A Model for the Spread of an Invasive Weed, Tradescantia fluminensis

Abstract

Tradescantia fluminensis is an invasive weed and a serious threat to native forests in eastern Australia and New Zealand. Current methods of eradication are often ineffective, so understanding the growth mechanisms of Tradescantia is important in formulating better control strategies. We present a partial differential equation (PDE) model for Tradescantia growth and spatial proliferation that accounts for Tradescantia’s particular creeping and branching morphology, and the impact of self-shading on plant growth. This is the first PDE model to represent a weed that spreads via a creeping growth habit rather than by seed dispersal. We use a travelling wave analysis to investigate how Tradescantia extends to colonise new territory. Numerical simulations and analysis show that the model provides a good qualitative representation of the behaviour of this plant. This model provides a foundation for assessing different control and eradication strategies for Tradescantia.

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Acknowledgements

The authors thank Erin Walsh for creating the illustration of Tradescantia morphology; Charlie Macaskill for assistance with the numerical simulations; David Galloway for providing code to animate the travelling wave solution; and Kerry Landman for helpful discussions about the travelling wave analysis.

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Correspondence to Alexandra B. Hogan.

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Hogan, A.B., Myerscough, M.R. A Model for the Spread of an Invasive Weed, Tradescantia fluminensis . Bull Math Biol 79, 1201–1217 (2017). https://doi.org/10.1007/s11538-017-0280-7

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Keywords

  • Tradescantia fluminensis
  • Commelinaceae
  • Biological invasion
  • Travelling wave analysis
  • Partial differential equation model
  • Self-shading