how is shrub cover related to soil moisture and patch geometry in
TRANSCRIPT
Abstract Among the major challenges of land-
scape ecologists is to develop relatively simple
models to quantify ecological processes over large
areas. Application of such models can be well
demonstrated in fragmented semi-arid ecosys-
tems where competition over resources is intense
due to habitat loss, however, only a few studies
have done so. Our aim was to model and study
the integrated effect of spatial variation in po-
tential soil moisture and patch size and shape on
shrub–grass ratio (SGR) in a semi-arid frag-
mented environment. We specifically ask: (i) what
factors most strongly relate to SGR in large
remnant patches (>1.6 ha), and (ii) do different
factors more strongly relate to SGR in small
patches ( <1.6 ha)? The study was carried out
using 60 patches within a semi-arid fragmented
environment in the Northern Negev of Israel.
Aerial photographs and digital elevation models
were used to map six environmental variables:
wetness index, aspect, rock cover, rock pattern,
patch area, and patch shape. The variables were
designed in GIS and were modeled using fuzzy
logic procedures to predict SGR, and these pre-
dictions were compared to shrub cover maps ex-
tracted using maximum likelihood classification
of aerial photographs taken in September 2003.
We found that in the study area, factors indicating
potential soil moisture are most strongly related
to SGR in large patches, whereas patch geometric
attributes are more strongly relate to SGR in
small patches.
Keywords Aerial photographs Æ Digital
elevation models (DEM) Æ Fuzzy logic Æ Patch
scale Æ Geographical information systems (GIS)
Introduction
Semi-arid and arid regions occupy approximately
one third of the global land surface and constitute
an important source of living for pastoral societies
(Hille Ris Lambers et al. 2001). These regions
were widely studied as indicators to desertifica-
tion processes that may occur due to climate and/
or land-use changes (Le Houerou 1996). The
vegetation in these regions is dominated by two
contrasting formations (Schlesinger et al. 1990;
Milne et al. 1996; House et al. 2003). The first is
woody vegetation, such as shrubs and dwarf
shrubs that are usually spatially structured as
single or multiple shrub patches. The second
formation is herbaceous vegetation, which is
usually grasses forming the matrix or intercanopy
space between shrub patches.
T. Svoray (&) Æ S. Mazor Æ P. Bar (Kutiel)Department of Geography and EnvironmentalDevelopment, Ben-Gurion University of the Negev,Beer-Sheva 84105, Israele-mail: [email protected]
Landscape Ecol (2007) 22:105–116
DOI 10.1007/s10980-006-9004-3
123
RESEARCH ARTICLE
How is shrub cover related to soil moisture and patchgeometry in the fragmented landscape of the NorthernNegev desert?
Tal Svoray Æ Shira Mazor Æ Pua Bar (Kutiel)
Received: 31 July 2005 / Accepted: 30 March 2006 / Published online: 19 May 2006� Springer Science+Business Media B.V. 2006
The relative covers of the two forma-
tions—named in several studies as the shrub–
grass ratio (SGR)—determine many ecosystem
properties (Belsky 1994; Scholes and Archer
1997). This ratio is related to demographic pro-
cesses such as plant germination, establishment
and transition to maturity. These processes are
usually limited by climatic variation, grazing and
fire (Sankaran et al. 2004). However, studies
show that in semi-arid ecosystems, SGR depends
mostly on variation in soil moisture in both ver-
tical and horizontal dimensions and less on
demographic processes. The effect of vertical soil
moisture variation on SGR has been widely
studied (e.g., Fernandez-Illescas and Rodriguez-
Iturbe 2003), mainly based on Walter’s two-layer
model (Walter 1971). Vertical soil moisture in the
root zone depends mainly on soil porosity be-
cause of greater evaporation rates (van Wijk and
Rodriguez-Iturbe 2002). In the horizontal
dimension, the spatial variation of soil moisture
has been studied mainly through the effect of
shrubs as landscape engineers (Wilby and Sha-
chak 2004), focusing on variation between canopy
and intercanopy areas (Schlesinger et al. 1990).
