Figure 1
This diagram shows the first tier of the SES framework, where components of the SES are broadly divided into four subsystems (solid boxes with multiples instances): resource system (RS), resource unit (RU), governance (GS) and actors (A). These components are further unravelled as second tier and third tier variables. The components are linked to and influence each other via a ‘Focal Action situation ’ that includes interactions and outcomes. The exogenous influences from other ecosystems and external social, ecological and political settings are also included that can vary at multiple scale (McGinnis & Ostrom,2014; Ostrom, 2007, 2009).
Figure 2
An example of input simulated image with LULC classification. We defined eight LULC classes-forest, wet land, water body, grassland, rural built-up, agricultural land, wasteland, and urban built-up.
Figure 3
Flow diagram summarizing the steps followed in the model for urban land-use transformation.
Table 1
Spatial configuration and composition metrics used to describe outcomes. Cells in the following table correspond to the smallest unit in the image and patch refers to a homogenous area in the landscape which differs from its surroundings. A patch is a non-linear group of contiguous cells belonging to the same class (Turner & Gardner, 2015).
| NAME OF LANDSCAPE METRIC | SPATIAL LEVEL | DESCRIPTION |
|---|---|---|
| Number of urban cells | Class | Total number of urban cells in a landscape |
| Total Urban Patch Area (PA) | Class | Total area occupied by the urban class |
| Number of urban patches (NP) | Class | Total number of urban patches |
| Edge Density (ED) | Class | Measure of shape complexity of the resulting urban patches |
| Clumpy Index (CLUMPY) | Class | Aggregation measure independent of landscape composition |
| Aggregation Index (AI) | landscape | Aggregation measure |
| Mean Fractal Dimension index (FRAC_MN) | landscape | Shape complexity measure based on perimeter-area relationship. |
Figure 4
Number of urban cells occupied at every iteration.For the purpose of clarity, we only include every alternate level of resistance. Blue line at year 24 marks the saturation points for level 1. We take the saturation point of level 1 as the point of references for the landscape metrics. Thick curved lines represent the average value of amount of urban cells for each level of resistance and dotted lines represent the variation (standard deviation) for all 100 images.
Figure 5
Response of six landscape metrics to the varying level of resistance. (a) to (d) are class level metrics including (a) number of urban patches, (b) patch area, (c) edge density and (d) clumpy index showing the pattern in the urban class. (e) Aggregation index and (f) frac_mean index are landscape level metrics showing patterns at the landscape level.
Table 2
Curve fitted to the mean value of all six landscape metrics and the corresponding statistics. R2 describes the proportion of variance explained by the curve and Cohen’s d measures the effect size. There are two resistance levels given in the last column. The first value is the resistance level at which the t-test value was significant and second value of the resistance level which correspond to the inflection point for each curve. For the goodness of fit measures, see supplement.
| LANDSCAPE METRICS | EQUATIONS (X IS THE RESISTANCE LEVEL) | R2 VALUE | COHEN’S d | RESISTANCE LEVELS (T-TEST, INFLECTION POINT) |
|---|---|---|---|---|
| Number of urban patches | 0.9864 | d (26.7127) = 0.97, d(20.42) = 0.66, and d (–0.2106) = 0.95 | 4,7.5 | |
| Total area of urban patches | 0.9 | d (6.961 × 105) = 0.69, d(–4.493) = 0.54, and d(67230) = 0.61 | 4,4.5 | |
| Edge Density | –0.0067x2 + 0.09453 + 0.4086 | 0.9802 | d(–0.0067) = –0.34, d(2) = 0.92, d(0.09453) = 0.81, and d(0.40862) = 0.98 | 2, Inflection point doesn’t exist for a quadratic curve. |
| Clumpy index | 0.9846 | d (0.0186) = 0.98, d(0.13) = 0.97, d(–0.735) = 0.72, and d(0.975) = 0.99 | 1,3 | |
| Aggregation Index | 0.9977 | d(1.63) = 0.99, d(0.068) = 0.71, d(–0.74) = 0.97, and d (96.99) = 0.99 | 2,3.5 | |
| Mean Fractal Dimension index | –0.00017x2 + 0.00226x + 1.026 | R2 = 0.9442; | d(0.00017) = 0.95, d(.002261) =0.96, d(2) = 0.91, and d(1.026) = 0.99 | 2, Inflection point doesn’t exist for a quadratic curve. |