m, 700 m and 1500 m sitesrespectively. *P< 0.05; **P< 0.01; ***P< 0.001).

500 m 700 m 1500 m

SOC 0.44** 0.47** �0.08DOC 0.14 0.51** 0.48*pH �0.17 �0.25 0.25N 0.51** 0.48** 0.11C/N �0.49** �0.13 �0.27BD �0.54*** 0.32 0.52**SWC �0.46** 0.38 �0.16Root 0.30 �0.29 �0.29Stone 0.44** 0.02 0.02L layer 0.28 0.22 0.20F layer �0.04 �0.04 �0.20A horizon �0.01 0.18 0.37

-0.321

-0.160

0.000

0.160

0.321

0.00 10.00 20.00 30.00

Co

rrelo

gram

Separation Distance (h)

0.00 10.00 20.00 30.00

Separation Distance (h)

0.00 10.00 20.00 30.00Separation Distance (h)

0.00 10.00 20.00 30.00

Separation Distance (h)

0.00 10.00 20.00 30.00

Separation Distance (h)

0.00 10.00 20.00 30.00

Separation Distance (h)

SMB x BD: Isotropic Correlogram

-2.26

-1.70

-1.13

-0.57

0.00

Sem

ivaria

nc

e

SMB x BD: Isotropic Cross Variogram

Gaussian model (Co = -0.17000; Co + C = -2.35000; Ao = 16.76; r2 = 0.990;RSS = 0.0258)

-0.148

-0.074

0.000

0.074

0.148

Co

rrelo

gram

SMB x DOC: Isotropic Correlogram

0.07.5

14.922.429.8

Sem

ivaria

nc

e

SMB x DOC: Isotropic Cross Variogram

Spherical model (Co = 0.01000; Co + C = 22.48000; Ao = 6.10; r2 = 0.000;RSS = 130.)

-0.142

-0.071

0.000

0.071

0.142

Co

rrelo

gram

SMB x BD: Isotropic Correlogram

0.0000.1970.3940.5910.788

Sem

ivaria

nc

e

SMB x BD: Isotropic Cross Variogram

Linear model (Co = 0.52153; Co + C = 0.52153; Ao = 26.18; r2 = 0.535;RSS = 0.314)

550 m

700 m

1500 m

Fig. 5. Cross-variograms of SMB–bulk density at the 550 m and 1500 m sites, and SMB–DOC at the 700 m site.

X. Zhao et al. / Soil Biology & Biochemistry 41 (2009) 1466–14741472

<3.6 m (Moran’s I¼ 0.166). In contrast, the residuals for the 1500 msite were not significant at any distance.

GLS was then carried out on the data from the 550 and 700 msites, and the OLS and GLS regression results for these sites aregiven in Table 5. GLS was seen to improve the r2 at both sites,although the Moran’s I from the 700 m site was larger after GLSthan OLS, indicating that the improvement was insignificant at thissite. This was probably due to low significance level spatial auto-correlation remains in the OLS residuals for the site. Moreover, noimprovement was seen at the 1500 m site, since the spatial auto-correlation of this site’s OLS residuals was not significant. Therelative performance of GLS over OLS largely depends on the fit ofcross-variograms, which under many cases, has no accurate var-iogram model which consequently blurs the performance of GLS.

4. Discussion

4.1. Spatial autocorrelation of SMB and compatibility with soilproperties

The Moran’s I and semivariogram results suggested the presenceof SMB spatial autocorrelations at different scales in the beechecosystems. Small-scale spatial dependence was observed at scalesof <3.5 m at the 550 m site. Moreover, each site had large semi-variogram nugget values, which suggested spatial variation in SMBat much smaller scales than attainable under the applied samplingresolution. This observation is consistent with many previousstudies that have examined micro-scale SMB spatial autocorrela-tion in different ecosystems (e.g. Smith et al., 1994; Robertson et al.,

1997; Ritz et al., 2004). For instance, studies from steppe andagricultural ecosystems have suggested that SMB may be spatiallydependent at scales <1 m (Smith et al., 1994; Robertson et al.,1997).

A medium-scale (stand scale or field scale) SMB autocorrelationwas also observed in the 10–18 m range, although this was onlysignificant at the 1500 m site (P¼ 0.036, lag distance¼ 10.6 m).Even so, a P value of 0.062 was observed at the 550 m site forMoran’s I at a lag distance of 17.9 m, and a P of 0.099 was observedat a lag distance of 13.1 m at the 700 m site. Furthermore, of all thelag distances examined at the 700 m and 550 m sites, these gavethe smallest and second smallest P values, respectively. Thisfinding may be important as it could provide evidence for an SMBautocorrelation over a larger scale. Such a result has been sug-gested by previous studies, although it has not been proved. Forinstance, the range of SMB spatial dependence in a mixed spruce–birch stand has been reported to be 7.7 m (Saetre, 1999), a scalethat is comparable to the stand scale in the presented study. Ritzet al. (2004) found a number of soil microbial properties showa linear increase in semi-variance with no indication of a sill, butfailed to determine a geostatistical range for the properties,asserting that the range might be over 6.5 m. Accordingly, theresults presented here provide evidence to support their suggestedupper range.

Apparently, the understanding of micro-scale variability of SMBis currently widely acknowledged, as supported by a large nuggetvariance in many studies, which in other words, samples withincentimeters of each other may be as similar, or dissimilar, to thosewithin several tens of meters of each other (Mummey and Stahl,

-25

-20

-15

-10

-5

0

5

10

15

20

25

Resid

uals (g

C m

-2)

Resid

uals (g

C m

-2)

Resid

uals (g

C m

-2)

550 m

-20

-15

-10

-5

0

5

10

15

20

25700 m

-20

-15

-10

-5

0

5

10

15

20

251500 m

Fig. 6. OLS residuals for SMB in the three experimental sites.

