Modelling the front dynamics of invasive plant pathogens through the analysis of spatial gradients

Variables of phytopathological interest correlated to the impact of plant diseases, such as incidence and severity, may display a spatial pattern resulting from an underlying, yet unknown gradient. Along the main direction of the gradient the variable assessed at the site level either increases, or decreases. Spatial gradients may also arise because of the movement of a front of invasion, an imaginary moving contour separating areas already infested by a plant pathogen from those still pathogen-free. Adequate geostatistical tools may shed light on gradients directional properties, as well as on the direction the front of invasion is coming from or moving to. Tools currently available for that may be impractical due to the advanced computational and programming skills required for their application. Hence, the goals of this study were: (I) to develop, test and validate a new user-friendly geostatistical tool named DirGrad (Direction of Gradient) aimed at analyzing spatial gradients resulting from the impact of plant diseases; (II) to build an algorithm able to run DirGrad on R, one the most widespread open source software for statistics; and (III) to apply DirGrad for the ex post modelling of the invasion front dynamics. The designed algorithm was successfully validated both in silico and in the field by using data from real case studies such as those of the invasive fungal pathogens Heterobasidion irregulare and Ophiostoma novo-ulmi in a forest stand of Central Italy and across the Swedish island of Gotland, respectively. The algorithm is released as a user-friendly open-source script.