Open Journal of Forestry
2013. Vol.3, No.1, 23-29
Published Online January 2013 in SciRes (http://www.scirp.org/journal/ojf) http://dx.doi.org/10.4236/ojf.2013.31005
Copyright © 2013 SciRes. 23
Enhanced Structural Complexity Index: An Improved Index for
Describing Forest Structural Complexity
Philip Beckschäfer1, Philip Mundhenk1, Christoph Kleinn1, Yinqiu Ji2,
Douglas W. Yu2,3, Rhett D. Harrison4
1Chair of Forest Inventory and Remote Sensing, Georg-August-Universität Göttingen, Göttingen, Germany
2State Key Laboratory of Genetic Resources and Evolution, Kunming Institute of Zoology, Chinese Academy of
Sciences, Kunming, China
3School of Biological Sciences, University of East Anglia, Norwich, UK
4Key Laboratory for Tropical Forest Ecology, Xishuangbanna Tropical Botanical Garden, Chinese Academy of
Sciences, Menglun, China
Received November 19th, 2012; revised December 19th, 2012; accepted December 30th, 2012
The horizontal distribution of stems, stand density and the differentiation of tree dimensions are among
the most important aspects of stand structure. An increasing complexity of stand structure is often linked
to a higher number of species and to greater ecological stability. For quantification, the Structural Com-
plexity Index (SCI) describes structural complexity by means of an area ratio of the surface that is gener-
ated by connecting the tree tops of neighbouring trees to form triangles to the surface that is covered by
all triangles if projected on a flat plane. Here, we propose two ecologically relevant modifications of the
SCI: The degree of mingling of tree attributes, quantified by a vector ruggedness measure, and a stem
density term. We investigate how these two modifications influence index values. Data come from forest
inventory field plots sampled along a disturbance gradient from heavily disturbed shrub land, through
secondary regrowth to mature montane rainforest stands in Mengsong, Xishuangbanna, Yunnan, China.
An application is described linking structural complexity, as described by the SCI and its modified ver-
sions, to changes in species composition of insect communities. The results of this study show that the
Enhanced Structural Complexity Index (ESCI) can serve as a valuable tool for forest managers and ecolo-
gists for describing the structural complexity of forest stands and is particularly valuable for natural for-
ests with a high degree of structural complexity.
Keywords: Forest Structure Index; Structural Complexity; Stem Map; Species Composition; NMDS
The importance of ecosystem structure to species richness
has been established through many studies. Already in the early
1960s MacArthur and MacArthur (1961) showed that the physi-
cal structure of a plant community was of greater importance
than the composition of plant species in determining bird diver-
sity. A meta-analysis by Tews et al. (2004) found that 85% of
85 reviewed studies on habitat heterogeneity and species rich-
ness conducted between 1960 and 2003 found a positive corre-
lation between richness and structural variables. As plants play
an important role in shaping the physical structure of many
environments (Lawton, 1983; McCoy & Bell, 1991) the struc-
tural complexity of plant communities has frequently been used
as an indicator of the diversity in other taxa (Whittaker, 1972;
Franzreb, 1978; Temple et al., 1979; Aber, 1979; Recher et al.,
1996; Moen & Gutierrez, 1997). Moreover, the habitat hetero-
geneity hypothesis (Simpson, 1949; MacArthur & Wilson,
1967) relates this positive association between species diversity
and structural complexity by suggesting that more complex
environments provide increased niche space and thus facilitate
specialization and avoidance of competition through spatial
segregation (Cramer & Willig, 2005). This further implies that
the structural complexity of a forest is of great importance for
the number and composition of species inhabiting it (Willson,
1974; Ambuel & Temple, 1983; Freemark & Merriam, 1986;
Spanos & Feest, 2007).
