Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes.

For water-limited arid ecosystems, where water distribution and infiltration play a vital role, various models have been set up to explain vegetation patterning. On sloped terrains, vegetation aligned in bands has been observed ubiquitously. In this paper, we consider the appearance, stability, and bifurcations of 2D striped or banded patterns in an arid ecosystem model. We numerically show that the resilience of the vegetation bands is larger on steeper slopes by computing the stability regions (Busse balloons) of striped patterns with respect to 1D and transverse 2D perturbations. This is corroborated by numerical simulations with a slowly decreasing water input parameter. Here, long wavelength striped patterns are unstable against transverse perturbations, which we also rigorously prove on flat ground through an Evans function approach. In addition, we prove a "Squire theorem" for a class of two-component reaction-advection-diffusion systems that includes our model, showing that the onset of pattern formation in 2D is due to 1D instabilities in the direction of advection, which naturally leads to striped patterns.

Empirical and theoretical challenges in aboveground-belowground ecology.

A growing body of evidence shows that aboveground and belowground communities and processes are intrinsically linked, and that feedbacks between these subsystems have important implications for community structure and ecosystem functioning. Almost all studies on this topic have been carried out from an empirical perspective and in specific ecological settings or contexts. Belowground interactions operate at different spatial and temporal scales. Due to the relatively low mobility and high survival of organisms in the soil, plants have longer lasting legacy effects belowground than aboveground. Our current challenge is to understand how aboveground-belowground biotic interactions operate across spatial and temporal scales, and how they depend on, as well as influence, the abiotic environment. Because empirical capacities are too limited to explore all possible combinations of interactions and environmental settings, we explore where and how they can be supported by theoretical approaches to develop testable predictions and to generalise empirical results. We review four key areas where a combined aboveground-belowground approach offers perspectives for enhancing ecological understanding, namely succession, agro-ecosystems, biological invasions and global change impacts on ecosystems. In plant succession, differences in scales between aboveground and belowground biota, as well as between species interactions and ecosystem processes, have important implications for the rate and direction of community change. Aboveground as well as belowground interactions either enhance or reduce rates of plant species replacement. Moreover, the outcomes of the interactions depend on abiotic conditions and plant life history characteristics, which may vary with successional position. We exemplify where translation of the current conceptual succession models into more predictive models can help targeting empirical studies and generalising their results. Then, we discuss how understanding succession may help to enhance managing arable crops, grasslands and invasive plants, as well as provide insights into the effects of global change on community re-organisation and ecosystem processes.