Directory UMM :Data Elmu:jurnal:A:Applied Soil Ecology:Vol12.Issue3.Jul1999:
Applied Soil Ecology 12 (1999) 227±238
Designing belowground ®eld experiments with the help
of semi-variance and power analyses
John N. Klironomosa,*, Matthias C. Rilligb, Michael F. Allenc
a
Department of Botany, Fungal and Soil Ecology Lab, University of Guelph, Guelph, Ont., Canada N1G 2W1
Department of Plant Biology, Carnegie Institution of Washington, 260 Panama Street, Stanford, CA 94305, USA
c
Center for Conservation Biology, University of California, Riverside, CA 92521-0334, USA
b
Received 23 March 1998; received in revised form 14 January 1999; accepted 8 February 1999
Abstract
Soil microorganisms mediate below- and aboveground processes, but it is dif®cult to monitor such organisms because of the
inherent cryptic nature of the soil. Traditional `blind' sampling methods yield high sample variance. Coupled with low sample
size, this results in low statistical power and thus high type II error rates. Consequently, when null hypotheses are rejected they
are dif®cult to interpret further (either biologically insigni®cant or biologically signi®cant but statistically insigni®cant). To
help alleviate this problem and remove the `blindness' from belowground sampling we suggest researchers perform
geostatistical analyses to describe the spatial distribution of the organisms/processes coupled with power analyses to assess
required sample sizes. To illustrate this we intensively sampled the soil of a 3 m 10 m plot from a southern Californian
chaparral ecosystem and spatially-described a series of biological and chemical parameters. We then sampled again and
strati®ed the data in relation to plant location and evaluated the probability of detecting a 30% increase in abundance for each
variable. Overall, we found that soil organisms do not all function at similar scales, and preliminary spatial analyses help
determine which organisms are suitable for study under the scales of interest. Furthermore, the results predict that required
sample sizes and type II error rates will be signi®cantly reduced for many belowground variables parameters when using a
strati®ed sampling design. An understanding of how this spatial structure changes over time is also required to properly design
strati®cations and avoids bias. Thus, a priori spatial- and power-analyses can be useful tools in constructing samplingstrategies for belowground ®eld studies. # 1999 Elsevier Science B.V. All rights reserved.
Keywords: Soil ecosystem; Geostatistics; Power analysis; Microarthropods; Nematodes; Fungi; Bacteria; Arbuscular mycorrhiza; Soil
nutrients
1. Introduction
Soil organisms strongly in¯uence nutrient cycles
and primary productivity (Coleman and Crossley,
1996), and thus are important at regulating ecosystems
*Corresponding author. Tel.: +1-519-824-4120 x6007; fax:
+1-519-767-1991; e-mail: jklirono@uoguelph.ca
(Anderson, 1995). It is therefore crucial that soil
organisms be evaluated in experiments that assess
effects of perturbation on ecosystem functioning.
Yet, our understanding of the functioning of soil
organisms under ®eld settings has not advanced at
the same rate as other aboveground organisms, mostly
because of their cryptic nature which makes them
dif®cult to monitor (Dindal, 1990).
0929-1393/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 9 - 1 3 9 3 ( 9 9 ) 0 0 0 1 4 - 1
228
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Soil organisms are highly aggregated (Allen and
MacMahon, 1985; Klironomos et al., 1993; Smith et
al., 1994; Klironomos and Kendrick, 1995). Predicting
the locations of such clusters (hot spots) has not been
an easy task. More recently, geostatistics have been
used to describe the spatial distribution of soil organisms (Robertson and Freckman, 1995; Boerner et al.,
1996; Robertson et al., 1997), illustrating that they are
structured at various spatial scales. This is taken for
granted in aboveground studies where we can visualize the organisms of interest; in the belowground we
rarely have an a priori idea of where the organisms live
within the de®ned experimental areas. As a result,
researchers either sample in a random fashion, which
leads to an underestimation of population sizes,
increased population variance, and low statistical
power, or they develop strati®ed sampling schemes
based on erroneous strata weights, which leads to bias
(Van Noordwijk et al., 1985).
In laboratory pot experiments, it is not uncommon
to ®nd moderate to high changes in the abundance of
soil organisms (: 20±100%) in response to altered
environmental conditions such as elevated atmospheric CO2 or nutrient deposition (Klironomos et
al., 1996, 1997; Rillig et al., 1997). However, the
detection of such responses under ®eld conditions
has been less frequent (O'Neill, 1994). Typically in
®eld experiments, soil ecologists take 5±10 random
samples per treatment, and are often left reporting
non-signi®cant treatment effects. It has traditionally
been dif®cult to make any hard conclusions from such
results. The combination of low sample size and
highly clustered spatial distributions (lognormal data)
often lead to low statistical power in below-ground
monitoring programs, and thus high Type II error rates
(Peterman, 1990). The classical conclusion is that
soils are `well buffered' and `stable' and thus their
functioning are not affected by mild or even moderate
perturbation (Lucier and Haines, 1990).
This study is part of a larger study whose objectives
are to assess the effects of elevated CO2 on microbial
activity belowground in a Mediterranean-type ecosystem (Klironomos et al., 1996; Rillig et al., 1997). The
CO2 study is ongoing and utilizes a Free-Air CO2
Enrichment (FACE) ring (Hendrey, 1993) to manipulate the atmospheric CO2 concentration within the
14-m diam ring. Using a plot next to the FACE ring,
the objectives of the present study were to (1) describe
the spatial structure of various below-ground biotic
and abiotic parameters, (2) relate this spatial structure
to the location of the vegetation, and stratify the soil in
relation to areas of high and low activity, and (3) using
a separate dataset, test whether a strati®ed sampling
design is potentially better than a fully randomized
sampling design (i.e. reduce type II error rates) at
detecting changes in the belowground.
2. Materials and methods
2.1. Study site
This study was conducted at Sky-Oaks Biological
Field Station (338230 N, 1168370 W) in San Diego
County, California. The site is located approximately
75 km from the Paci®c Ocean to the west and 20 km
from the desert ¯oor to the east, at a 1300 m elevation.
The vegetation type is chaparral, and the soil is a sandy
loam (Ultic Haploxeroll). Over most of the chaparral
area at Sky-Oaks Adenostoma fasciculatum, A. sparsifolium and Ceanothus greggii account for more than
70% of the plant cover. This study was performed at a
portion of the site dominated by A. fasciculatum,
which was burned 2 years earlier, in order to monitor
above- and belowground responses to CO2 fertilization during succession in a Mediterranean-type ecosystem. This study is part of a preliminary analysis
prior to CO2 monitoring in a Free-Air CO2 Enrichment
(FACE) ring system.
2.2. Experimental design and sampling
On June 15, 1994, a 3 m 10 m plot was established next to a FACE ring. Forty-four samples were
taken at 1-m intervals throughout the plot and then 27
samples around each of three A. fasciculatum shrubs at
0.125-m intervals (total of 125 soil samples). Samples
were taken to a depth of 15 cm using a 10-cm diameter
corer. All samples were bagged and returned to the
laboratory for immediate analysis.
