Skip to main content
Log in

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

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript


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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others


  • Aikman D, Watkinson A (1980) A model for growth and self-thinning in even-aged monocultures of plants. Ann Bot 45(4):419–427

    Article  Google Scholar 

  • Balding D, McElwain D (1985) A mathematical model of tumour-induced capillary growth. J Theor Biol 114(1):53–73

    Article  Google Scholar 

  • Barnes P, Beyschlag W, Ryel R, Flint S, Caldwell M (1990) Plant competition for light analysed with a multi species canopy model, III: influence of canopy structure in mixtures and monocultures of wheat and wild oat. Oecologia 82(4):560–566

    Article  Google Scholar 

  • Bastian P, Chavarría-Krauser A, Engwer C, Jäger W, Marnach S, Ptashnyk M (2008) Modelling in vitro growth of dense root networks. J Theor Biol 254(1):99–109. doi:10.1016/j.jtbi.2008.04.014

    Article  Google Scholar 

  • Burns JH (2008) Demographic performance predicts invasiveness of species in the Commelinaceae under high-nutrient conditions. Ecol Appl 18(2):335–346. doi:10.1890/07-0568.1

    Article  Google Scholar 

  • Byrne H, Chaplain M (1995) Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions. Bull Math Biol 57(3):461–486

    Article  MATH  Google Scholar 

  • CABI (2008) Tradescantia fluminensis. Accessed 18 Nov 2015

  • Calado G, Duarte P (2000) Modelling growth of Ruppia cirrhosa. Aquat Bot 68(1):29–44. doi:10.1016/S0304-3770(00)00104-2

    Article  Google Scholar 

  • Edelstein L (1982) The propagation of fungal colonies: a model for tissue growth. J Theor Biol 98(4):679–701

    Article  MathSciNet  Google Scholar 

  • Fowler SV, Barreto R, Dodd S, Macedo DM, Paynter Q, Pedrosa-Macedo JH, Pereira OL, Peterson P, Smith L, Waipara N, Winks CJ, Forrester G (2013) Tradescantia fluminensis, an exotic weed affecting native forest regeneration in New Zealand: ecological surveys, safety tests and releases of four biocontrol agents from Brazil. Biol Control 64(3):323–329. doi:10.1016/j.biocontrol.2012.11.013

    Article  Google Scholar 

  • Griffiths G, Schiesser WE (2011) Traveling wave analysis of partial differential equations. Elsevier, Amsterdam

    Google Scholar 

  • Hogan A (2009) A mathematical model for the growth and spread of an invasive weed, Tradescantia fluminensis, Honours Thesis. School of Mathematics and Statistics, The University of Sydney

  • James A, Molloy SM, Ponder-Sutton A, Plank MJ, Lamoureaux SL, Bourdôt GW, Kelly D (2015) Modelling Tradescantia fluminensis to assess long term survival. PeerJ 3:e1013. doi:10.7717/peerj.1013

    Article  Google Scholar 

  • Kelly D, Skipworth JP (1984) Tradescantia fluminensis in a Manawatu (New Zealand) forest: I. Growth and effects on regeneration. N Z J Bot 22(3):393–397. doi:10.1080/0028825X.1984.10425270

    Article  Google Scholar 

  • Maule H, Andrews M, Morton J (1995) Sun/shade acclimation and nitrogen nutrition of Tradescantia fluminensis, a problem weed in New Zealand native forest remnants. N Z J Ecol 19(1):35–46

    Google Scholar 

  • Murray JD (2002) Mathematical biology: I. An introduction, 3rd edn. Springer, New York

    MATH  Google Scholar 

  • Perry LG, Neuhauser C, Galatowitsch SM (2003) Founder control and coexistence in a simple model of asymmetric competition for light. J Theor Biol 222(4):425–436. doi:10.1016/S0022-5193(03)00055-9

    Article  MathSciNet  Google Scholar 

  • Standish R, Robertson AW, Williams PA (2001) The impact of an invasive weed Tradescantia fluminensis on native forest regeneration. J Appl Ecol 38(6):1253–1263

    Article  Google Scholar 

  • Standish R, Williams P, Robertson A, Scott NA, Hedderley DI (2004) Invasion by a perennial herb increases decomposition rate and alters nutrient availability in warm temperate lowland forest remnants. Biol Invasions 6(1):71–81. doi:10.1023/B:BINV.0000010127.06695.f4

    Article  Google Scholar 

  • Vance RR, Nevai AL (2007) Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning. J Theor Biol 245(2):210–219. doi:10.1016/j.jtbi.2006.10.015

    Article  MathSciNet  Google Scholar 

  • Wiles L, Wilkerson G (1991) Modeling competition for light between soybean and broadleaf weeds. Agric Syst 35(1):37–51

    Article  Google Scholar 

Download references


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.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Alexandra B. Hogan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hogan, A.B., Myerscough, M.R. A Model for the Spread of an Invasive Weed, Tradescantia fluminensis . Bull Math Biol 79, 1201–1217 (2017).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: