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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
3. DUALITY : FORMULATION AND ASSESSMENT 
Duality hypothesis states that there is mutuality and 
complementarity in the way SW and WAP of patch patterns 
change and that relationships between SW and WAP represent 
characteristics of the spatial processes. Relationships between 
fragmentation and shape were first assessed by us with real 
patch pattern data derived from processing historical air 
photographs (Shoshany, 2002) made on three dates between 
1956 and 1990 (Figure 1). 
1956 
  
  
  
1976 
  
  
  
  
  
1990 
  
  
  
  
  
Figure 1. Soil (in black) and Vegetation (in white) patches as 
mapped from historical air-photographs. 
561 
Broadening the information basis was achieved by looking both 
at soil and vegetation patch characteristics and by utilizing the 
phase difference in the process between north and south facing 
slopes (approximately 12 years). A hypothetical continuum of 
90 years was thus formed representing the recovery process, 
from almost bare terrain in 1920 (realistic assumption due to the 
extensive use of wood for fuel during the Ottoman rule in 
Palestine) to almost total shrub cover, which could be achieved 
in 2010. 
SW and WAP" indices > 
  
  
  
B 
6 
4 
2 
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920 1940 1950 1980 2000 
Y eat 
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SW and WAP! indices 
e 
i 1 i 1 
1920 1940 1960 1980 2000 
Year 
Figure 2. Graphically generalized curves of Shannon and 
Weiner Information Index (SW) with thin lines and Weighted 
Area-Perimeter Index (WAPI) with bold lines: vegetation (a) 
and soil (b) on south facing (broken lines) and north facing 
slopes (solid lines). Represent extrapolation of data derived 
from air photographs interpretation for dates between 1956 and 
1990. 
Figures 2a and 2b provide a graphic generalization of the 
change in fragmentation and shape within this hypothetical time 
frame. The WAPI and SW indices are generally inversely 
related: while low WAP1 and high SW characterized the initial 
spread of vegetation or the end of soil fragmentation; high 
WAPI and low SW were inferred when vegetation clumped 
into large patches and when the large soil clumps began to 
disaggregate. In addition to representing the stages of patch 
dynamics, these graphs exhibit differences in the rate of change 
between slope aspects, indicating sensitivity to differences in 
the types of process occurring respectively on south and north 
facing slopes. Based on this data, it may be suggested that soil- 
vegetation patch dynamics is embedded within the generalized 
graphic 4description and it furthermore provides empirically 
based support for the duality hypothesis. Further verification 
and generalization of the validity of these fragmentation-shape 
relationships was obtained by simulating patch pattern 
dynamics.