Roots were separated from the soil by dry sieving.
They were then oven-dried at 808C for 24 h to determine dry mass. Total organic matter was estimated as
loss on ignition at 5508C for 6 h (Jenny, 1980).
A differential ¯uorescent staining (DFS) procedure
was used to measure fungal and bacterial biomass as
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
described in Morris et al. (1997). Stained material was
then viewed under UV light (620 nm), where active
cells were detected as red ¯uorescence. Images under
the microscope were analyzed using a computer
image-analysis program. Preliminary analyses suggest
that this DFS method stains living bacterial cells and
active hyphal tips, making it a good indicator of
microbial activity (Morris et al., 1997).
Roots were stored in formalin acetic acid alcohol
(FAA) for at least 24 h. Roots were then cleared by
autoclaving for 15 min in 10% potassium hydroxide,
acidi®ed in FAA for 3 min and stained using Trypan
Blue. Fungal infection was quanti®ed using the magni®ed intersections method (McGonigle et al., 1990)
by inspecting intersections between the microscope
eyepiece cross-hair and roots at 200 magni®cation.
The proportion of root length containing arbuscules,
vesicles, and hyphae was determined.
Mycorrhizal spore abundance was calculated
directly by extracting AM fungal spores from soil
using (a) a wet-sieving technique (Klironomos et al.,
1993), and (b) differential centrifugation technique
(Ianson and Allen, 1986). They were then sorted at the
genus level.
Nematodes were extracted by the same wet-sieving/
sucrose centrifugation technique used for mycorrhizal
spores (Klironomos et al., 1993). Microarthropods
were extracted onto dishes containing ethylene glycol,
using a high ef®ciency canister-type soil-arthropod
extractor (Lussenhop, 1971). Collembolans and mites
were sorted and counted.
Soil nutrients measured included total Kjeldahl
nitrogen (Bremner and Mulvaney, 1982), ammonium,
and nitrate (Keeney and Nelson, 1982); total and
bicarbonate-extractable phosphorous (Olsen and Sommers, 1982). pH was determined electrometrically
(McLean, 1982). Soil moisture was calculated after
heating soil in an oven at 68C for 24 h.
2.3. Statistical analyses
Parametric descriptive statistics were calculated for
each of the biotic and abiotic parameters using the
SPSS software (version 6.1.1, SPSS, Chicago, IL).
These include the sample mean, standard deviation, as
well as the skewness and kurtosis of each set of
distributions. Where appropriate, data was log(x 1)
transformed prior to analysis.
229
The geostatistics software MGAP (Version 1.0,
RockWare, Wheat Ridge, CO) was used to calculate
semi-variograms from the ®eld data and to ®t various
models. Using unweighted least squares analysis, the
spherical models showed the best ®t in all cases. For
variables with skewed distributions, the data was
log(x 1) transformed prior to analysis. Spatial
dependence was de®ned as the proportion of the model
sample variance (C Co) explained by the structural
variance (C). Contour maps were created using MacGridzo (Version 3.3, RockWare, Wheat Ridge, CO)
following ordinary block kriging.
With this spatial information, it may be possible to
stratify the soil by abundance of each parameter. If the
abundance of each parameter is predictable over space
and time, then a strati®ed sampling design may lead to
higher statistical power in ®eld experiments. On the
other hand, if these distributions are not predictable,
then strati®cation may lead to increased bias. It was
not possible in this study to test the predictability of
distributions over time (seasons throughout the year),
but we could test for predictability over space. Distributions for each parameter were drawn of abundance Vs distance from the base of the nearest A.
fasciculatum shrub. With these distributions we then
described the boundary conditions for each parameter
using a form of boundary line analysis (Maller et al.,
1983). This better illustrates the maximum performance of each parameter at different distances.
Hot-spots and locations adjacent to hot-spots were
identi®ed using these distributions. We considered
hot-spots to be areas of peak activity with adjacent
areas of similar size-interval having a reduction in
activity by at least 25%. If these criteria were not met,
then hot-spots were not identi®ed and strati®cation
was not performed for that parameter since this would
lead to bias. On June 30, 1994, we collected another
125 samples from the same site, processed them as
described above, and tested the probability of detecting a 30% increase in abundance with strati®ed versus
fully random sampling. A 30% increase relates to
changes in abundance of soil organisms previously
found in CO2-enrichment experiments (Klironomos et
al., 1996). Twenty random samples were chosen either
from the predicted hot-spots, adjacent to the hot-spots
or from the total dataset. Power analyses were performed on a two-mean t-test using NCSS/PASS (Version 6.0, NCSS, Kaysville, UT).
230
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Table 1
Below-ground parameters in the 3 m 10 m plot at Sky-Oaks Biological Field Station
Soil variable
Mean
SD
Root biomass (mg kg soil)
Arbuscular infection (%)
Vesicular infection (%)
Hyphal infection (%)
Acaulospora spores (mm3 gÿ1 soil)
Glomus spores (mm3 gÿ1 soil)
Scutellospora spores (mm3 gÿ1 soil)
Total spores (mm3 gÿ1 soil)
Bacteria (mg kgÿ1 soil)
Fungi (mg kgÿ1 soil)
Microbial biomass (mg kgÿ1 soil)
Nematodes (# kgÿ1 soil)
Collembola (# kgÿ1 soil)
Mites (# kgÿ1 soil)
120.3
5.6
16.5
54.8
0.017
0.004
0.035
0.056
5.9
11.1
17.1
279.4
100.2
207.1
39.9
6.0
14.5
24.3
0.029
0.006
0.064
0.069
3.4
5.5
6.3
227.6
317.4
458.7
25.0
0
0
7.0
0
0
0
0
0.9
1.7
3.8
0.0
0.0
0.0
pH
% Water
% Organic matter
Total N (mg gÿ1 soil)
NH4 (mg kgÿ1 soil)
NO3 (mg kgÿ1 soil)
Avail P (mg kgÿ1 soil)
Total P (mg kgÿ1 soil)
6.86
1.74
5.98
1.22
2.24
6.05
12.96
251.24
0.14
0.64
3.44
0.44
0.59
3.51
2.49
86.98
6.44
0.39
0.92
0.73
1.00
1.00
7.20
104.00
ÿ1
Min.
Max.