Attempts have also been made to couple the two
dimensions of soil moisture variation (Breshears
and Barnes 1999).
These existing frameworks are very useful in
understanding the effect of spatial variations in
potential soil moisture on plants in a spatially
homogenous environment, yet they ignore the
effect of other environmental variables, such as
rock cover, aspect and topographic drainage area.
As such, these frameworks would be insufficient
in recognizing the factors and mechanisms that
govern SGR at patch and landscape scales. This
research gap is especially enhanced in fragmented
semi-arid areas, where in many cases habitat
subdivision complicates shrub–grass competition–
facilitation (Levin 1974; Shmida and Ellner 1984).
Due to extensive use of open areas for agri-
cultural purposes in large parts of the world,
many ecosystems in different environments suffer
habitat loss (Fahrig 2003). Agricultural fields and
urban areas divide the natural environment,
causing landscape fragmentation and reducing
habitat areas. The resulting patches subsequently
create different habitat characteristics than their
pre-fragmented habitat. The most significant ef-
fect of habitat loss on vegetation is expressed by
reduced species richness in remnant patches
(Haila 2002) and by diminishing genetic diversity
(Gibbs 2001). Therefore, we expect that a frag-
mented area in a semi-arid environment will
maintain a complex competition–facilitation
relationship that will yield spatial variation in
SGR depending on potential soil moisture and
geometric factors of the remnant patches.
Despite the need to understand the mecha-
nisms that govern SGR in remnant patches, few
studies provide a spatially explicit examination of
the combined effect of soil moisture and patch
geometry on SGR in fragmented lands. This
might be due to the difficulties involved in map-
ping rock cover and topographic characteristics at
the plant to patch scale. It might also be related to
the lack of an advanced modeling approach that
expresses the complexity of the environment and
the integrated effect of environmental variables.
The aim of this research is to study how spatial
variations in potential soil moisture and patch
geometry relate to SGR based on 60 remnant
patches in a semi-arid fragmented environment.
There are four specific objectives: (i) to explore
the spatial patterns of environmental and geo-
metric properties in the patches; (ii) to relate
these patterns with the spatial pattern of SGR
observed from aerial photographs; (iii) to discuss
the implications and underlying mechanisms of
the spatial patterns found; and (iv) to discuss the
mechanisms that prevent the patches from real-
izing their SGR potential. In exploring how spa-
tial variations in environmental variables relate to
the SGR, we specifically addressed two questions:
(i) what factors most strongly relate to SGR in
large remnant patches (>1.6 ha), and (ii) do dif-
ferent factors more strongly relate to SGR in
small patches ( <1.6 ha)?
Study site
The study area (Fig. 1) is approximately 1,000 ha
in size and is located in the Northern Negev, Is-
rael (31�19¢E; 54�34¢N; 200–350 m a.s.l.). Its cli-
mate is semi-arid according to the Koppen
climatic regions (class BSh). Mean annual rainfall
106 Landscape Ecol (2007) 22:105–116
123
is 300 mm, falling mostly in the winter, between
October and March. Mean annual temperatures
are 25�C in summer and 11.5�C in winter
(Zangvil 1988). The lithology is formed from
Eocene calcareous rocks, including chalk, lime-
stone, and flint with a Nari cover (calcareous
caliche crust—Buchbinder 1969). The soil is light
brown Loess (soil from aeolian source charac-
terized by large presence of calcareous
material— Dan 1988). The natural vegetation
association is Sarcopoterium spinosum and
Phlomis brachyodon dwarf shrubs, with diverse
annual and perennial herbaceous species (Danin
1988). Differences in shrub cover between south-
and north-facing slopes and there is a close
association between rock cover and shrub cover
due to improved water conditions in the margins
of the Nari rocks (Danin 1988). Studies on a
more detailed scale have reported high spatial
variation in shrub cover between slope sub-units
and with some association to topographic units
and rock cover (Sternberg and Shoshany 2001;
Shoshany and Svoray 2002; Ackermann et al.
