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: tsvoray@bgu.ac.il

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.

References

Ackermann O, Maeir AM, Bruins HJ (2004) Unique hu-man-made catenary changes and their effect on soiland vegetation in the semi-arid Mediterranean zone: acase study on Sarcopoterium spinosum distributionnear Tell es-Safi/Gath, Israel. Catena 57:309–330

Bar [Kutiel] P, Negoitza D, Svoray T (2005) The impact offragmentation on vegetation in embedded naturalhabitat within arable lands. Presented in: EuropeanIALE congress ‘‘Landscape ecology in the Mediter-ranean: inside and outside approaches’’ Faro, 29March–2 April 2005

Barling RD, Moore ID, Grayson RB (1994) A quasi dy-namic wetness index for characterizing the spatialdistribution of zones of surface saturation and soilwater content. Water Resour Res 30:1029–1044

Belsky AJ (1994) Influences of trees on savanna produc-tivity – tests of shade, nutrients, and tree–grass com-petition. Ecology 75:922–932

Bojorquez-Tapia LA, Juarez L, Cruz-Bello G (2002)Integrating fuzzy logic, optimization, and GIS forecological impact assessments. Environ Manage30:418–433

Breshears DD, Barnes FJ (1999) Interrelationships be-tween plant functional types and soil moisture heter-ogeneity for semi-arid landscapes within thegrassland/forest continuum: a unified conceptualmodel. Landscape Ecol 14:465–478

Buchbinder B (1969) Geological map of Hashphela region,Israel with explanatory notes. The Geological Surveyof Israel, Jerusalem

Burrough PA, McDonnell RA (2000) Principals of geo-graphical information systems. Oxford UniversityPress, New York

Canfield HE, Lopes VL, Goodrich DC (2001) Hillslopecharacteristics and particle size composition of surfi-cial armoring on a semi-arid watershed in the south-western United States. Catena 44:1–11

Collinge SK, Palmer TM (2002) The influences of patchshape and boundary contrast on insect response tofragmentation in California grasslands. LandscapeEcol 17:647–656

Dan Y (1988) The soils of the southern Shefelah. In: Ur-man D, Stern E (eds) Man and environment in thesouthern Shefelah-studies in regional geography andhistory. Masada, Givataim, Israel, pp 50– 59 (in He-brew)

Danin A (1988) The vegetation of the southern Shefelah.In: Urman D, Stern E (eds) Man and environment inthe southern Shefelah-studies in regional geographyand history. Masada, Givataim, Israel, pp 59 – 64 (inHebrew)

de Blois S, Domon G, Bouchard A (2002) Landscape is-sues in plant ecology. Ecography 25:244–256

Debinski DM, Holt RD (2000) A survey and overview ofhabitat fragmentation experiments. Conserv Biol14:342–355

DeMeres MN (2000) Fundamentals of geographic infor-mation systems. John Wiley & Sons, New-York

Efrat E (1994) Rural geography of Israel. Achiasaf Pub-lishing House Ltd, Tel Aviv

Fahrig L (2003) Effects of habitat fragmentation on bio-diversity. Annu Rev Ecol Syst 34:487–515

Fernandez-Illescas CP, Rodriguez-Iturbe I (2003) Hydro-logically driven hierarchical competition-colonizationmodels: the impact of interannual climate fluctua-tions. Ecol Monogr 73:207–222

Forman RTT, Godron M (1986) Landscape ecology. Wi-ley, New York

Gibbs JP (2001) Demography versus habitat fragmenta-tion as determinants of genetic variation in wildpopulations. Biol Conserv 100:15–20

Haila Y (2002) A conceptual genealogy of fragmentationresearch: from island biogeography to landscapeecology. Ecol Appl 12:321–334

Landscape Ecol (2006) 22:105–116 115

123

Hille Ris Lambers R, Rietkerk M, van den Bosch F, PrinsHHT, de Kroon H (2001) Vegetation pattern forma-tion in semi-arid grazing systems. Ecology 82:50–61

House JI, Archer S, Breshears DD, Scholes RJ, NCEASTree–Grass Interactions Participants (2003) Conun-drums in mixed woody-herbaceous plant systems. JBiogeogr 30:1763–1777

Kutiel P (1992) Slope aspect effect on soil and vegetationin a Mediterranean ecosystem. Isr J Bot 41:243–250