Skewness
Kurtosis
185.0
22.0
61.0
99.0
0.143
0.027
0.376
0.384
17.7
26.8
31.6
956.0
1784.0
2291.0
ÿ0.639
0.746
0.483
0.044
2.241
2.291
2.741
2.171
0.945
0.652
0.171
0.548
3.965
3.033
ÿ0.367
ÿ0.693
ÿ0.526
ÿ1.040
4.960
4.664
8.405
5.277
0.791
ÿ0.243
ÿ0.709
ÿ0.092
15.700
9.487
7.21
5.28
17.73
5.20
3.60
21.50
18.20
451.60
ÿ0.228
1.946
0.945
6.040
ÿ0.019
1.070
ÿ0.186
0.409
0.228
7.591
0.791
52.861
ÿ0.739
2.057
ÿ0.438
ÿ0.660
Table 2
Variogram model parameters for soil variables in the 3 m 10 m plot at Sky-Oaks Biological Field Station
Soil variable
Lag
Sill
Root biomass
Arbuscular infection
Vesicular infection
Hyphal infection
Acaulospora spores
Glomus spores
Scutellospora spores
Total spores
Bacteria
Fungi
Microbial biomass
Nematodes
Collembola
Mites
pH
% Water
% Organic matter
Total N
NH4
NO3
Avail P
Total P
13
13
13
13
7
5
15
6
13
15
10
13
18
13
13
13
52
10
15
52
15
13
1200
37.0
0.22
630.0
111
215
42
750
8
15
298
50000
59000
120000
0.02
1.52
2.80
0.38
0.19
3.00
780
5630
Nugget
650.0
37.0
0.22
630.0
5.0
168.0
23.0
100.0
6.0
8.0
35.0
10000.0
30000.0
55000.0
0.01
1.52
1.45
0.12
0.10
2.57
630.0
2500.0
Range
r2
C/(C Co)
100
±
±
±
30
33
120
30
120
80
39
50
100
80
65
±
425
39
50
350
38
55
0.521
0.316
0.117
0.596
0.516
0.318
0.553
0.362
0.436
0.516
0.708
0.828
0.725
0.494
0.912
0.698
0.394
0.936
0.711
0.341
0.508
0.699
0.458
0.0
0.0
0.0
0.957
0.219
0.452
0.867
0.250
0.467
0.883
0.800
0.492
0.542
0.500
0.0
0.482
0.684
0.474
0.143
0.192
0.556
s2
1669.2
50.3
0.30
655.6
125.6
488.6
71.9
848.6
10.5
23.7
347
51983.6
99897
208641
0.02
10.6
7.0
0.40
0.34
12.31
1045
7892
Sill/s2
0.719
0.735
0.733
0.961
0.884
0.441
0.584
0.884
0.762
0.633
0.859
0.962
0.591
0.575
1.000
0.143
0.400
0.950
0.559
0.244
0.746
0.713
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
231
Fig. 1. Population isopleths for (a) root biomass, (b) bacterial biomass, and (c) fungal biomass in the 3 m 10 m plot. Black filled circles
represent locations for Adenostoma fasciculatum shrubs. Biomass intervals for roots >0, >30, >60, >90, >120, >150 mg gÿ1 soil;
bacteria >0, >3, >6, >9, >12, >15 mg kgÿ1 soil; fungi >0, >4.2, >8.4, >12.6, >16.8, >21 mg kgÿ1 soil.
3. Results
The biological and chemical variables analyzed in
this study were not randomly distributed in the soil,
and each had a unique distribution pattern (Table 1).
The distributions varied greatly, from the close-tonormally distributed `soil pH', to others such as
mycorrhizal spores, the two animal groups, and total
soil nitrogen which were highly skewed with high
levels of kurtosis. Soil nutrients and microbial populations varied across 1±2 orders of magnitude throughout the plot, but soil animal populations varied across
more than 3 orders of magnitude.
The proportion of the total model variance attributable to spatial structure [C/(C Co)] was high for
some variables but low for others (Table 2). It ranged
from 0.0 for all root infection parameters and water
content to > 0.80 for Acaulospora spores, total spores,
microbial biomass, and nematodes.
Some of the above variables that exhibited spatial
dependence were further explored by kriged maps
(Figs. 1±4). Mycorrhizal spores (Fig. 2) and microarthropods (Fig. 3) exhibited spatial gradients from
distinctive areas of low to high activity. Therefore,
samples taken close together would be more likely to
be correlated than samples taken farther apart. These
variables are very strongly structured spatially. Other
variables such as root biomass (Fig. 1), fungal and
bacterial biomass (Fig. 1), soil nutrients (Fig. 4), and
nematodes (Fig. 3) showed small isolated areas of
either very high or very low activity, within a larger
matrix of intermediate activity. Most of the isolated
points with low activity were associated with sites of
concentration of rocks (data not shown).
To determine if shrub location is important in
structuring biotic soil properties, we graphed the
respective activity versus the distance away from
the nearest A. fasciculatum shrub (Figs. 5±7). Some
232
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Fig. 2. Population isopleths for (a) Acaulospora, (b) Glomus, and (c) Scutellospora spore levels in the 3 m 10 m plot. Black filled circles
represent locations for Adenostoma fasciculatum shrubs. Spore number intervals for Acaulospora >0, >4, >8, >12, >16, >20 spores gÿ1 soil;
Glomus >0, >10, >20, >30, >40, >50 spores gÿ1 soil; Scutellospora >0, >6, >12, >18, >24, >30 spores gÿ1 soil.
variables had distinct peaks of activity in relation to
shrub location, i.e., root biomass and Acaulospora
spores, which peaked at a distance of 30±40 cm from
the base of the nearest shrub. Peaks for some other
parameters were not as sharp, but based on the criteria
mentioned in the methods, there were distinct peaks in
bacterial and nematode biomass near the base of the
shrubs and fungal biomass at a distance of 50 cm. For
each parameter we then attempted to stratify the data
based on distance and peak activity. ``Hot-spot'' (area
with peak activity) and ``adjacent-to-hotspot'' (area
next to peak activity) were de®ned for the ®ve parameters that showed peak activity at speci®c distances
(root biomass, bacterial biomass, fungal biomass,
Acaulospora spores and nematodes). For the other
parameters no attempt was made to stratify the data.
Using strati®ed and non-strati®ed datasets, we performed a power analysis on a two-sample t-test, where
one mean was the sample mean, and the other was a
30% increase of that mean (Table 3). Twenty random
samples were chosen to perform the test, and this was
repeated three times and then averaged. With all ®ve
groups, a strati®ed approach resulted in higher statistical power in detecting a 30% change in either the
hot-spot or the area adjacent to the hot-spot, compared
to using 20 random samples from the entire dataset
(Table 3). Results from the power analyses were used
to generate power curves for each parameter (Fig. 8).
It is clear that for root biomass, strati®ed sampling
does not greatly increase statistical power for any
particular sample size. This is because variability is
low, so power is high regardless of sample size.
However, for bacterial biomass, fungal biomass,
Acaulospora spores and nematodes, higher statistical
power can be reached with a signi®cantly smaller
sample size provided strati®ed sampling is used. If
Fig. 3. Population isopleths for (a) collembolan, (b) mite, and (c) nematode levels in the 3 m 10 m plot. Black filled circles represent
locations for Adenostoma fasciculatum shrubs. Intervals for collembolans >0, >100, >200, >300, >400, >500 individuals kgÿ1 soil;
mites >0, >100, >200, >300, >400, >500 individuals kgÿ1 soil; nematodes >0, >110, >220, >330, >440, >550 individuals kgÿ1 soil.