The multidimensional character of forest stands makes it
hard to describe structural complexity holistically. Canopy la-
yering, the presence of particular understory species, trees with
different bark types, and decaying logs and hollow trees (Do-
herty et al., 2000) have all been considered to be important
components of structural complexity. However, three-dimen-
sional stand structures are probably the most important of all
characteristics (Pretzsch, 1997). According to Pretzsch (2009),
the horizontal distribution pattern of trees, stand density, the
differentiation of dimensions, and species intermingling con-
stitute the most important aspects of stand structure that influ-
ence growth processes, habitats, species richness, and stability
of forest ecosystems. Kimmins (2005) suggests the spatial ar-
rangement of plants, both horizontally and vertically, the struc-
ture of tree canopies and the presence of canopy gaps, and
snags, and coarse woody debris are the principal characteristics
that influence the diversity of animals. While some of these
attributes are hard to define and difficult to measure in the field,
tree stem diameter and position are standard in measurement
protocols of forest inventories in countries like, for example,
the USA (United States Department of Agriculture Forest Ser-
vice, 2011) and Germany (Polley, 2007). Hence, this study fo-
cuses on these variables and defines structural complexity as
P. BECKSCHÄFER ET AL.
the spatial arrangement of plant dimensions, both horizontally
and vertically (Zenner & Hibbs, 2000).
Several indices have been developed in the past decades to
provide interpretable metrics of structural complexity and thus
facilitate comparisons among stands (Pommerening, 2002;
LeMay & Staudhammer, 2005; McElhinny, 2005). LeMay &
Staudhammer (2005) identify three groups of indices: 1) indices
based on tree attributes, 2) indices of spatial heterogeneity and
3) indices combining tree attributes and spatial heterogeneity.
While indices in groups 1) and 2) focus on only one aspect of
forest structural complexity, indices in group 3) intend to retain
more information and thus may provide more comprehensive
measures of structural complexity.
In this study we propose an index that integrates the hori-
zontal distribution of trees, stand density, and the differentiation
and intermingling of tree dimensions into one measure, while
requiring only data on tree position and diameter-at-breast-
height (DBH) for its calculation. Our index is a modification of
the Structural Complexity Index (SCI) developed by Zenner &
Hibbs (2000). In the first part of this study, we describe limita-
tions of the SCI and propose two modifications to create an
Enhanced Structural Complexity Index (ESCI). In the second
part, the SCI and ESCI are calculated for forest inventory data
from an upland landscape in Xishuangbanna, South China, and
results are compared. In the last part, we compare how the SCI
and ESCI correlate with turnover in insect species composition.
The Structural Complexity Index (SCI)
Zenner & Hibbs (2000) introduced the SCI, a formula that
mathematically integrates both vertical (size differentiation)
and horizontal (spatial position) components of forest structure.
It is based on the position of trees whose xy-coordinates are
complemented with a tree attribute, such as DBH or height, as a
z-coordinate. By a spatial tessellation approach (Delaunay,
1934) each tree is connected to its neighbours such that train-
gles are defined that form a continuous faceted surface, i.e. a
triangulated irregular network (TIN) (Figure 1). If tree height is
selected as the z-coordinate, this TIN can be visualized as con-
necting the tops of neighbouring trees. Instead of tree height,
any measured continuously or ordinally scaled tree attribute can
be chosen as the z-coordinate. The SCI is defined as the surface
area of the TIN in three dimensional space divided by the area
covered by its projection on a plane surface (Equation (1)). If all
trees have the same z-value (e.g. all trees have the same height
or basal area as in an even aged plantation) the SCI equals 1,
the lower limit of the SCI. For structurally more complex forest
stands the SCI is >1.
surface area ofTIN
rojected area ofTIN
Limitations of the SCI
We illustrate basic characteristics of the SCI with a set of
four simple forest stands which differ in their structural com-
plexity but have the same SCI value. All stands cover the same
area but vary in number of trees, range of tree height, and spa-
tial mingling of trees with different heights (Table 1, Figure 2).
