We propose an individual-based models (IBM) of a terrestrial plant sys- tems. Each individual plant is explicitly represented as well as the basic mechanisms acting on each individual: natural birth and death, dispersion, death due to compe- tition. The resulting model is a Markovian model of branching particles with diffu- sion. We describe the model and the associated Monte Carlo procedure. We study the asymptotic properties of this model in a large population setup.