Site percolation threshold of composite square lattices and its agroecology applications.

Abstract

We analyze the percolation threshold of square lattices comprising a combination of sites with regular and extended neighborhoods. We found that the percolation threshold of these composed systems smoothly decreases with the fraction of sites with extended neighbors. This behavior can be well-fitted by a Tsallis q-Exponential function. We found a relation between the fitting parameters and the differences in the gyration radius among neighborhoods. We also compared the percolation threshold with the critical susceptibility of nearest and next-to-nearest neighbor monoculture plantations vulnerable to the spread of phytopathogen. Notably, the critical susceptibility in monoculture plantations can be described as a linear combination of two composite systems. These results allow the refinement of mathematical models of phytopathogen propagation in agroecology. In turn, this improvement facilitates the implementation of more efficient computational simulations of agricultural epidemiology that are instrumental in testing and formulating control strategies.