2004). The study area has been extensively
cultivated since 1948 by means of modern agro-
technology, leaving remnant patches of the prior
habitats (Efrat 1994). Wheat and peas are the
main agricultural crops that are grown during
winter, which are harvested in late spring (May
and June). From June to September herds of
sheep graze on the stubble left on the cropland
and occasionally on the vegetation they find in
the remaining remnant patches. Thus, the earlier
semi-natural environment has experienced habi-
tat loss and fragmentation, and shrubs and
grasses in remnant patches strongly compete for
soil moisture and other resources (Bar [Kutiel]
et al. 2005).
Methods
We used fuzzy modeling techniques embedded in
a high-resolution GIS to predict environmental
Fig. 1 The study area within the Northern Negev—Israel. The landscape is fragmented into 60 patch surrounded by wheatfields. The aerial photograph was acquired on 20 September 2003 under late summer conditions
Landscape Ecol (2006) 22:105–116 107
123
variables and geometric attributes for remnant
patches. Rock cover and topography were used to
predict the spatial variation in potential soil
moisture and patch shape and size represented
the geometric limitations of the patches.
Environmental variables
The study area was aerially photographed on 20
September 2003 (at noon, under clear sky condi-
tions) using four stereo-pairs with 60% overlap at
a spatial resolution of 12.5-cm pixels. The aerial
photographs were geometrically adjusted to the
Israel New Grid, with 24 ground control points
that were measured in the field with a Differential
GPS (sub-meter resolution). The resulting root
mean square error of the geometric adjustments
is, in all cases, of less than 1 pixel. The Ortho-
BASE PRO module of ERDAS IMAGINE was
used for the extraction of a stereoscopic model of
the study area, A triangulation model was used
for production of a 1-m grid resolution Digital
Elevation Model (DEM) covering the overlap-
ping areas of the stereo-pairs. The DEM accuracy
was tested against actual field measurements for
slope gradient, based on the procedure suggested
in Walker and Willgoose (1999). A high correla-
tion was achieved between the predicted slope
gradient values and actual field measurements
(r2 = 0.86; n = 22; P < 0.0001).
The aerial photographs and the DEMs were
used to map six variables.
Wetness index (WI)
Water redistribution along the slopes results from
accumulated moisture created by upper and lower
runoff flow. In a given area, accumulated runoff
may depend on two topographic factors: the up-
per drainage area and the slope gradient. The
wetness index constitutes the mathematical
expression of these two factors and expresses the
potential moisture accumulation of each cell in
the raster data file that represents the study area
(Barling et al. 1994):
WIi ¼ LnAsi
tan bi
� �ð1Þ
where As is the upper drainage area of a given
cell (i) in m2, and b represents the gradient angle
of the cell’s slope in degrees. Using this topo-
graphic-based index, cells that are in close
proximity to the watershed divide would have
lower potential moisture values than those closer
to the channel, and cells with a steeper gradient
would have lower moisture values than those
with a more moderate slope. Runoff yield may
also depend on factors such as surface cover, soil
type and rainfall intensity (Yair and Kossovsky
2002), but we expect that WI will represent the
effect of topography on redistribution of water
in the down-slope direction by overland and
subsurface flow, which are largely generated
from bare intercanopy patches. The water will
redistribute to adjacent, lower, vegetated inter-
canopy patches, demonstrating connectivity be-
tween the vegetated and non-vegetated patches
(Reid et al. 1999). Shachak (unpublished data)
reported that at similar sites, shrub patches on
the slopes capture the surface runoff water,
where it can become subsurface flow and move
down slope. A mean WI value was assigned for
each patch.
