Multi-vector composition and its application in landscape patch shape deformation and dynamic analysis

The quantitative expression and monitoring of patch shape deformation is an important content of landscape ecology. In this paper, a new multi-vector method is put forward based on curve representation in differential geometry, which is the composition of Centroid Displacement Vector (CDV), Local Deformation Vector (LDV) and the unit normal vector on the patch boundary. These composition vectors (CVs) not only add a new direction dimension to the landscape pattern metrics already available, but also provide multi-scale information, i.e. CV at every point and the boundary segment CV (BSCV). This new information can provide a quantification basis for a deeper understanding of the mechanisms of shape deformation and dynamic analysis. An application of CVs to patch dynamics in the Yancheng National Nature Reserve (YNNR) in China is given to validate the methodology. The susceptibility to invasion of the Common Seepweed in the core area of YNNR is evaluated quantitatively by CVs method. Our results indicate that the rate of invasion of Smooth Cord-grass into Common Seepweed patch has increased by 1.5 times from 1995 to 2002. This is considered to be the dominant factor causing Common Seepweed patches to shrink and change dynamically. These results help us better understand the landscape patch shape deformation and analyze the driver forces of landscape change, and they also provide the quantitative basis for the effective protection of the nature reserve area.

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