Table 3
Probability of detecting a 30% increase in abundance when sampling predicted hot-spots, areas next to hot-spots, and total area at random
(N 20)
Root biomass
Hot-spot
Adjacent to hot-spot
Total dataset
Mean
SD
30% increase of the mean
Power
162.31
114.28
130.02
15.11
21.70
37.28
211.00
148.56
169.03
1.000
0.999
0.911
Acaulospora biovolume
Hot-spot
Adjacent to hot-spot
Total dataset
0.046
0.002
0.014
0.021
0.010
0.028
0.060
0.0026
0.0182
0.559
0.054
0.076
Bacterial biomass
Hot-spot
Adjacent to hot-spot
Total dataset
7.33
5.61
6.20
3.41
2.26
3.38
9.53
7.29
8.06
0.532
0.652
0.413
Fungal biomass
Hot-spot
Adjacent to hot-spot
Total dataset
18.91
9.25
14.36
5.41
4.73
5.98
24.58
12.03
18.67
0.912
0.460
0.625
Nematodes
Hot-spot
Adjacent to hot-spot
Total dataset
450.21
313.16
322.88
139.23
122.68
193.34
585.27
407.11
419.74
0.866
0.678
0.354
234
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Fig. 4. Isopleths for (a) ammonium, (b) nitrate and (c) total nitrogen levels in the 3 m 10 m plot. Black filled circles represent locations for
Adenostoma fasciculatum shrubs. Intervals for ammonium >0, >0.5, >1, >1.5, >2, >2.5 mg kgÿ1 soil; nitrate >0, >3, >6, >9, >12,
>15 mg kgÿ1 soil; total nitrogen >0, >0.5, >1, >1.5, >2, >2.5 mg gÿ1 soil.
we target for power 0.75, then using the total dataset
one would need more than 200 samples for Acaulospora spores, 60 samples for nematodes, 50 samples for
bacterial biomass, and 35 samples for fungal biomass.
Using hot-spots, and provided that the spatial distribution remains constant, this is reduced to 35, 20, 35, and
20 respectively.
4. Discussion
The results from this study clearly illustrate that
many biotic and abiotic variables in soil are spatially
structured at scales of less than one meter. This spatial
information, particularly if it can be described over
time, can be used to design more statistically-powerful
experiments in the ®eld. The spatial organization of
soil micro-organisms and chemical cycles are linked
to that of primary producers (Allen and MacMahon,
1985; Jackson and Caldwell, 1993; Schlesinger et al.,
1996; Robertson et al., 1997) so plants can be used as
reference points to predict below-ground hot spots.
Different groups of organisms do not co-occur within
this relatively small area. Each is reacting to environmental conditions in different ways.
Nutrient and biotic variables were not randomly
distributed in this study. As a result, random sampling
without any a priori knowledge of distribution will
typically lead to high sample variance and low statistical power and thus high type II error rates (failure to
reject a null hypothesis that is false). For example,
mycorrhizal fungi have been shown to respond greatly
to increases in the concentration of atmospheric CO2
under laboratory conditions (O'Neill, 1994; Klironomos et al., 1996). Yet, this response is rarely statistically signi®cant in the ®eld (O'Neill, 1994). The
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Fig. 5. (a) Root, (b) bacterial and (c) fungal abundance in relation
to Adenostoma shrub location. H hot-spot; A Adjacent to hotspot. The line represents the upper boundary of maximum
performance for each variable.
present study indicates that spatial and power analyses
need to be performed as a preliminary study prior to
designing ®eld experiments. This may seem to be a
large amount of extra work, but without this preliminary information experiments may be doomed from
the start. Furthermore, a ``spatially structured'' sampling design will likely reduce sample size and
235
Fig. 6. (a) Acaulospora, (b) Glomus and (c) Scutellospora spore
abundance in relation to Adenostoma shrub location. H hot-spot;
A Adjacent to hot-spot. The line represents the upper boundary
of maximum performance for each variable.
increases statistical power, which would then be less
labor intensive in the long run.
The present analysis also demonstrates that most of
the soil variables measured here are spatially structured, but the scale at which each group functions is
different. As a result, independent sampling methods
need to be devised for each variable. Furthermore,
some variables are less suitable for ®eld monitoring
because they function at scales much smaller than
236
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Fig. 7. (a) Nematode, (b) collembolan, and (c) mite abundance in
relation to Adenostoma shrub location. H hot-spot;
A Adjacent to hot-spot. The line represents the upper boundary
of maximum performance for each variable.
those typically used by researchers. An example of
this is mycorrhizal root infection. This parameter is
highly dependent on root phenology (Allen, 1991;
Smith and Read, 1997) and its variance was not
explained by spatial autocorrelation. Thus, it was
spatially expressed at scales below the minimum
average separation distance used in this analysis.
Yet this is the most widely used parameter to track
mycorrhizal functioning in plants (Allen, 1991; Smith
and Read, 1997). Mycorrhizal fungal spores, on the
other hand, are more appropriate with regards to scale,
but even with a priori spatial analysis, they are still
quite variable and require high sample sizes. Moreover, there is still considerable debate on how to
interpret mycorrhizal spores levels in soil (Allen,
1991; Klironomos et al., 1993). At the present site,
fungal and bacterial biomass and nematodes proved to
be very good candidates. They had relatively low
variability in their distributions, and when combined
with hot-spots, less than 35 samples were required to
achieve adequate statistical power.
Other issues that need to be resolved are: does this
spatial heterogeneity change with season? And how
predictable is it among years? These questions need to
be addressed if we are going to use this method to its
fullest potential. It must be remembered that this
study, although sampling was intensive, reports data
from one location (one plot) and one point in time.
Thus, the results are speci®c to the Sky-Oaks site, and
furthermore it is certainly dangerous to extrapolate to
other seasons and locations. Robertson and Freckman
(1995) found autocorrelation with nematode trophic
groups, but this was in an agronomic system, and the
spatial heterogeneity was de®ned by tillage structure
at a larger spatial resolution than in our present study.
Also, Schlesinger et al. (1996) found very high spatial
autocorrelation structure in southwestern US desert
systems, but this was dependent on the present-day
shrub distribution of those areas as well as the grasslands that were present a century ago prior to invasion
by the shrubs.
The below-ground system has traditionally been
regarded as `out of sight, out of mind', and when
investigators took samples they tended to do so haphazardly. We need an a priori understanding of the
spatial organization of any variable in studies involving below-ground systems, if there is any hope for
powerful conclusions and interpretation of results. We
have shown that such an approach can increase statistical power and at the same time reduce sample size.
The strati®ed hot-spot approach may prove very useful. Hot-spots may be important for ecosystem function, but we are interested in changes, and these may
not be most important at hot-spots, but rather at
locations next to hot-spots. A small increase may
stimulate areas next to hot-spots proportionally more
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
237
Fig. 8. Relationship between sample size and statistical power when trying to detect a 30% increase in abundance ( 0.05), using data from
predicted hot-spots, areas adjacent to hot-spots, and total dataset. (a) root biomass, (b) Acaulospora spores, (c) bacterial biomass, (d) fungal
biomass, and (e) nematode individuals.
than at hot-spots. By knowing the location of hot-spots
it is then possible to design a study where one can use
random, strati®ed sampling (Krebs, 1989).
tance. This study was supported by a grant to MFA by
the Department of Energy, Program for Ecosystem
Research.
