Negative plant soil feedback explaining ring formation in clonal plants.

Ring shaped patches of clonal plants have been reported in different environments, but the mechanisms underlying such pattern formation are still poorly explained. Water depletion in the inner tussocks zone has been proposed as a possible cause, although ring patterns have been also observed in ecosystems without limiting water conditions. In this work, a spatially explicit model is presented in order to investigate the role of negative plant-soil feedback as an additional explanation for ring formation. The model describes the dynamics of the plant biomass in the presence of toxicity produced by the decomposition of accumulated litter in the soil. Our model qualitatively reproduces the emergence of ring patterns of a single clonal plant species during colonisation of a bare substrate. The model admits two homogeneous stationary solutions representing bare soil and uniform vegetation cover which depend only on the ratio between the biomass death and growth rates. Moreover, differently from other plant spatial patterns models, but in agreement with real field observations of vegetation dynamics, we demonstrated that the pattern dynamics always lead to spatially homogeneous vegetation covers without creation of stable Turing patterns. Analytical results show that ring formation is a function of two main components, the plant specific susceptibility to toxic compounds released in the soil by the accumulated litter and the decay rate of these same compounds, depending on environmental conditions. These components act at the same time and their respective intensities can give rise to the different ring structures observed in nature, ranging from slight reductions of biomass in patch centres, to the appearance of marked rings with bare inner zones, as well as the occurrence of ephemeral waves of plant cover. Our results highlight the potential role of plant-soil negative feedback depending on decomposition processes for the development of transient vegetation patterns.