Concerns around herbicide resistance, human risk, and the environmental impacts of current weed control strategies have led to an increasing demand for alternative weed management methods. Many new weed management strategies are under development; however, the poor availability of accurate weed maps, and a lack of confidence in the outcomes of alternative weed management strategies, has hindered their adoption. Developments in field sampling and processing, combined with spatial modelling, can support the implementation and assessment of new and more integrated weed management strategies. Our review focuses on the biological and mathematical aspects of assembling within-field weed models. We describe both static and spatio-temporal models of within-field weed distributions (including both cellular automata (CA) and non-CA models), discussing issues surrounding the spatial processes of weed dispersal and competition and the environmental and anthropogenic processes that affect weed spatial and spatio-temporal distributions. We also examine issues surrounding model uncertainty. By reviewing the current state-of-the-art in both static and temporally dynamic weed spatial modelling we highlight some of the strengths and weaknesses of current techniques, together with current and emerging areas of interest for the application of spatial models, including targeted weed treatments, economic analysis, herbicide resistance and integrated weed management, the dispersal of biocontrol agents, and invasive weed species.

Lolium multiflorum (annual Italian ryegrass) and other grass weeds are an increasing problem in cereal cropping systems in Denmark. Grass weeds are highly competitive and an increasing number of species develop resistance against the most commonly used herbicide modes of action. A diverse management strategy provides a better overall control of grass weeds and decreases the reliance on herbicides. The bio-economic decision support system, DK-RIM (Denmark-Ryegrass Integrated Management), was developed to assist integrated management of L. multiflorum in Danish cropping systems, based on the Australian RIM model. DK-RIM provides long-term estimations (10-year period) and visual outputs of L. multiflorum population development, depending on management strategies. The dynamics of L. multiflorum plants within the season and of the soil seed bank across seasons are simulated. The user can combine cultural weed control practices with chemical control options. Cultural practices include crop rotation changes, seeding density, sowing time, soil tillage system, and cover crops. Scenarios with increasing crop rotation diversity or different tillage strategies were evaluated. DK-RIM aims at being an actual support system, aiding the farmer’s decisions and encouraging discussions among stakeholders on alternative management strategies.