JIA-2018-09

2100 WANG Di et al. Journal of Integrative Agriculture 2018, 17(9): 2096–2106 S 2 = ( w i. + w .j ) 2 ∑ n i =1 (6) Where, w i. is the sum of all elements belonging to the i th line in the spatial adjacency matrix w ij ; w . j is the sum of all elements belonging to the j th row in the spatial adjacency matrix w ij . 2.5. Design of sampling unit sizes We chose a square grid as the shape of the sampling units to facilitate the calculation of the adjacency matrix and hence Moran’s I . To determine the influence of sampling unit size on the spatial autocorrelation of the variables, we formulated 25 levels of sampling unit size. Using a size interval of 200 m, the 25 sampling unit sizes were 200 m×200 m, 400 m× 400 m, …, 5 000 m×5 000 m. The study area was then divided into these square grids to construct 25 sampling frames. When a square grid crossed or was within the administrative boundary of the study area, it belonged to the sampling frame. 2.6. Stratification on crop planting intensity within sampling units Crop planting intensity (CPI) is the proportion of a sampling unit being cropped. In this study, we calculated the CPI of each crop, for each sampling unit, by independently overlaying the maize and rice spatial distribution data on the sampling frame. Comprehensively considering the decrease of variance within the strata, the feasibility of sample selection and the computation of spatial autocorrelation among crop areas in the sampling units, the CPI values in all sampling units were then divided into five strata: (1) 0.01–20%; (2) 20–40%; (3) 40–60%; (4) 60–80%; and (5) 80–100%. Accordingly, all sampling units were also divided into five strata based on the stratification of their CPI value. The spatial autocorrelation level among crop acreages included in the sampling units of each stratum was determined using the global Moran’s I . Using seven sampling unit sizes (200 m×200 m, 500 m×500 m, 1000 m× 1 000 m, 2 000 m×2 000 m, 3 000 m×3 000 m, 4 000 m× 4000 m, 5000 m×5000 m), as examples, we computed the spatial autocorrelation level among crop acreages included in the sampling units of each stratum at each sampling unit size. Although the size of 500 m×500 mwas not listed above, this is widely used to field survey crop acreage in China, so we added this size between 200 m×200 m and 1 000 m× 1 000 m as a representative example. Using the sampling unit size of 1 000 m×1 000 m as an example, Fig. 6 shows the spatial distribution of the sampling units stratified by the maize and rice CPI values. 2.7. Stratification on cultivated land fragmentation within the sampling units Cultivated land fragmentation is often defined as the division of a cropland type into smaller parcels (Nagendra et al. 2006). The stratification on cultivated land fragmentation may have a potential influence on the spatial autocorrelation level of crop area in the sampling units, as crops are generally planted on cultivated land. We designed a fragmentation index (FRG) to quantitatively describe the degree of cultivated land fragmentation within each sampling unit. The FRG is calculated using eq. (7). FRG i = N i / A i (7) Where, FRG i is the cultivated land fragmentation within the i th sampling unit; N i is the number of cultivated land plots within the i th sampling unit; A i is the total area (in ha) of all cultivated land plots within the i th sampling unit. We sorted the FRG of all sampling units into ascending order and divided them into five strata based on their rank, keeping the number of sampling units within each stratum almost equal. The five strata of FRG were: (1) 0.05–0.16; (2) 0.16–0.20; (3) 0.20–0.26; (4) 0.26–0.35; and (5) 0.35–9.20. Jilin Province Dehui County 122°0´E123°0´E123°0´E125°0´E 126°0´E127°0´E 128°0´E 129°0´E 130°0´E 131°0´E 132°0´E 125°10´E125°20´E 125°30´E125°40´E 125°50´E 126°0´E 126°10´E 126°20´E126°30´E 126°40´E 122°0´E 121°0´E 120°0´E 46°0´N 45°0´N 44°0´N 43°0´N 42°0´N 45°0´N 45°0´N 44°50´N 44°40´N 44°30´N 44°20´N 44°40´N 44°30´N 44°20´N 44°10´N 44°0´N N 43°0´N 42°0´N 41°0´N 40°0´N Provincial boundaries County boundaries Dehui county 0 50 100 150 200 km County boundary Village boundaries 0 15000 30000 m 123°0´E 123°0´E 125°0´E 126°0´E 127°0´E 128°0´E 129°0´E 130°0´E 125°10´E 125°0´E 125°20´E 125°30´E125°40´E 125°50´E 126°0´E 126°10´E 126°20´E126°30´E N Fig. 2 Location of the study area in Jilin Province, Northeast China.