Table 1 FSTI system.
Subsystem | Indicators | Calculation formula | Indicator significance |
|---|---|---|---|
Scale transition | Average farmland area per laborer | \({ {LF}}=A/L\) | Scale of mechanized farming within farmland |
Average plot size | \({ {MPS}}=A/N\) | Size of land parcels in farmland | |
Patch density index | \({ {PD}}=N/A\) | Degree of farmland fragmentation | |
Regularization transition | Farmland edge density | \({ {ED}}=E/A\times {10}^{6}\) | Degree of fragmentation of farmland patches by boundaries |
Farmland patch shape index | \({{SHAPE}}\_{{MN}}=\frac{\mathop{\sum }\limits_{i=1}^{m}\mathop{\sum }\limits_{j=1}^{n}\left(\frac{0.25{{{p}}}_{{{ij}}}}{\sqrt{{\alpha }_{{{ij}}}}}\right)}{N}\) | Level of complexity of farmland patch shapes compared to an equivalent-sized square | |
Average patch fractal dimension index | \({ {FRAC}}\_{{MN}}=\frac{\mathop{\sum }\nolimits_{{i}=1}^{{m}}\mathop{\sum }\nolimits_{{j}=1}^{{n}}\left(\frac{2\,{ln}(0.25{{p}}_{{ij}})}{{ln}\,{\alpha }_{{ij}}}\right)}{N}\) | Complexity of patch boundaries | |
Agglomeration transition | Average nearest neighbor distance index | \({ {MNN}}=\mathop{\sum }\limits_{{i}=1}^{{m}}{h}_{i}/N\text{'}\) | Dispersal of farmland patches in distribution |
Aggregation index | \({ {AI}}=\left[\mathop{\sum }\limits_{i=1}^{m}\left(\frac{{p}_{ij}}{{\rm{max}}{p}_{ij}}\right){p}_{i}\right]\times 100\) | Degree of spatial clustering of farmland patches | |
Contagion index | \({ {CONTAG}}=\left[1+\mathop{\sum }\limits_{i=1}^{m}\mathop{\sum }\limits_{{j}=1}^{n}\left(\frac{{p}_{ij}\,\mathrm{ln}\,{p}_{ij}}{2\,\mathrm{ln}\,m}\right)\right]\times 100\) | Aggregation and diffusion trends of farmland patches | |
Patch cohesion index | \({ {COHESION}}=\left[1-\frac{\mathop{\sum }\nolimits_{j=1}^{{n}}{p}_{ij}}{\mathop{\sum }\nolimits_{j=1}^{n}{p}_{ij}\sqrt{{\alpha }_{ij}}}\right]\times {\left(1-\frac{1}{\sqrt{A}}\right)}^{-1}\times 100\) | Indicators of spatial connectivity in farmland landscape | |
Specialization transition | Simpson dominance index extension | \({ {SDI}}=\sum {q}_{{k}}^{2}\) | Regional crop dominance |
Shannon evenness index extension | \({ {SHEI}}=\frac{-\mathop{\sum }\nolimits_{k=1}^{z}({q}_{k}\times \,{\mathrm{ln}}\,{q}_{k})}{{\mathrm{ln}}\,{z}}\) | Level of specialization in regional crops |