Acknowledgements
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Designing belowground ®eld experiments with the help
of semi-variance and power analyses
John N. Klironomosa,*, Matthias C. Rilligb, Michael F. Allenc
a
Department of Botany, Fungal and Soil Ecology Lab, University of Guelph, Guelph, Ont., Canada N1G 2W1
Department of Plant Biology, Carnegie Institution of Washington, 260 Panama Street, Stanford, CA 94305, USA
c
Center for Conservation Biology, University of California, Riverside, CA 92521-0334, USA
b
Received 23 March 1998; received in revised form 14 January 1999; accepted 8 February 1999
Abstract
Soil microorganisms mediate below- and aboveground processes, but it is dif®cult to monitor such organisms because of the
inherent cryptic nature of the soil. Traditional `blind' sampling methods yield high sample variance. Coupled with low sample
size, this results in low statistical power and thus high type II error rates. Consequently, when null hypotheses are rejected they
are dif®cult to interpret further (either biologically insigni®cant or biologically signi®cant but statistically insigni®cant). To
help alleviate this problem and remove the `blindness' from belowground sampling we suggest researchers perform
geostatistical analyses to describe the spatial distribution of the organisms/processes coupled with power analyses to assess
required sample sizes. To illustrate this we intensively sampled the soil of a 3 m 10 m plot from a southern Californian
chaparral ecosystem and spatially-described a series of biological and chemical parameters. We then sampled again and
strati®ed the data in relation to plant location and evaluated the probability of detecting a 30% increase in abundance for each
variable. Overall, we found that soil organisms do not all function at similar scales, and preliminary spatial analyses help
determine which organisms are suitable for study under the scales of interest. Furthermore, the results predict that required
sample sizes and type II error rates will be signi®cantly reduced for many belowground variables parameters when using a
strati®ed sampling design. An understanding of how this spatial structure changes over time is also required to properly design
strati®cations and avoids bias. Thus, a priori spatial- and power-analyses can be useful tools in constructing samplingstrategies for belowground ®eld studies. # 1999 Elsevier Science B.V. All rights reserved.
Keywords: Soil ecosystem; Geostatistics; Power analysis; Microarthropods; Nematodes; Fungi; Bacteria; Arbuscular mycorrhiza; Soil
nutrients
1. Introduction
Soil organisms strongly in¯uence nutrient cycles
and primary productivity (Coleman and Crossley,
1996), and thus are important at regulating ecosystems
*Corresponding author. Tel.: +1-519-824-4120 x6007; fax:
+1-519-767-1991; e-mail: jklirono@uoguelph.ca
(Anderson, 1995). It is therefore crucial that soil
organisms be evaluated in experiments that assess
effects of perturbation on ecosystem functioning.
Yet, our understanding of the functioning of soil
organisms under ®eld settings has not advanced at
the same rate as other aboveground organisms, mostly
because of their cryptic nature which makes them
dif®cult to monitor (Dindal, 1990).
0929-1393/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 9 - 1 3 9 3 ( 9 9 ) 0 0 0 1 4 - 1
228
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Soil organisms are highly aggregated (Allen and
MacMahon, 1985; Klironomos et al., 1993; Smith et
al., 1994; Klironomos and Kendrick, 1995). Predicting
the locations of such clusters (hot spots) has not been
an easy task. More recently, geostatistics have been
used to describe the spatial distribution of soil organisms (Robertson and Freckman, 1995; Boerner et al.,
1996; Robertson et al., 1997), illustrating that they are
structured at various spatial scales. This is taken for
granted in aboveground studies where we can visualize the organisms of interest; in the belowground we
rarely have an a priori idea of where the organisms live
within the de®ned experimental areas. As a result,
researchers either sample in a random fashion, which
leads to an underestimation of population sizes,
increased population variance, and low statistical
power, or they develop strati®ed sampling schemes
based on erroneous strata weights, which leads to bias
(Van Noordwijk et al., 1985).
In laboratory pot experiments, it is not uncommon
to ®nd moderate to high changes in the abundance of
soil organisms (: 20±100%) in response to altered
environmental conditions such as elevated atmospheric CO2 or nutrient deposition (Klironomos et
al., 1996, 1997; Rillig et al., 1997). However, the
detection of such responses under ®eld conditions
has been less frequent (O'Neill, 1994). Typically in
®eld experiments, soil ecologists take 5±10 random
samples per treatment, and are often left reporting
non-signi®cant treatment effects. It has traditionally
been dif®cult to make any hard conclusions from such
results. The combination of low sample size and
highly clustered spatial distributions (lognormal data)
often lead to low statistical power in below-ground
monitoring programs, and thus high Type II error rates
(Peterman, 1990). The classical conclusion is that
soils are `well buffered' and `stable' and thus their
functioning are not affected by mild or even moderate
perturbation (Lucier and Haines, 1990).
This study is part of a larger study whose objectives
are to assess the effects of elevated CO2 on microbial
activity belowground in a Mediterranean-type ecosystem (Klironomos et al., 1996; Rillig et al., 1997). The
CO2 study is ongoing and utilizes a Free-Air CO2
Enrichment (FACE) ring (Hendrey, 1993) to manipulate the atmospheric CO2 concentration within the
14-m diam ring. Using a plot next to the FACE ring,
the objectives of the present study were to (1) describe
the spatial structure of various below-ground biotic
and abiotic parameters, (2) relate this spatial structure
to the location of the vegetation, and stratify the soil in
relation to areas of high and low activity, and (3) using
a separate dataset, test whether a strati®ed sampling
design is potentially better than a fully randomized
sampling design (i.e. reduce type II error rates) at
detecting changes in the belowground.
2. Materials and methods
2.1. Study site
This study was conducted at Sky-Oaks Biological
Field Station (338230 N, 1168370 W) in San Diego
County, California. The site is located approximately
75 km from the Paci®c Ocean to the west and 20 km
from the desert ¯oor to the east, at a 1300 m elevation.
The vegetation type is chaparral, and the soil is a sandy
loam (Ultic Haploxeroll). Over most of the chaparral
area at Sky-Oaks Adenostoma fasciculatum, A. sparsifolium and Ceanothus greggii account for more than
70% of the plant cover. This study was performed at a
portion of the site dominated by A. fasciculatum,
which was burned 2 years earlier, in order to monitor
above- and belowground responses to CO2 fertilization during succession in a Mediterranean-type ecosystem. This study is part of a preliminary analysis
prior to CO2 monitoring in a Free-Air CO2 Enrichment
(FACE) ring system.
2.2. Experimental design and sampling
On June 15, 1994, a 3 m 10 m plot was established next to a FACE ring. Forty-four samples were
taken at 1-m intervals throughout the plot and then 27
samples around each of three A. fasciculatum shrubs at
0.125-m intervals (total of 125 soil samples). Samples
were taken to a depth of 15 cm using a 10-cm diameter
corer. All samples were bagged and returned to the
laboratory for immediate analysis.
Roots were separated from the soil by dry sieving.