Observe that a stand composed of 36 regularly planted trees
with a range of tree heights between 14 and 18 meters (Figure
2(a)) has the same SCI value as a stand with 8 trees and a range
of tree heights between 1 and 12 meters (Figure 2(c), Table 2).
Intuitively, these two stands have very different structures, and
it may be considered an undesirable property of the SCI that it
is not able to differentiate these stands.
Spatial distribution of stems (upper panel). Tri-
angulated irregular network calculated for stems
in the upper panel (lower panel).
Stand characteristics of example forest stands from Figure 2.
Range of tree
a) 160036 14 - 18 16.0 2.03 2
b) 160036 1 - 21 11.0 6.92 6
c) 16008 1 - 12 7.03 5.38 3
d) 160014 1 - 21 10.0 8.55 5
Four different forest stands (a, b, c, d) having the same Structural Com-
plexity Index (SCI) value. For stand characteristics see Tables 1 and 2.
Copyright © 2013 SciRes.
P. BECKSCHÄFER ET AL.
Structural Complexity Index (SCI) and Enhanced Structural Complex-
ity Index (ESCI’ and ESCI) values of example stands from Figure 2
and Table 1.
Stand SCI ESCI’ ESCI TIN area [m²] projected area [m²] VRM Trees/10 m2
a) 1.17 1.33 1.63 1295.77 1111.11 1.14.23
b) 1.17 1.17 1.43 1295.77 1111.11 1.00.23
c) 1.17 1.33 1.40 1295.77 1111.11 1.15.05
d) 1.17 1.17 1.27 1295.77 1111.11 1.00.09
The Enhanced Structural Complexity Index
We propose two modifications to the SCI to avoid the ambi-
guity described above and to better distinguish specific proper-
ties of structural complexity.
The two proposed modifications of the SCI towards the En-
hanced SCI (ESCI) are:
1) Incorporation of triangle orientations;
2) Incorporation of triangle orientations + stem density.
The first modification enables the index to distinguish forest
type a from type b, as in Figure 2. The two types do not differ
in stem density, and trees in both stands are located on a regular
grid with a spacing of 4 m. However, they differ in the range of
tree heights and in the mingling of tree dimensions. In forest
type b, there is a clear trend from small trees in the first row
towards larger trees in the last row. This can be imagined as a
forest edge in which tree height gradually increases towards the
forest interior or as adjacent strips of clear cuts, each at a dif-
ferent age. In contrast, forest type a is composed of only two
distinct tree heights; rows of 14 m high trees alternate with
rows of 18 m high. The resulting TINs have the same surface
area for both stands, resulting in the same SCI value.
To distinguish between these stand types, the orientation of
triangles in the TINs is quantified by a vector ruggedness
measure (VRM) (Equation (3)), adapted from a method pro-
posed by Hobson (1972) and Sappington et al. (2007). Here,
unit vectors are used to represent the orientation of a triangle
(Figure 3). To centre a unit vector at triangle i, the cross prod-
uct of triangle sides ai and bi is calculated. This results in a
vector that is divided by its own length to standardize length to
one. To ensure that all unit vectors are oriented upwards, unit
vectors with a negative z-coordinate are mirrored. All unit vec-
tors are summed, resulting in a new vector whose strength
(VSTR, Equation (2)) is divided by the number of triangles in
the TIN (n) and subtracted from 2 (Equation (3)). The resulting
VRM is a dimensionless measure that ranges from 1 (non-rug-
ged) to 2 (most rugged).
The ESCI’ is calculated by multiplying the SCI with the
VRM (Equation (4)). Based on the ESCI’ forest types a (ESCI’
= 1.6) and b (ESCI’ = 1.3) can clearly be distinguished (see
VSTR |ab |
ESCI'SCI *VRM (1)
The second modification enables one to discriminate among
forest types a and c and types b and d (Figure 2). Compared to
forest types a and b, types c and d contain fewer trees (8 and 12
trees respectively) and cover different height ranges (Table 1).
