Modelling spatio-temporal dynamics of herbicide resistance

A mathematical model has been developed for the risk assessment of the spread of genes conferring herbicide resistance in plant populations. The model combines an age-and-stage-structured population dynamic model, a population genetic model and a model of spatial spread. This is achieved by embedding a local matrix population model into a cellular automaton model with raster cells as spatial units. The dynamics of each cell is determined by both its local dynamics and the interaction with neighbouring cells. The model is applied to the evaluation of management strategies to delay or even to prevent long-term evolution of resistance in an annual grass weed. The results show that the appearance and spread of resistant genes is a highly non-linear process exhibiting threshold phenomena, which occur for a wide range of parameters. The properties of the seed survival curve constitute the `genetic memory' of the system and thus determine its long-term dynamics. It is possible to delay the evolution of resistance by suspension of treatment, reduction in herbicide application rate and introducing fallow periods. Spatial spread from an infested plot is inhibited by leaving untreated strips between adjacent fields.