They were then oven-dried at 808C for 24 h to determine dry mass. Total organic matter was estimated as
loss on ignition at 5508C for 6 h (Jenny, 1980).
A differential ¯uorescent staining (DFS) procedure
was used to measure fungal and bacterial biomass as
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
described in Morris et al. (1997). Stained material was
then viewed under UV light (620 nm), where active
cells were detected as red ¯uorescence. Images under
the microscope were analyzed using a computer
image-analysis program. Preliminary analyses suggest
that this DFS method stains living bacterial cells and
active hyphal tips, making it a good indicator of
microbial activity (Morris et al., 1997).
Roots were stored in formalin acetic acid alcohol
(FAA) for at least 24 h. Roots were then cleared by
autoclaving for 15 min in 10% potassium hydroxide,
acidi®ed in FAA for 3 min and stained using Trypan
Blue. Fungal infection was quanti®ed using the magni®ed intersections method (McGonigle et al., 1990)
by inspecting intersections between the microscope
eyepiece cross-hair and roots at 200 magni®cation.
The proportion of root length containing arbuscules,
vesicles, and hyphae was determined.
Mycorrhizal spore abundance was calculated
directly by extracting AM fungal spores from soil
using (a) a wet-sieving technique (Klironomos et al.,
1993), and (b) differential centrifugation technique
(Ianson and Allen, 1986). They were then sorted at the
genus level.
Nematodes were extracted by the same wet-sieving/
sucrose centrifugation technique used for mycorrhizal
spores (Klironomos et al., 1993). Microarthropods
were extracted onto dishes containing ethylene glycol,
using a high ef®ciency canister-type soil-arthropod
extractor (Lussenhop, 1971). Collembolans and mites
were sorted and counted.
Soil nutrients measured included total Kjeldahl
nitrogen (Bremner and Mulvaney, 1982), ammonium,
and nitrate (Keeney and Nelson, 1982); total and
bicarbonate-extractable phosphorous (Olsen and Sommers, 1982). pH was determined electrometrically
(McLean, 1982). Soil moisture was calculated after
heating soil in an oven at 68C for 24 h.
2.3. Statistical analyses
Parametric descriptive statistics were calculated for
each of the biotic and abiotic parameters using the
SPSS software (version 6.1.1, SPSS, Chicago, IL).
These include the sample mean, standard deviation, as
well as the skewness and kurtosis of each set of
distributions. Where appropriate, data was log(x 1)
transformed prior to analysis.
229
The geostatistics software MGAP (Version 1.0,
RockWare, Wheat Ridge, CO) was used to calculate
semi-variograms from the ®eld data and to ®t various
models. Using unweighted least squares analysis, the
spherical models showed the best ®t in all cases. For
variables with skewed distributions, the data was
log(x 1) transformed prior to analysis. Spatial
dependence was de®ned as the proportion of the model
sample variance (C Co) explained by the structural
variance (C). Contour maps were created using MacGridzo (Version 3.3, RockWare, Wheat Ridge, CO)
following ordinary block kriging.
With this spatial information, it may be possible to
stratify the soil by abundance of each parameter. If the
abundance of each parameter is predictable over space
and time, then a strati®ed sampling design may lead to
higher statistical power in ®eld experiments. On the
other hand, if these distributions are not predictable,
then strati®cation may lead to increased bias. It was
not possible in this study to test the predictability of
distributions over time (seasons throughout the year),
but we could test for predictability over space. Distributions for each parameter were drawn of abundance Vs distance from the base of the nearest A.
fasciculatum shrub. With these distributions we then
described the boundary conditions for each parameter
using a form of boundary line analysis (Maller et al.,
1983). This better illustrates the maximum performance of each parameter at different distances.
Hot-spots and locations adjacent to hot-spots were
identi®ed using these distributions. We considered
hot-spots to be areas of peak activity with adjacent
areas of similar size-interval having a reduction in
activity by at least 25%. If these criteria were not met,
then hot-spots were not identi®ed and strati®cation
was not performed for that parameter since this would
lead to bias. On June 30, 1994, we collected another
125 samples from the same site, processed them as
described above, and tested the probability of detecting a 30% increase in abundance with strati®ed versus
fully random sampling. A 30% increase relates to
changes in abundance of soil organisms previously
found in CO2-enrichment experiments (Klironomos et
al., 1996). Twenty random samples were chosen either
from the predicted hot-spots, adjacent to the hot-spots
or from the total dataset. Power analyses were performed on a two-mean t-test using NCSS/PASS (Version 6.0, NCSS, Kaysville, UT).
230
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Table 1
Below-ground parameters in the 3 m 10 m plot at Sky-Oaks Biological Field Station
Soil variable
Mean
SD
Root biomass (mg kg soil)
Arbuscular infection (%)
Vesicular infection (%)
Hyphal infection (%)
Acaulospora spores (mm3 gÿ1 soil)
Glomus spores (mm3 gÿ1 soil)
Scutellospora spores (mm3 gÿ1 soil)
Total spores (mm3 gÿ1 soil)
Bacteria (mg kgÿ1 soil)
Fungi (mg kgÿ1 soil)
Microbial biomass (mg kgÿ1 soil)
Nematodes (# kgÿ1 soil)
Collembola (# kgÿ1 soil)
Mites (# kgÿ1 soil)
120.3
5.6
16.5
54.8
0.017
0.004
0.035
0.056
5.9
11.1
17.1
279.4
100.2
207.1
39.9
6.0
14.5
24.3
0.029
0.006
0.064
0.069
3.4
5.5
6.3
227.6
317.4
458.7
25.0
0
0
7.0
0
0
0
0
0.9
1.7
3.8
0.0
0.0
0.0
pH
% Water
% Organic matter
Total N (mg gÿ1 soil)
NH4 (mg kgÿ1 soil)
NO3 (mg kgÿ1 soil)
Avail P (mg kgÿ1 soil)
Total P (mg kgÿ1 soil)
6.86
1.74
5.98
1.22
2.24
6.05
12.96
251.24
0.14
0.64
3.44
0.44
0.59
3.51
2.49
86.98
6.44
0.39
0.92
0.73
1.00
1.00
7.20
104.00
ÿ1
Min.
Max.
