In harsh or resource-deprived environments, plants tend to interact in two opposite ways, namely by exerting facilitative plant-plant interactions through their aerial parts and competitive interactions via their root systems. Such dual interactions are liable to produce highly contrasted vegetation patterns (i.e. where relatively high biomass alternate with virtually bare soils), which are indeed frequently observed in the field over very large areas, and maybe thought of as self-organized.

We report here a line of modelling that address the emergence of such patterns from a minimalistic modelling of biomass dynamics using a single integro-differential equation that features logistic growth, seed diffusion and non-local kernels of interactions, the range of which relate to the sizes of the crown and root systems of the individual plants.

This modelling framework has been applied to various types of vegetation and proved able to account for the emergence of patterns by emphasizing the role of individual plant morphology via an allometric parameter of crown to rhizosphere sizes. Two examples are attached: periodic patterns made of tall shrubs in the African Sahel and grass tussocks in the Andean Altiplano. In the latter case, interactions are modelled at the scale of basic plant modules (ie ramets) as to account for the modal size of the tussocks themselves.