A threshold area ratio of organic to conventional agriculture causes recurrent pathogen outbreaks in organic agriculture

Conventional agriculture uses herbicides, pesticides, and chemical fertilizers that have the potential to pollute the surrounding land, air and water. Organic agriculture tries to avoid using these and promotes an environmentally friendly approach to agriculture. Instead of relying on herbicides, pesticides and chemical fertilizers, organic agriculture promotes a whole system approach to managing weeds, pests and nutrients, while regulating permitted amendments. In this paper, we consider the effect of increasing the total area of agricultural land under organic practices, against a background of conventional agriculture. We hypothesized that at a regional scale, organic agriculture plots benefit from existing in a background of conventional agriculture, that maintains low levels of pathogens through pesticide applications. We model pathogen dispersal with a diffusive logistic equation in which the growth/death rate is spatially heterogeneous. We find that if the ratio of the organic plots to conventional plots remains below a certain threshold l_c, the pest population is kept small. Above this threshold, the pest population in the organic plots grows rapidly. In this case, the area in organic agriculture will act as a source of pest to the surrounding region, and will always infect organic plots as they become more closely spaced. Repeated localized epidemics of pest outbreaks threaten global food security by reducing crop yields and increasing price volatility. We recommend that regional estimates of this threshold are necessary to manage the growth of organic agriculture region by region.