Aspect category (AC)
Variation in radiation flux density causes differ-
ences in the levels of ground evaporation on
slopes with different orientations. Consequently,
evaporation on the steep south-facing slopes in
the northern hemisphere can be up to three times
higher than on equivalent north-facing slopes and
therefore, soil moisture on south-facing slopes is
expected to be low in comparison to north-facing
slopes (Kutiel 1992). Slope aspect was calculated
in degrees per cell using the Topographic Anal-
ysis tool of the ERDAS IMAGINE. Then slope
aspect values were recoded into four categories:
North, East, South, and West. The category of the
majority of the cells in each patch was assigned as
its aspect category.
Rock cover (RC)
Rocks and stones increase the infiltration rate of
water into the soil (Poesen and Lavee 1994), and
108 Landscape Ecol (2007) 22:105–116
123
therefore may provide better conditions for the
growth of woody vegetation (Schlesinger et al.
1996). A supervised Maximum Likelihood Clas-
sification was used to classify four land cover
classes from the September 2003 aerial photo-
graphs: rock, bare soil, shrubs, and herbaceous
vegetation. After reliable classification was
achieved, the rock and shrub cover for each
patch was calculated separately based on the
ratio between the area covered by rock and
shrub classes relative to the patch area. An
accuracy assessment of the classification was
carried out using a visual interpretation of the
aerial photographs on a sample of 200 pixels per
class and field observations; accuracy was tabu-
lated in a confusion matrix (a table within each
predicted class is plotted against the actual class
and the number of items within each is com-
pared).
Rock pattern (RP)
The pattern of rocks may also influence the
spatial pattern of potential soil moisture (For-
man and Godron 1986). A clustered pattern
leads to a concentration of moister areas in
remote parts of the patch and thereby limits
the expansion of shrubs within the patch. On
the contrary, a random spatial distribution of
rocks will likely form more heterogeneous wa-
ter distribution pattern over the area and allow
better connectivity between the shrubs, even-
tually forming a higher SGR. The rock pattern
(RP) was determined here using a ‘‘Nearest
Neighbor’’ index, which compares the expected
patterns with the measured value of the aver-
age distances between neighboring rock frag-
ments.
RP ¼P
ri
n� 2
ffiffiffin
a
rð2Þ
where n is the number of rock fragments within
the patch, a is the total patch area, and ri is the
distance between the closest neighboring rock
fragments. The index value ranges from 0 to 2.149
where 0 indicates a clustered pattern, 1 indicates a
random distribution, and 2.149 indicate a regular
pattern (DeMers 2000).
Patch area (PA)
A large patch is more likely to comprise a
higher number of micro-habitats than a small
patch (Bar [Kutiel] et al. 2005). The larger pat-
ches, therefore, would be conducive to more
species with different habitat requirements
(Debinski and Holt 2000). Furthermore, the
margin areas of a large patch are relatively small
in relation to its entire area, and a large patch is
less likely to be vulnerable to external distur-
bances (Yao et al. 1999). Therefore, we expect
that a higher SGR will be found in large pat-
ches. The patch area in hectares was calculated
based on delineating polygons along patch
boundaries and calculating the total area of
polygon.
Patch shape (PS)
Patch shapes are related to their agricultural
surroundings (the matrix) and are vulnerable to
the effects of agricultural activities around them
(Marshall and Moonen 2002). In many cases, the
richness and variety of vegetation in a patch
changes from its margins to its core (de Blois
et al. 2002). Patch margins in our study area have
a different vegetation composition from that of
the patches’ cores. These areas have much higher
percentages of grass growth, such as oat—Avena
sterilis (Bar [Kutiel] et al. 2005), which benefit
from the surrounding agricultural fertilization.
Hence, when the shape of the patch is more
compact (i.e., closer to a circle), its margin areas
are smaller in relation to the total area, and the
patch is less related to the ‘‘edge effect,’’ and vice
versa (Collinge and Palmer 2002). Moreover,
when the number of patches spread over the area
is larger, the impact of the different aspects of
‘‘edge effect’’ (composition and structure) is
greater. The level of similarity of the ith patch to a
circle (Si) was calculated with the shape index
(Schumaker 1996) which expresses the level of
the patch’s shape complexity by comparing it to a
circle:
Si ¼pi
2ffiffiffiffiffiffiffiffiffiffiffiffiffip� aip ð3Þ
Landscape Ecol (2006) 22:105–116 109
123
where pi is the patch’s circumference and ai des-
ignates its area.