Table 5GLS and OLS regressions for the two sites with significant spatial autocorrelations betwe

Site Variable OLS GLS Stan

550 m Constant 7.820 12.175 0.0DOC 1.969 1.842 0.4N 54.98 58.843 0.3BD �49.339 �52.171 �0.6Root 2.263 2.415 0.3r2 0.636 0.716Moran’s I 257.667 253.430

700 m Constant 59.657 76.457 0.0DOC 1.034 1.216 0.6pH �13.566 �18.339 �0.3r2 0.343 0.390Moran’s I 195.676 197.707

X. Zhao et al. / Soil Biology & Biochemistry 41 (2009) 1466–1474 1473

2003; Ritz et al., 2004). However, our results indicate that bi-scalespatial autocorrelations exist within the examination ranges. Thisagrees with previous studies, which have suggested that soilecological variables may be characterized by more than one scale ofvariability, since factors influencing variability operate at differentscales (Robertson and Gross, 1994). Saetre (1999) also showed thatpatches of spruce and birch correspond with a humus qualitygradient formed by accumulated leaf and/or root litter, which inturn are driven by canopy coverage and SMB. Similarly, the stand-scale SMB autocorrelation in beech forests may be due to gapdistributions, since different shrub species dominate the gaps (e.g.Sasa spp.) and each species provides different inputs to thebelowground ecosystem. However, topographic controls may alsocontribute to such inputs, and therefore these different factorsrequire further study.

Ordinary correlation analysis suggested that SMB spatialdistribution is controlled by different environmental factors. Forexample, SMB was found to be significantly correlated with bulkdensity at the 550 and 1500 m sites, DOC at the 700 and 1500 msites, and N at the 550 and 700 m sites. All of these relationshipsremained significant at P< 0.05 after correction for the spatialautocorrelation degrees of freedom effect. Similarly, all of theindependent variables from the 500 and 700 m sites were signifi-cant in both the OLS and GLS regressions (see Table 4).

None of the examined environmental factors showed a signifi-cant correlation at all of the three sites, and some of the factorsshowed different (negative or positive) correlations with SMB atdifferent sites. Hence, the factors controlling the spatial distributionof SMB may be diverse and responsive to local in situ conditions.This may lead to difficulties in discriminating between the factorsthat control SMB distribution above the stand scale, therebyhindering an important requirement of understanding landscape-scale variations. Nevertheless, we only examined three plots in ourstudy, and this is not adequate for landscape-scale modeling.Surveying more stands would greatly increase the chance ofdiscovering vital information, which could be used to draw generalconclusions about landscape-scale SMB spatial distribution.

4.2. Sample size of SMB and other soil properties

The appropriate sample sizes (n) for the measurement of SMBand other soil parameters were established by determining thedifferent relative minimum detectable differences (MDDs) prior tocalculating the iterative process of Mollitor et al. (1980):

n ¼ t2S2

MDD2 (9)

where: t is the value given by a Student’s t-test at n� 1 degrees offreedom, a¼ 0.05, and S is the standard deviation (normalized withaverage data).

en SMB and environmental parameters.

dard coefficient Standard error t P value

00 15.827 0.769 0.44855 0.548 3.362 0.00238 20.040 2.936 0.00727 13.822 �3.774 <0.00127 0.897 2.693 0.012

00 86.723 0.882 0.38723 0.299 4.061 <0.00183 7.251 �2.529 0.019

X. Zhao et al. / Soil Biology & Biochemistry 41 (2009) 1466–14741474

The results suggested that 10–19 samples are generally requiredfor SMB to meet a relative MDD of 20%, whereas only 6–10 samples areneeded for SOC (approximately half that of SMB). As a result, theirratio (SMB/SOC) generally requires a sample size of 9–16 at each site.

5. Conclusions

A geostatistical approach was used to analyze stand-scalespatial heterogeneity in SMB and various soil properties of Japanesecold-temperate beech forests. The results suggested SMB spatialautocorrelation generally exists at a lag distance of 10–18 m in all ofthe studied sites, and significant small-scale dependency was alsoobserved at the 550 m site (lag distance¼ 3.5 m).

Both ordinary correlation and geostatistical analyses revealedthat SMB was significantly correlated with bulk density at the 550and 1500 m sites, DOC at the 700 and 1500 m sites, and N at 550and 700 m sites. However, no factor was statistically significant atevery site, and some factors showed different (positive or negative)correlations with SMB at different sites. Hence, SMB tends torespond locally to in situ environmental conditions, which mayprevent the development of any general regression models that tryto estimate SMB from environmental factors above the stand scale,e.g. landscape scale.

OLS and GLS models were used to simulate the spatial distri-bution of SMB at each site. The OLS model residuals revealedsignificant spatial autocorrelations, and therefore the data requiredreprocessing. GLS models were seen to be superior to OLS models,but only where cross-variograms could be accurately fitted.

Although previous studies have emphasized micro-scale varia-tions in SMB, the stand-scale spatial autocorrelations identified inthe present study add to the understanding of SMB spatial distri-butions on practical and landscape scales.

Acknowledgments

We thank the members of the Institute of Silviculture, ShizuokaUniversity, for their support in both the field sampling and labo-ratory analyses.

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