Assessing the effectiveness of barrier allocation strategies against the propagation of phytopathogens and pests with percolation

Abstract: We investigate the connectivity properties of square lattices with nearest-neighbor interactions, where some sites have a reduced coordination number, meaning that certain sites can only connect through three or two adjacent sites. This model is similar to the random placement of physical barriers in plantations aimed at decreasing connectivity between susceptible individuals, which could help prevent the spread of phytopathogens and pests. In this way, we estimate the percolation threshold as a function of the fraction of sites with a reduced coordination number ($p_d$), finding that the critical curves can be well described by a $q$-exponential function. Additionally, we establish the correlation between $p_d$ and the fraction of barriers effectively placed, which follows a power law behavior. The latter is helpful in estimating the relative costs of the barrier allocation strategies. In particular, we found that the allocations of two barriers per site model ${ \ulcorner, \lrcorner }$ can produce savings between 5% and 10% of the strategy cost compared to the independently random barrier allocations (joint site-bond percolation). From an agroecology perspective, adding barriers to the plantation gives farmers the opportunity to sow more vulnerable plant varieties.