Since stem density is considered an important structural
characteristic (e.g. Pretzsch, 2009), the number of stems per
unit area is included in the ESCI by multiplying the number of
stems per 10 m2 with the ESCI’ (Equation (5)). Hence, the in-
dex calculated for stands with low stem densities is lower than
for stands with high stem densities. To avoid too much weight
being assigned to the stem density, a value of 1 is added to the
number of stems per 10 m2. The ESCI is a dimensionless meas-
ure >1 that increases with stem density, the intermingling of
trees with different attributes, and differences between tree at-
1No. of stems per 10 mESCI ESCI'* (5)
Case Study from Mengsong, Xishuangbanna,
Data Collection and Analysis
To investigate the ESCI and the ESCI’ compared to the SCI,
these indices were calculated for 28 plots of a forest inventory
carried out in Mengsong township, Xishuangbanna, Yunnan,
China (UTM/WGS84: 47 N 656355 E, 2377646 N, alt = 1600 m)
(Figure 4). Plots cover the study site along a disturbance gra-
dient from heavily disturbed shrub land, through secondary re-
growth to mature montane rainforest stands. Each plot consists
of nine circular 10 m-radius sub-plots (314.16 m2) arranged on
Unit vectors centred at each triangle of a TIN. The
vector ruggedness measure (VRM) quantifies the dis-
persion of these vectors: (a) Low VRM (low vector
dispersion); (b) High VRM (high vector dispersion).
VRM is used as a measure of the diversity of triangle
orientations, hence a measure to describe the min-
gling of tree dimensions.
Copyright © 2013 SciRes. 25
P. BECKSCHÄFER ET AL.
Location of the study site Mengsong in Xishuang-
banna, China. Black squares show plot locations
within the site.
a square grid with 50 m spacing (Figure 5). For sub-plots lar-
ger 250 m2, mean and median SCI values have been shown to
be scale-invariant (Zenner, 2005).
In each sub-plot, DBH and position (azimuth and distance to
sub-plot centre) were recorded for all trees with a DBH ≥ 10 cm.
SCI, ESCI’, and ESCI were calculated for each sub-plot using
basal area of each tree as the z-coordinate. Sub-plots without at
least three trees were assigned SCI, ESCI’ and ESCI values of
zero. The R statistical software (R Core Team, 2012) and the
geometry package (Grasman et al., 2011) were used for the
Delaunay triangulation. Per plot values were derived by aver-
aging all 9 sub-plot values per plot.
In five sub-plots (No. 1, 3, 5, 7, 9) per plot, insects were col-
lected using Malaise traps in April-May 2011. Malaise traps
were left in place for one week per plot and for each plot, spe-
cies composition was determined using high-throughput DNA
metabarcoding of the cytochrome oxidase subunit I (COI) bar-
code gene (Yu et al., 2012). Insect species were approximated
with 97% threshold-similarity Operational Taxonomic Units
(OTUs), each representing a cluster of similar COI sequences.
Insect community composition was examined by non-metric
multidimensional scaling (NMDS) (Legendre & Legendre,
1998; Quinn & Keough, 2002). NMDS maps the position of
plots in species space, in our case represented by the Jaccard
dissimilarities of Hellinger transformed per plot OTU counts
(Yu et al., 2012), onto a predefined number of axes in an itera-
tive search for an optimal solution. NMDS is commonly re-
garded as the most robust unconstrained ordination method in
community ecology (Minchin, 1987). The R package vegan
(Oksanen et al., 2007) was used for the ordination analysis. To
investigate whether a relationship exists between structural
complexity and turnover in insect species composition we used
the function envfit in the package vegan to calculate the fit of
environmental variables to the ordination scores. envfit maxi-
mises the correlation of environmental variables to the matrix
of ordination scores and uses a permutation test to evaluate the
probability of obtaining the resulting or a higher r2 value. P-
values stated here are based on 1000 permutations. To test whe-
ther differences in correlation coefficients between SCI, ESCI’
and ESCI are significant we took 1000 subsamples (without
replacement) of 26 observations from our field data. NMDS
ordinations were calculated for each subsample and the corre-
sponding r² values with SCI, ESCI’ and ESCI were calculated.
