Flow of genetic information through agricultural ecosystems : a generic modelling framework with application to pesticide-resistance weeds and genetically modified crops

Unintended spatial spread of genetic information is one of the major problems in modern agriculture. The vertical distribution of transgenic properties and the spatial spread of resistant weeds and pests are likely to develop under long-term pesticide use. These are complex systems that require an integrated view of population dynamics, genetics, and physical transport processes. Mathematical models may be utilised to support of risk assessment and to derive appropriate risk management strategies. In this contribution we propose a generic modelling framework that provides an explicit simulation of the spatial patterns of gene flow through agro-ecosystems. Pollen dispersal is modelled with traditional transport equations from atmospheric physics that are applied to outcrossing studies of genetically modified maize. Transport equations were coupled to models of population dynamics and genetics with partial differential equations that combine dispersal, growth and genetics. The overall model consists of a set of coupled partial differential equations for pollen dispersal, and the spatial and temporal dynamics of each biotype involved. Initial boundary value problems are set up for the dispersal of resistance in dependence on spatial spread patterns, which are solved by finite element methods.