Limiting Effect of Self-Shading on the Height of Tradescantia fluminensis Mats

Tradescantia fluminensis is an invasive plant species in New Zealand, Australia and parts of the USA. It reproduces vegetatively and can grow to form dense mats up to 60 cm deep. Growth is limited by available light, and shading is one of the few effective methods of control. In this paper, we develop a dynamic model of a vertical cross section of a T. fluminensis mat, capturing vertical variation in its biomass and internal light intensity. We measure both variables at different heights in experimental mats of the species and use these data to parameterize the model. The model produces realistic vertical biomass and light intensity profiles. We show that the mat grows to a steady-state biomass that depends only on: (i) the light absorption coefficient, which we estimate from experimental data and (ii) the ratio of photosynthesis to respiration rate. This steady state undergoes a transcritical bifurcation; when the ambient light intensity falls below a critical level, the biomass shrinks to zero and the mat cannot survive.