The more dissimilar the patch is to a circle, the
greater its assumed complexity. The output index
values range from unity to infinity: 1 designates a
circle, and the more complex the shape is, the
more the index advances toward infinity.
Fuzzy logic modelling
Fuzzy logic is a theory in formal mathematics that
enables arriving at a definitive solution for com-
plex, uncertain and unstructured problems (Bo-
jorquez-Tapia et al. 2002). A general fuzzy
system is composed of three primary elements
(Burrough and McDonnell 2000): membership
functions, fuzzy production rules and fuzzy sets.
A fuzzy set (A) could be defined as:
A ¼ fx; lAðxÞg for each x 2 X ð4Þ
where X = {x} is a finite set of points and lA(x) is
a membership function of X in A. The member-
ship functions describe the variables’ membership
in A and therefore the influence of the variable on
the predicted phenomenon based on the re-
searcher understanding (Burrough and McDon-
nell 2000). The set A is defined in our research as
the set of cells with optimal conditions for the
maximal SGR possible in the study area.
Numerous membership functions are available in
the literature (Robinson 2003) and to avoid
defining membership threshold, which will be
empirical in nature, we chose two relatively sim-
ple membership functions to represent the mem-
bership of the six variables in the set A (Fig. 2).
The linear function that was chosen for all vari-
ables (except WI):
lA ¼xi � ab� a
ð5Þ
where xi is the value of ith environmental variable
x; and a and b are the minimum and maximum
values of the environmental variable x. For WI we
assigned a sigmoid-type membership function
since it was found in sensitivity tests to be more
suitable to express the membership of WI in sets
of potential soil moisture.
lA ¼1
1þ ebðxi�aÞ ð6Þ
where b is the crossover point (l = 0.5) and a is
the minimum value of the variable x.
To integrate the effect of all variables, we
established a new set A that is based on the joint
membership function (JMF) of all sets A1...Ak.
This set can be any act of unification, separation
and the like between the groups to form a single
score that would express the level of each patch’s
potential for high SGR values. Here, we defined
the JMF as the weighted sum of the patches’
membership score for each variable:
JMF ¼ k1lA1 þ k2lA2 þ � � � þ knlAn ð7Þ
Fig. 2 Membershipfunctions for sixenvironmental variables:patch shape (PS), rockcover (RC), rock pattern(RP), wetness index (WI),aspect category (AC) andpatch area (PA). Note theAC is represented by acategorical membershipfunction and that WI isrepresented by a sigmoid-type membership function
110 Landscape Ecol (2007) 22:105–116
123
where kj is the weight of membership function Aj,Pkj¼1 kj¼1; kj[0:
By using fuzzy rules, environmental attributes
can be defined and mapped out in an explicit
fashion. The calculation of membership functions
also enables the use of different types of variables
and units, without requiring the conversion or
normalization of units.
To explore the research questions, patches
were divided according to a threshold value of
patch area of 1.6 ha. This threshold was found to
determine the differences between large and
small patches based on Bar [Kutiel] et al. (2005).
Where the level of similarity between the patch’s
vegetation structure and that of the adjacent
nature reserve (the mainland) in immediate
proximity to the patches is most strongly depen-
dent on the patch size. Patches larger than 1.6 ha
revealed varying percentages of shrubs, reaching
up to percentages of cover similar to those in the
adjacent natural areas.
Patches were further divided according to as-
pect characteristics. Field studies in the research
area (Perevolotsky, unpublished data) have re-
vealed that the composition and structure of
shrubs on west-facing slopes is similar to that on
north-facing slopes, while on east-facing slopes
the vegetation composition is similar to that on
south-facing slopes. The reason for this could be
the frequent wind direction (west–east) in this
part of Israel that may cause higher rainfall depth
on the west-facing slopes (Sharon et al. 2002).
