Simpson Index Calculation of Land Fragmentation
农地细碎化度测度指数计算的改进

Farmland fragmentation is one of the main problems facing China's agricultural production. With the implementation of the household contract responsibility system in China in the late 1970s, average farmland allocation resulted in serious farmland fragmentation and may hinder the development of agricultural production, slow down agricultural modernization, and lead to a decline in the efficiency of agricultural production and rural labor force. The Simpson index is one of the most important indexes to measure farmland fragmentation, but the spatial interaction among farmlands is often ignored. In order to comprehensively and more accurately measure farmland fragmentation we build on the Simpson index. First, the relationship between farmland integrity and fragmentation was analyzed. Second, without considering the spatial interaction among farmlands, the farmland integrity index function was expanded using the Taylor formula. The farmland integrity index was equivalent to 1-Simpson index. Later, under a hypothesis of farmland spatial interaction, a spatial contiguity matrix was introduced to construct the farmland integrity index formula. The farmland integrity index was the Eigenvalue of the farmland integrity matrix. The improved index formula was applied to calculate farmland integrity indexes for Huayuan and Miaoshan village, Yizheng City, Jiangsu province. Data sources were acquired from land-use surveys in 2010 and images in 2000. When the spatial interaction among farmlands was neglected, farmland integrity indexes in plain terrain were higher than that in hilly areas. However, when spatial interaction was considered, the spatial clustering coefficient in hilly areas was higher than that in plain terrain. This conclusion is consistent with previous findings. Farmland integrity indexes were contrasted in different periods, the farmland integrity index of Huayuan village in 2010 was lower than that in 2000.