Andrew Mead, Andrea Grundy (HRI), Phil Brain (IACR)

The primary cause of heterogeneity in the spatial distribution of weed seeds in the soil is the re-distribution caused by cultivation following an initial shedding on the soil surface. Previous research has produced models for either the horizontal movement of seeds (Brain & Marshall, 1999) or the vertical movement of seeds (Cousens & Moss, 1990; Grundy & Mead, 1998), but in both cases with no account taken of movement in the other dimension.

Based on data from an experiment using plastic beads to imitate seeds, we are now trying to develop a fully 3-dimensional model for weed seed movement following cultivation. Two simple approaches have already been developed – the first (Grundy, Mead & Burston, 1999) extends the transition matrix approach developed to model vertical movement, producing vertical transition matrices for each of a number of horizontal distance ranges (backward movement, no movement, forward movement), whilst in the second approach, horizontal movement functions are calculated for each of the cells of the vertical transition matrix. Both approaches, however, can only predict movement from the initial depths used in the experiment.

A more general approach can be developed by modelling the combined vertical and horizontal movement as a continuous re-distribution function, as an extension of the approach developed by Brain and Marshall (1999). In this approach the vertical profile is divided into a number of thin slices, and 2-dimensional Fast Fourier Transforms are used to evaluate the horizontal movement integral in each slice. The overall movement function is then obtained by summing the horizontal movement functions across these thin slices. Effectively this generates the product of a vertical transition matrix and a matrix of horizontal movement functions, the difference from the approach described earlier being that we can have as many thin slices as we want, and can therefore predict the probability of movement from any depth, not just from those depths used in the experiment.

The early vertical movement models have already being incorporated into a prototype simulation system, MOSAICS, into which the 3-dimensional models will be incorporated once they are complete.

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