Therefore, we decided to analyze our results
based on two slope orientation categories: (1)
north and west-facing slopes; and (2) east and
south-facing slopes.
Our assumption is that soil moisture for vege-
tation on east/south-facing slopes would be lower
than on west/north-facing slopes. As such, the
factors that influence soil moisture (WI, AC, RC,
RP) would have greater importance in east/south-
facing patches than west/north-facing patches.
The patch’s geometric attributes (PA, PS) would
have higher importance in small patches than in
large patches. According to this assumption, we
assigned weights to the six variables for the four
patch size-aspect categories as described in
Table 1.
Spatial analysis
The continuous data of shrub cover per patch (0–
60%) and of the JMF from Eq. 7 (based on the
weights in Table 1) were categorized into five
levels, from very high to very low, using the
standard deviation classification procedure in
ArcMap 2000. This procedure uses the mean va-
lue of each variable and locates class breaks
above and below the mean at an interval of 1 SD.
To compare the map of potential shrub cover
(JMF based on patch area and aspect) with actual
shrub cover, we subtracted the two categorical
maps, assuming: that a result of zero represents
patches that their actual shrub cover categories fit
their potential shrub cover category; that positive
values represent the number of categories that a
patch needs to cross to self-realize its potential;
and that negative values represent patches on
which observed shrub cover is higher than its
potential.
Results
Environmental variables
The 60 patches of the study area represent a case
study with a relatively wide variety of environ-
mental conditions (Fig. 3). Rock cover within the
patches varies between 0 and 8% while the rock
pattern varies normally between clustered and
random (with a peak at NN ~0.5 m). As expected,
very few patches have a regular pattern of rock
cover. The wetness index also shows normal dis-
tribution, with a peak at ~4.9 category and very few
patches of WI near 7. Twenty-four of the patches
are east and south facing while the other 36 are west
and north-facing. The size of 35 patches is 0–1 ha;
Table 1 The weights assigned for each of the variables forthe patch size and aspect categories
Patch Size-aspect Weights of variables [kj]
AC WI RP RC PA PS
Large N 0.14 0.14 0.29 0.29 0.07 0.07Small N 0.07 0.07 0.14 0.14 0.29 0.29Large S 0.14 0.14 0.29 0.29 0.07 0.07Small S 0.07 0.07 0.21 0.21 0.21 0.21
Landscape Ecol (2006) 22:105–116 111
123
the other 25 were 1–9 ha. The shrub cover in the
patches varies between 0 and 60%.
The WI and AC maps are based on generic
procedures that were applied to the DEMs and
have been verified in many previous studies.
Similarly, the calculation of PA and PS is based
on manual delineation of the patch’s boundary
and very common operators for actual calcula-
tions. Therefore, we did not test the certainty of
these four output layers. However, the classifica-
tion of the aerial photographs is based on local
parameterization and therefore required verifi-
cation. The confusion matrix shows that the
overall accuracy is satisfactory (88%; Table 2)
and is similar to other achievements in aerial
photograph classifications of other studies that
were applied to the four land cover classes in
adjacent study areas (Svoray and Carmel 2005).
The rock and shrub classes—which we use in the
current study—show even better classification
accuracy results than the overall test, with errors
of commission of 96 and 94%, respectively, and
errors of omission—90 and 91%, respectively.
The integration of the six environmental
variables in a model required prior testing to
determine whether the spatial distribution pat-
tern of any of these variables depends on an-
other variable. For this purpose, we used
Pearson’s product moment coefficient of corre-
lation. This test provides a measure of both
direction and strength of the relationship be-
tween two continuous variables. The test was
implemented on all 60 patches of the study area.