Subsequently, we applied Mann-Whitney U tests to investigate
whether differences of mean r² values of the replicated samples
From a total of 2890 trees that were recorded, each sub-plot
contained on average 11.47 trees, with numbers ranging from 0
to 34 trees per sub-plot. The basal area of individual trees var-
ied from 78.61 cm2 to 11,750 cm2.
Across all sub-plots, ESCI values are consistently higher and
cover a larger range than do ESCI’ values. The same is ob-
served if ESCI’ and SCI are compared (Figure 6).
In addition to the observed differences in index value range,
the indices treat special cases of tree arrangements differently.
For example, sub-plots 49_2 and 372_9 (Figure 7, upper panels)
have similar SCI values (1% difference), but their ESCI’ values
differ substantially (22.75% difference) (Table 3). However, in
Figure 7, sub-plots 49_2 and 90_1 still have similar structural
complexities, as measured by the ESCI’.
Plot design: Cluster plot consisting of
9 sub-plots arranged on a square grid
with 50 meters spacing between sub-
Box and ladder plot comparing paired SCI and ESCI’
observations (left) and paired SCI and ESCI observa-
Copyright © 2013 SciRes.
P. BECKSCHÄFER ET AL.
Depiction of tree positions (xy-coordinates; in meters) complemented
with basal area (BA) as the z-coordinates of sub-plots listed in Table 3.
Upper panels: Sub-plot 49_2 has a SCI value similar to sub-plot 372_9.
Based on the ESCI’ value 49_2 is similar to 90_1. Lower panels:
Sub-plots with similar ESCI’ values which would be distinguished by
their ESCI values. Note: ESCI ranks the sub-plots in a different order
Index values calculated for sub-plots shown in Figure 7.
[m²] SCI ESCI’ ESCI VRMNo. of
49_2 47.53 24911.01 524.15528.26 595.51 1.014
372_9 222.35 119133.61 535.791014.81 1790.07 1.8924
90_1 113.11 33290.73 294.31532.38 667.95 1.818
189_9 36.94 40896.36 1107.081445.78 1629.86 1.314
398_3 43.86 40417.48 921.441452.41 1729.81 1.586
192_8 166.83 133784.66 801.911473.12 2551.62 1.8423
The effect of the incorporation of the stem density term be-
comes clear when the sub-plots in Figure 7 (lower panels) are
examined. According to their SCI values, sub-plot 189_9 has a
higher structural complexity than does 398_3 or 192_8. ESCI
ranks sub-plot 189_9 as the least structurally complex and
192_8 as the most structurally complex (Table 3).
The number of NMDS dimensions was fixed to three after
visual examination of the scree plot of stress vs dimensions.
Three dimensions provided a satisfactory stress value of 9.24%.
There were highly significant (p < .001) correlations between
all three structural complexity indices and the NMDS ordina-
tion. The SCI shows the lowest r2 value of .51 followed by the
ESCI’ with r2 = .54 and ESCI with r2 = .59. Mean r2 values
based on 1000 sample replicates were significantly different
among all combinations of indices (p < .0001).
The number of stems per 10 m2 is a critical factor in the
ESCI formula. In the data set used in this study, we found that
(1 + No. of stems per m²) results in a range of values from 1 to
2.02, for 0 and 32 trees per sub-plot respectively. This range
does not assign a weight to the number of stems that outweighs
the other terms of the equation. SCI, VRM and stem density are
hence of approximately equivalent importance in determining
the ESCI value. For other data sets with a higher number of
stems per unit area, the relation to the base of 10 m2 probably
leads to density values that dominate the resulting ESCI value.
