Optimizing crop clustering to minimize pathogen invasion in agriculture.

The initial rate of pathogen invasion in crops is influenced by the spatial clustering of susceptible crops and the characteristics of pathogen dispersal. Previous studies have shown that various degrees of crop clustering can effectively reduce this invasion rate. However, the optimal degrees of clustering that minimize pathogen invasion have not previously been identified. This study aims to determine analytically the range of crop clustering that minimizes the initial rate of pathogen invasion. We studied artificial agricultural landscapes with crop areas arranged in identical square clusters on a regular square lattice. For pathogen dispersal, we used several common dispersal kernels, including Gaussian, negative exponential, and power-law. The optimal degree of clustering, defined by cluster size and separation distance, was calculated using a new analytical approximation for the pathogen invasion rate, which showed strong agreement with computer simulations. Additionally, we analysed a realistic cassava landscape at risk of invasion by cassava brown streak virus. We identified a range of optimal cluster sizes and corresponding separation distances that minimize pathogen invasion rates for various dispersal kernels and landscapes with clusters of crop fields arranged on a regular square lattice. The methods can be extended to other geometrical configurations, such as long narrow fields. Using a cassava landscape as an example, we show how optimal crop clustering strategies can be derived to mitigate the potential invasion of cassava brown streak virus. The methods provides analytical insights that can help farmers and agricultural planners to optimize the spatial structure of agricultural landscapes to minimize initial pathogen invasion rates.