The Mathematica Journal
Volume 10, Issue 2


In This Issue
In and Out
Trott's Corner
Beyond Sudoku
New Products
New Publications
News Bulletins
New Resources

Download This Issue 

About the Journal
Editorial Policy
Staff and Contributors
Back Issues
Contact Information

Individual-Based Models of the Spread of Disease, Weeds, and Insects
Art Diggle
Moin Salam
Marta Monjardino

Spread of Weeds

A variant of the model has been used to model spread of weeds by harvesting equipment. Numbers of seeds and growing plants for the weed and crop species are maintained for each of the infested cells of the map. This model is driven by a sequence of events which represent stages of the life cycle of the plants and activities of the farmer. These events include:

  • germination--translates a proportion of the seeds into growing plants
  • spray and tillage--reduces the number of growing plants
  • seedset--produces new seed on the growing plants
  • harvest--calculates the amount of weed seed that is removed with the crop seed and spreads the weed seed

The map used in this model represents a cropping field. The cell size used is set equal to the width of the harvesting equipment (10m for the example shown here) and the spread path is defined by a list of cell coordinates in the order that the harvester moves over them. Spread distances along the path of the harvester are generated from a Cauchy distribution as before, with an additional constant probability that seeds will move sideways into cells adjacent to the path of the harvester.

Figure 3 shows the simulated distribution of the weed Bedstraw in a 1km square field 11 years after an initial incursion of 100 randomly placed seeds. In each year the harvester followed a counter-clockwise spiral path from the lower right corner to the centre and then travelled diagonally back to the starting point. Shading is proportional to the density of the seed.

Figure 3. Simulated pattern of seeds of the weed Bedstraw spread by harvesting equipment in a 1km square field.

About Mathematica | Download Mathematica Player 
© Wolfram Media, Inc. All rights reserved.