Skewness
Kurtosis
185.0
22.0
61.0
99.0
0.143
0.027
0.376
0.384
17.7
26.8
31.6
956.0
1784.0
2291.0
ÿ0.639
0.746
0.483
0.044
2.241
2.291
2.741
2.171
0.945
0.652
0.171
0.548
3.965
3.033
ÿ0.367
ÿ0.693
ÿ0.526
ÿ1.040
4.960
4.664
8.405
5.277
0.791
ÿ0.243
ÿ0.709
ÿ0.092
15.700
9.487
7.21
5.28
17.73
5.20
3.60
21.50
18.20
451.60
ÿ0.228
1.946
0.945
6.040
ÿ0.019
1.070
ÿ0.186
0.409
0.228
7.591
0.791
52.861
ÿ0.739
2.057
ÿ0.438
ÿ0.660
Table 2
Variogram model parameters for soil variables in the 3 m 10 m plot at Sky-Oaks Biological Field Station
Soil variable
Lag
Sill
Root biomass
Arbuscular infection
Vesicular infection
Hyphal infection
Acaulospora spores
Glomus spores
Scutellospora spores
Total spores
Bacteria
Fungi
Microbial biomass
Nematodes
Collembola
Mites
pH
% Water
% Organic matter
Total N
NH4
NO3
Avail P
Total P
13
13
13
13
7
5
15
6
13
15
10
13
18
13
13
13
52
10
15
52
15
13
1200
37.0
0.22
630.0
111
215
42
750
8
15
298
50000
59000
120000
0.02
1.52
2.80
0.38
0.19
3.00
780
5630
Nugget
650.0
37.0
0.22
630.0
5.0
168.0
23.0
100.0
6.0
8.0
35.0
10000.0
30000.0
55000.0
0.01
1.52
1.45
0.12
0.10
2.57
630.0
2500.0
Range
r2
C/(C Co)
100
±
±
±
30
33
120
30
120
80
39
50
100
80
65
±
425
39
50
350
38
55
0.521
0.316
0.117
0.596
0.516
0.318
0.553
0.362
0.436
0.516
0.708
0.828
0.725
0.494
0.912
0.698
0.394
0.936
0.711
0.341
0.508
0.699
0.458
0.0
0.0
0.0
0.957
0.219
0.452
0.867
0.250
0.467
0.883
0.800
0.492
0.542
0.500
0.0
0.482
0.684
0.474
0.143
0.192
0.556
s2
1669.2
50.3
0.30
655.6
125.6
488.6
71.9
848.6
10.5
23.7
347
51983.6
99897
208641
0.02
10.6
7.0
0.40
0.34
12.31
1045
7892
Sill/s2
0.719
0.735
0.733
0.961
0.884
0.441
0.584
0.884
0.762
0.633
0.859
0.962
0.591
0.575
1.000
0.143
0.400
0.950
0.559
0.244
0.746
0.713
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
231
Fig. 1. Population isopleths for (a) root biomass, (b) bacterial biomass, and (c) fungal biomass in the 3 m 10 m plot. Black filled circles
represent locations for Adenostoma fasciculatum shrubs. Biomass intervals for roots >0, >30, >60, >90, >120, >150 mg gÿ1 soil;
bacteria >0, >3, >6, >9, >12, >15 mg kgÿ1 soil; fungi >0, >4.2, >8.4, >12.6, >16.8, >21 mg kgÿ1 soil.
3. Results
The biological and chemical variables analyzed in
this study were not randomly distributed in the soil,
and each had a unique distribution pattern (Table 1).
The distributions varied greatly, from the close-tonormally distributed `soil pH', to others such as
mycorrhizal spores, the two animal groups, and total
soil nitrogen which were highly skewed with high
levels of kurtosis. Soil nutrients and microbial populations varied across 1±2 orders of magnitude throughout the plot, but soil animal populations varied across
more than 3 orders of magnitude.
The proportion of the total model variance attributable to spatial structure [C/(C Co)] was high for
some variables but low for others (Table 2). It ranged
from 0.0 for all root infection parameters and water
content to > 0.80 for Acaulospora spores, total spores,
microbial biomass, and nematodes.
Some of the above variables that exhibited spatial
dependence were further explored by kriged maps
(Figs. 1±4). Mycorrhizal spores (Fig. 2) and microarthropods (Fig. 3) exhibited spatial gradients from
distinctive areas of low to high activity. Therefore,
samples taken close together would be more likely to
be correlated than samples taken farther apart. These
variables are very strongly structured spatially. Other
variables such as root biomass (Fig. 1), fungal and
bacterial biomass (Fig. 1), soil nutrients (Fig. 4), and
nematodes (Fig. 3) showed small isolated areas of
either very high or very low activity, within a larger
matrix of intermediate activity. Most of the isolated
points with low activity were associated with sites of
concentration of rocks (data not shown).
To determine if shrub location is important in
structuring biotic soil properties, we graphed the
respective activity versus the distance away from
the nearest A. fasciculatum shrub (Figs. 5±7). Some
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J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Fig. 2. Population isopleths for (a) Acaulospora, (b) Glomus, and (c) Scutellospora spore levels in the 3 m 10 m plot. Black filled circles
represent locations for Adenostoma fasciculatum shrubs. Spore number intervals for Acaulospora >0, >4, >8, >12, >16, >20 spores gÿ1 soil;
Glomus >0, >10, >20, >30, >40, >50 spores gÿ1 soil; Scutellospora >0, >6, >12, >18, >24, >30 spores gÿ1 soil.
variables had distinct peaks of activity in relation to
shrub location, i.e., root biomass and Acaulospora
spores, which peaked at a distance of 30±40 cm from
the base of the nearest shrub. Peaks for some other
parameters were not as sharp, but based on the criteria
mentioned in the methods, there were distinct peaks in
bacterial and nematode biomass near the base of the
shrubs and fungal biomass at a distance of 50 cm. For
each parameter we then attempted to stratify the data
based on distance and peak activity. ``Hot-spot'' (area
with peak activity) and ``adjacent-to-hotspot'' (area
next to peak activity) were de®ned for the ®ve parameters that showed peak activity at speci®c distances
(root biomass, bacterial biomass, fungal biomass,
Acaulospora spores and nematodes). For the other
parameters no attempt was made to stratify the data.
Using strati®ed and non-strati®ed datasets, we performed a power analysis on a two-sample t-test, where
one mean was the sample mean, and the other was a
30% increase of that mean (Table 3). Twenty random
samples were chosen to perform the test, and this was
repeated three times and then averaged. With all ®ve
groups, a strati®ed approach resulted in higher statistical power in detecting a 30% change in either the
hot-spot or the area adjacent to the hot-spot, compared
to using 20 random samples from the entire dataset
(Table 3). Results from the power analyses were used
to generate power curves for each parameter (Fig. 8).
It is clear that for root biomass, strati®ed sampling
does not greatly increase statistical power for any
particular sample size. This is because variability is
low, so power is high regardless of sample size.
However, for bacterial biomass, fungal biomass,
Acaulospora spores and nematodes, higher statistical
power can be reached with a signi®cantly smaller
sample size provided strati®ed sampling is used. If
Fig. 3. Population isopleths for (a) collembolan, (b) mite, and (c) nematode levels in the 3 m 10 m plot. Black filled circles represent
locations for Adenostoma fasciculatum shrubs. Intervals for collembolans >0, >100, >200, >300, >400, >500 individuals kgÿ1 soil;
mites >0, >100, >200, >300, >400, >500 individuals kgÿ1 soil; nematodes >0, >110, >220, >330, >440, >550 individuals kgÿ1 soil.