Fig. 3 Frequency histograms for the six environmental variables: patch shape (PS), rock cover (RC), rock pattern (RP),wetness index (WI), aspect category (AC) and patch area (PA); and for the shrub cover (SC)
Table 2 Confusion matrix to test the accuracy of the MLCrelative to visual classification using the 2003 airphoto
Overallaccuracy = 88%
Visualinterpretation
Rocks Shrubs Grass Soil Totalrow
Imageclassification
Rocks 175 0 0 6 181Shrubs 0 190 11 0 201Grass 0 18 172 26 216Soil 19 0 17 171 207Totalcolumn
194 208 200 203 805
112 Landscape Ecol (2007) 22:105–116
123
In Pearson r, two variables are proportional to
each other positively when r = 1 and negatively
when r = )1. The correlation, in all cases, is
closer to 0 than to 1 or )1, and in most cases
insignificant (Table 3). Therefore, we assume
that the six environmental variables selected
here are independent of each other.
Relationship testing
A multiple regression analysis (Eq. 8) was exe-
cuted between the six environmental variables
and the measured SGR and achieved a relatively
poor, yet significant, correlation: r2 = 0.23; P-
value = 0.03; SE = 0.13; n = 60; while:
SGR ¼2:25RCþ 0:05RPþ 0:05AC þ 0:04WI
� 0:04PS� 0:02PA� 0:24:
The correlation was significantly improved
when the environmental variables were modeled
using Eq. 7 according to the size of patches and
their aspect (r2 = 0.43, P-value < 0.001).
To test the robustness of our model, we ana-
lyzed the effect of changing slightly the values of
weights in Table 1. The analysis shows that
gradual change in a range of –0.5 of the differ-
ence between the weights did not make any
significant change in the coefficient of determi-
nation. (Showing stability in current weights.)
Conversely, the use of weights with opposite
strategy (for example, giving larger weights to
soil moisture in small patches) or random
weights changed significantly the coefficient of
determination and did not yield any significant
relationship between the JMF and observed
SGR.
Spatial analysis
Patches in the western part of the study area are
characterized by very low SGR (Fig. 4a) whereas
many of the patches in the eastern part are of
higher SGR. This is despite the fact that the
patches in the western part are of low, medium
and high SGR potential (Fig. 4b). Figure 4c
shows that only 15.5% of the patches had realized
their potential in full in 2003. A very small num-
ber of the patches that year—5.2%—had SGR
that was higher than the potential, but these three
patches are only at a distance of one category
()1). The fact that these three patches showed a
ratio higher than their potential can be attributed
to the system error or due to phenomenon that
were not expressed in our models. The other
~80% of the patches did not reach their potential
environmental and geometric conditions for
shrub development. Of these, only 1.7% of the
patches were lacking in three categories in order
to increase SGR to potential, while another ~30%
needed two more categories to realize their po-
tential and ~50% were very close to realizing the
potential: only one category was lacking to in-
crease SGR.
Discussion
Previous studies (e.g., Poesen et al. 1998) show
that topography may relate to rock cover and
distribution. Relatively high erosion rates in sharp
topography can expose more rocks on steep
slopes (Canfield et al. 2001). South-facing slopes
may cause a decrease in aggregate stability and
therefore yield higher erosion rates (Kutiel 1992).
However, our study indicated that all six envi-
ronmental variables are independent. This im-
plies that the effect of topography on the rock
fragments’ movement and on soil erosion is lim-
ited in our site. This could be due to the relatively
mild topographic conditions of the patches, i.e.,
an area of hilly topography (Svoray et al. 2004).
Another reason could be the complex runoff and
erosion mechanisms that occur in the study area
(Yair and Kossovsky 2002) and limit the transfer
of soil materials along the slopes. The indepen-
dence of the other variables from one another is
Table 3 Pearson’s product moment coefficient ofcorrelation: the relationship between the input variables
PA PS RC RP WI AC
PA 1.00PS 0.43* 1.00RC 0.25 0.09 1.00RP )0.17 0.11 0.09 1.00WI )0.16 0.11 )0.15 0.40* 1.00AC )0.31* )0.01 )0.19 )0.04 )0.01 1.00
*Significant relationships
Landscape Ecol (2006) 22:105–116 113
123
thus expected. Patch size and shape may depend
on slope decline and soil depth through agro-
technical constraints, but mainly depend on the
plot owner and the operator of the tractor in the
field. Therefore, it is not surprising that these
variables did not correlate with topography or
with rock cover. The meaning of the low corre-
lation observed here is that the interrelationships
between environmental variables can be site
specific and should be tested prior to modeling in
any new site where vegetation attributes are
predicted through environmental variables.