Le Houerou HN (1996) Climate change, drought anddesertification. J Arid Environ 34:133–185

Levin SA (1974) Dispersion and population interaction.Am Nat 108:207–228

Marshall EJP, Moonen AC (2002) Field margins innorthern Europe: their functions and interactions withagriculture. Agricult Ecosyst Environ 89:5–21

Milne BT, Johnson AR, Keitt TH, Hatfield CA, David J,Hraber PT (1996) Detection of critical densitiesassociated with pinon-juniper woodland ecotones.Ecology 77:805–821

Noy-Meir I (1973) Desert ecosystems: environment andresources. Annu Rev Ecol Syst 4:25–51

Poesen J, Lavee H (1994) Rock fragments in top soils –significance and processes. Catena 23:1–28

Poesen JW, Wesemael B, Bunte K, Benet AS (1998)Variation of rock fragment cover and size along semi-arid hillslopes: a case-study from southeast Spain.Geomorphology 23:323–335

Reid KD, Wilcox BP, Breshears DD, MacDonald L (1999)Runoff and erosion in a pinon-juniper woodland:Influence of vegetation patches. Soil Sci Soc Am J63:1869–1879

Robinson VB (2003) A perspective on the fundamentals offuzzy sets and their use in Geographic InformationSystems. Trans GIS 7:3–30

Sankaran M, Ratnam J, Hanan NP (2004) Tree–grasscoexistence in savannas revisited – insights from anexamination of assumptions and mechanisms invokedin existing models. Ecol Lett 7:480–490

Schlesinger WH, Raikes JA, Hartley AE, Cross AE (1996)On the spatial pattern of soil nutrients in desert eco-systems. Ecology 77:364–374

Schlesinger WH, Reynolds JF, Cunningham GL, Hu-enneke LF, Jarrell WM, Virginia RA, Whitford WG(1990) Biological feedbacks in global desertification.Science 247:1043–1048

Scholes RJ, Archer SR (1997) Tree–grass interactions insavannas. Annu Rev Ecol Syst 28:517–544

Schumaker NH (1996) Using landscape indices to predicthabitat connectivity. Ecology 77:1210–1225

Sharon D, Margalit A, Berkowicz SM (2002) Locallymodified surface winds on linear dunes as derivedfrom directional raingauges. Earth Surf ProcessesLand 27:867–889

Shmida A, Ellner S (1984) Coexistence of plant specieswith similar niches. Vegetatio 58:29–55

Shoshany M, Svoray T (2002) Multidate adaptive unmix-ing and its application to analysis of ecosystem tran-sitions along a climatic gradient. Remote SensEnviron 82:5–20

Sternberg M, Shoshany M (2001) Influence of slope aspecton Mediterranean woody formations: a comparison ofa semi-arid and an arid site in Israel. Ecol Res 16:335–345

Svoray T, Carmel Y (2005) Empirical method for topo-graphic correction in aerial photographs. IEEE TransGeosci Remote Sens Lett 2:211–215

Svoray T, Bar-Yamin S, Henkin Z, Gutman M (2004)Assessment of herbaceous plant habitats in waterconstrained environments: predicting indirect effectswith fuzzy logic. Ecol Model 180:537–556

van Wijk MT, Rodriguez-Iturbe I (2002) Tree–grasscompetition in space and time: insights from a simplecellular automata model based on ecohydrologicaldynamics. Water Resour Res 38(9):Art. No. 1179

Walker JP, Willgoose GR (1999) On the effect of digitalelevation model accuracy on hydrology and geomor-phology. Water Resour Res 35:2259–2268

Walter H (1971) Ecology of tropical and sub tropicalvegetation. Oliver and Boyd, Edinburgh

Wilby A, Shachak M (2004) Shrubs, granivores and annualplant community stability in an arid ecosystem. Oikos106:209–216

Yair A, Kossovsky A (2002) Climate and surface proper-ties: hydrological response of small arid and semi-aridwatersheds. Geomorphology 42:43–57

Yao J, Holt RD, Rich PM, Marshall WS (1999) Woodyplant colonization in an experimentally fragmentedlandscape. Ecography 22:715–728

Zangvil A (1988) The climate of the southern Shefelah. In:Urman D, Stern E (eds) Man and environment in thesouthern Shefelah-studies in regional geography andhistory. Masada Givataim, Israel, pp 42 – 50 (in He-brew)

116 Landscape Ecol (2007) 22:105–116

123