Table 3
Probability of detecting a 30% increase in abundance when sampling predicted hot-spots, areas next to hot-spots, and total area at random
(N 20)
Root biomass
Hot-spot
Adjacent to hot-spot
Total dataset
Mean
SD
30% increase of the mean
Power
162.31
114.28
130.02
15.11
21.70
37.28
211.00
148.56
169.03
1.000
0.999
0.911
Acaulospora biovolume
Hot-spot
Adjacent to hot-spot
Total dataset
0.046
0.002
0.014
0.021
0.010
0.028
0.060
0.0026
0.0182
0.559
0.054
0.076
Bacterial biomass
Hot-spot
Adjacent to hot-spot
Total dataset
7.33
5.61
6.20
3.41
2.26
3.38
9.53
7.29
8.06
0.532
0.652
0.413
Fungal biomass
Hot-spot
Adjacent to hot-spot
Total dataset
18.91
9.25
14.36
5.41
4.73
5.98
24.58
12.03
18.67
0.912
0.460
0.625
Nematodes
Hot-spot
Adjacent to hot-spot
Total dataset
450.21
313.16
322.88
139.23
122.68
193.34
585.27
407.11
419.74
0.866
0.678
0.354
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J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Fig. 4. Isopleths for (a) ammonium, (b) nitrate and (c) total nitrogen levels in the 3 m 10 m plot. Black filled circles represent locations for
Adenostoma fasciculatum shrubs. Intervals for ammonium >0, >0.5, >1, >1.5, >2, >2.5 mg kgÿ1 soil; nitrate >0, >3, >6, >9, >12,
>15 mg kgÿ1 soil; total nitrogen >0, >0.5, >1, >1.5, >2, >2.5 mg gÿ1 soil.
we target for power 0.75, then using the total dataset
one would need more than 200 samples for Acaulospora spores, 60 samples for nematodes, 50 samples for
bacterial biomass, and 35 samples for fungal biomass.
Using hot-spots, and provided that the spatial distribution remains constant, this is reduced to 35, 20, 35, and
20 respectively.
4. Discussion
The results from this study clearly illustrate that
many biotic and abiotic variables in soil are spatially
structured at scales of less than one meter. This spatial
information, particularly if it can be described over
time, can be used to design more statistically-powerful
experiments in the ®eld. The spatial organization of
soil micro-organisms and chemical cycles are linked
to that of primary producers (Allen and MacMahon,
1985; Jackson and Caldwell, 1993; Schlesinger et al.,
1996; Robertson et al., 1997) so plants can be used as
reference points to predict below-ground hot spots.
Different groups of organisms do not co-occur within
this relatively small area. Each is reacting to environmental conditions in different ways.
Nutrient and biotic variables were not randomly
distributed in this study. As a result, random sampling
without any a priori knowledge of distribution will
typically lead to high sample variance and low statistical power and thus high type II error rates (failure to
reject a null hypothesis that is false). For example,
mycorrhizal fungi have been shown to respond greatly
to increases in the concentration of atmospheric CO2
under laboratory conditions (O'Neill, 1994; Klironomos et al., 1996). Yet, this response is rarely statistically signi®cant in the ®eld (O'Neill, 1994). The
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Fig. 5. (a) Root, (b) bacterial and (c) fungal abundance in relation
to Adenostoma shrub location. H hot-spot; A Adjacent to hotspot. The line represents the upper boundary of maximum
performance for each variable.
present study indicates that spatial and power analyses
need to be performed as a preliminary study prior to
designing ®eld experiments. This may seem to be a
large amount of extra work, but without this preliminary information experiments may be doomed from
the start. Furthermore, a ``spatially structured'' sampling design will likely reduce sample size and
235
Fig. 6. (a) Acaulospora, (b) Glomus and (c) Scutellospora spore
abundance in relation to Adenostoma shrub location. H hot-spot;
A Adjacent to hot-spot. The line represents the upper boundary
of maximum performance for each variable.
increases statistical power, which would then be less
labor intensive in the long run.
The present analysis also demonstrates that most of
the soil variables measured here are spatially structured, but the scale at which each group functions is
different. As a result, independent sampling methods
need to be devised for each variable. Furthermore,
some variables are less suitable for ®eld monitoring
because they function at scales much smaller than
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J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
Fig. 7. (a) Nematode, (b) collembolan, and (c) mite abundance in
relation to Adenostoma shrub location. H hot-spot;
A Adjacent to hot-spot. The line represents the upper boundary
of maximum performance for each variable.
those typically used by researchers. An example of
this is mycorrhizal root infection. This parameter is
highly dependent on root phenology (Allen, 1991;
Smith and Read, 1997) and its variance was not
explained by spatial autocorrelation. Thus, it was
spatially expressed at scales below the minimum
average separation distance used in this analysis.
Yet this is the most widely used parameter to track
mycorrhizal functioning in plants (Allen, 1991; Smith
and Read, 1997). Mycorrhizal fungal spores, on the
other hand, are more appropriate with regards to scale,
but even with a priori spatial analysis, they are still
quite variable and require high sample sizes. Moreover, there is still considerable debate on how to
interpret mycorrhizal spores levels in soil (Allen,
1991; Klironomos et al., 1993). At the present site,
fungal and bacterial biomass and nematodes proved to
be very good candidates. They had relatively low
variability in their distributions, and when combined
with hot-spots, less than 35 samples were required to
achieve adequate statistical power.
Other issues that need to be resolved are: does this
spatial heterogeneity change with season? And how
predictable is it among years? These questions need to
be addressed if we are going to use this method to its
fullest potential. It must be remembered that this
study, although sampling was intensive, reports data
from one location (one plot) and one point in time.
Thus, the results are speci®c to the Sky-Oaks site, and
furthermore it is certainly dangerous to extrapolate to
other seasons and locations. Robertson and Freckman
(1995) found autocorrelation with nematode trophic
groups, but this was in an agronomic system, and the
spatial heterogeneity was de®ned by tillage structure
at a larger spatial resolution than in our present study.
Also, Schlesinger et al. (1996) found very high spatial
autocorrelation structure in southwestern US desert
systems, but this was dependent on the present-day
shrub distribution of those areas as well as the grasslands that were present a century ago prior to invasion
by the shrubs.
The below-ground system has traditionally been
regarded as `out of sight, out of mind', and when
investigators took samples they tended to do so haphazardly. We need an a priori understanding of the
spatial organization of any variable in studies involving below-ground systems, if there is any hope for
powerful conclusions and interpretation of results. We
have shown that such an approach can increase statistical power and at the same time reduce sample size.
The strati®ed hot-spot approach may prove very useful. Hot-spots may be important for ecosystem function, but we are interested in changes, and these may
not be most important at hot-spots, but rather at
locations next to hot-spots. A small increase may
stimulate areas next to hot-spots proportionally more
J.N. Klironomos et al. / Applied Soil Ecology 12 (1999) 227±238
237
Fig. 8. Relationship between sample size and statistical power when trying to detect a 30% increase in abundance ( 0.05), using data from
predicted hot-spots, areas adjacent to hot-spots, and total dataset. (a) root biomass, (b) Acaulospora spores, (c) bacterial biomass, (d) fungal
biomass, and (e) nematode individuals.
than at hot-spots. By knowing the location of hot-spots
it is then possible to design a study where one can use
random, strati®ed sampling (Krebs, 1989).
tance. This study was supported by a grant to MFA by
the Department of Energy, Program for Ecosystem
Research.
Acknowledgements
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