Mathematical modelling of a new weed incursion and its control in large area cropping systems

Rohan T. Jayasuriya, Remy van de Ven and Randall E. Jones

CRC for Australian Weed Management and NSW Department of Primary Industries, Orange Agricultural Institute, Forest Road, Orange, New South Wales 2800, Australia.


A mathematical model incorporating weed growth, dispersal and control is developed to represent the spread of a weed from a point source in cropping fields. This model allows the simulation of theoretical rates of weed spread and the examination of spatial distribution of a new weed infestation on a large regional scale. The model is cellular in structure, dividing space into discrete units. The starting point is with an initial population at a point source, such as might arise with the arrival of a newly invading species, an emerging sleeper weed or the first herbicide-resistant plants in an arable field. The location of this point source is set in the centre of the hypothetical grid field. From this starting point, the spread of weeds is modelled at annual intervals. Risk is a critical issue to this modelling; the weed spread functions being stochastic (with different probability distributions incorporating rare events in the dispersal process), and the weed control effort decision being probabilistic. Six case study weed spread simulations were undertaken to demonstrate the model's applicability to different weed incursions with differences in weed biology, rates of spread and to demonstrate the effects of weed search and control effort. The simulated model results are discussed in relation to a case study of awnless barnyard grass (Echinochloa colona) spread and its control in northern New South Wales, Australia.