A higher stem density might occur, for example, in different
forest types, succession stages with high stem numbers, or if
the DBH threshold is lower than 10 cm. In these cases it might
be more informative to calculate ESCI’ and stem density sepa-
rately to describe structural complexity and to make inferences.
The addition of 1 to the number of stems per 10 m2 assigns a
greater weight to low stem densities but has little influence if
stem densities are high. This weighting takes into account that
with increasing density, the potential for a spatial differentia-
Sub-plots in which stems were mapped for this analysis
cover an area of 314.16 m2, which is sufficiently large for the
calculation of the SCI (Zenner, 2005). Nevertheless, due to the
high scale dependency of forest structure (Franklin et al., 2002;
Zenner, 2005), this plot size is probably at the lower bound of
an adequate size. A further investigation of the variability of
ESCI’ and ESCI values at varying scales is recommended to
achieve deeper insights regarding the minimum plot size for
calculations of these indices.
In the structural assessment of forests, the inclusion of small
diameter trees was found to enhance the detection of structure
types (Zenner et al., 2011). In future studies it might be inter-
esting to analyse whether ESCI’ and ESCI show a similar re-
sponse if trees with a DBH < 10 cm are considered.
Comparing SCI, ESCI’ and ESCI, we find that the stronger
emphasis on the intermingling of tree dimensions through the
incorporation of the VRM as a measure of surface ruggedness
improves the ability of the index to discriminate among stand
conditions. This might result in a better utility of the index. For
example, it could be used for a separation of forest edges with
increasing tree height from other spatial arrangements of tree
dimensions typical for forest interiors. Such discrimination
makes sense from an ecological point of view since forest edges
are characterized by a distinct microclimate and resource spec-
trum, with corresponding effects on species composition and
abundance (McDonald & Urban, 2006). If in addition to the
VRM, the stem density of a forest is taken into account, the
ability to unambiguously characterize forest structural comple-
xity is increased again. Ecologists and forest managers likewise
consider stem density as an important aspect of structural com-
plexity because it determines the mean growing space per plant
and hence is an indicator of competition for resources within
the stand (Pretzsch, 2009). Changing stem density is the princi-
pal way forest managers manipulate forests (Davis et al., 2001),
and these changes alter forest habitats with consequences for
A possible ecological relevance of the modifications of the
SCI is indicated by the correlation of the index values with the
NMDS ordination, which describes turnover in insect species
composition. Compared to the SCI, significantly stronger corre-
lations with the NMDS ordination were observed for the ESCI’
and the ESCI. The observed correlations support the habitat he-
terogeneity hypothesis by suggesting that the structural comple-
xity of a habitat influences the insect species community com-
position. The higher r2 values for ESCI’ and ESCI suggest that
Copyright © 2013 SciRes. 27
P. BECKSCHÄFER ET AL.
these indices perform at least as well and possibly better in de-
tecting this relationship. Nevertheless, the increase in r2 values
was only moderate, and hence it would be valuable to test the
indices for structural complexity against other data sets from
different geographic regions and taxa and to assess associations
at multiple spatial scales.
The results of this study show that the suggested modifica-
tions to the SCI are valuable improvements that increase the
ability to characterize the structural complexity of forests.
ESCI’ and ESCI allow for a more complete view of a forest
structure than the SCI. This makes these indices relevant to
ecologists, forest scientists, and forest managers who are inter-
ested in the relationship between ecosystem structure and bio-
Above all, we are indebted to the Advisory Group on Inter-
national Agricultural Research (BEAF) at the German Agency
for International Cooperation (GIZ) within the German Minis-
try for Economic Cooperation (BMZ) for funding this research
(project number 08.7860.3-001.00 “Making the Mekong Con-
nected”—MMC). We are grateful to all members of the
MMC-project for excellent support in coordinating and imple-
menting research and field work, and in particular to the head
of the project Prof. Dr. Xu Jianchu and the “various fathers” of
the project including Dr. Horst Weyerhäuser and Dr. Timm
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