Noy-Meir (1973) shows that the micro-habitat
of desert vegetation is determined by water
potential and water distribution in the soil and its
temporal and spatial dynamics. Our results show
that in a fragmented semi-arid environment it is
not only the soil moisture potential that governs
SGR but also the geometric attributes of the
patch boundaries. The spatial variation observed
in SGR between the patches is relatively high
(0–60% cover of shrubs per patch). Since annual
rainfall depth is assumed more or less equal in the
entire study area, and since disturbances and fire
are assumed to be equally distributed in the study
area, we can assume that the abiotic environ-
mental variables cause the spatial variation in
SGR within the patches.
The result of the multiple regression analysis
implies that a direct empirical modeling of the
environmental variables to predict SGR from the
six variables is limited. This is to be expected
since the environmental variables related to SGR
through their effect on water redistribution and
on the heterogeneity of resources within the
patches. Therefore, modeling these variables
according to patch size–aspect categories in-
creased significantly the coefficient of determi-
nation. This improvement in prediction is in line
with previous studies, e.g., Breshears and Barnes
(1999) and Schlesinger et al. (1990) that modeled
variation in SGR by variation in soil moisture. (It
can be noted, however, that these studies ignored
the effect of the abiotic environmental variables
on water distribution.)
The improvement in SGR prediction based on
mechanistic principals was further proved in the
fuzzy modeling. The partition of the patches
according to patch size, based on Bar (Kutiel)
et al. (2005), improved the results from r2 = 0.23
to r2 = 0.42. The effect of patch size may be
attributed to the matrix and edge effect on the
patches (Yao et al. 1999; Debinski and Holt
2000). A small patch, which maintains a relatively
small core (if any), is suspected to be composed
entirely of margin-type vegetation (Bar [Kutiel]
et al. 2005). Therefore, the division according to
patch size indeed expresses the difference be-
tween large patches that are more similar to the
mainland and small patches that are related to
their edges. Furthermore, with r2 = 0.42, the im-
pact of aspect should be combined with patch
size. The effect of aspect is important in small
patches where in west/north-facing patches, the
patch geometry is the more important factor,
while in east/south-facing patches the effect of
geometry is more limited by the effect of soil
moisture. In the large patches, however, SGR
Fig. 4 Potential and actual SGR map for the study area:(a) patches divided into five categories of SGR accordingto their aerial photograph classification, (b) division of the
patches based on potential shrub cover, and (c) thedifferences in potential-actual SGR
114 Landscape Ecol (2007) 22:105–116
123
depends mainly on soil moisture and is much less
limited by geometric attributes.
The spatial mapping can be a very important
tool in the analysis of the expected increase in
shrub cover within the patches. Patches with
higher levels of potential that in 2003 were clas-
sified, according to observations, as low SGR
patches, are expected to increase SGR in the
coming years. To this prediction it is necessary to
add the restriction related to the patches of the
western part of the study area. These areas can be
limited by disturbances that, even though they are
assumed to be equal along the study area, may be
revealed as the factors that limit the western
patches from reaching their potential.
Conclusions
The fuzzy rule-based model developed here and
the shrub cover map of 2003 (approximately five
decades after landscape fragmentation) supports
our assertion that in small patches ( <1.6 ha), on
north-facing slopes, geometric attributes govern
SGR, while on south-facing slopes geometric and
soil moisture are of equal importance. In the large
patches, in both aspects, the potential soil mois-
ture was found to govern SGR.
Acknowledgments We thank Dr. Marcelo Sternberg forhis comments on an earlier version of the manuscript. Partof this study was funded by the Yad Hanadiv Fund of theJewish National Fund.
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