Modelling the spread of fungal diseases using a nearest neighbour approach: effect of geometrical arrangement

Abstract

A discrete model of the nearest neighbour type is used to model the growth and spread of fungal disease in a two‐cultivar mixture assuming an unspecialized pathogen. Disease dynamics and dispersal are represented by a spatial, single pathotype version of Gumpert's (1992) model that simulated the temporal evolution of a number of pathotypes on a cultivar mixture. Spore dispersal occurs by discrete rules between a cell and its four orthogonal neighbours in a rectangular grid. Parameters termed transmission efficiency rates control the extent of successful inoculum exchange between two neighbouring cells depending on the cultivars present. Spatially averaged disease progress curves are computed for regular block and strip patterns in addition to the mean curve for twenty 1:1 random mixture patterns. These sets of curves are exhibited relative to the appropriate pure stand comparison for a range of auto‐ and cross‐deposition parameters. We conducted simulations for uniform initial infection and also averaged over 20 random initial infection patterns at a comparable mean level. In the former case, provided the ratio of cross‐deposition to auto‐deposition is high enough and the disease progress curves take sufficiently long to reach their saturation value, the ranking of the geometrical patterns can eventually be interpreted once initial oscillations have subsided. The geometry with the largest proportion of links between neighbouring cells of different cultivar type generally corresponds to the lowest average disease level, but not for averaged simulations based on random initial infection patterns.