Effect of Non-local Grazing on Dry-land Vegetation Dynamics

Abstract: Dry-land ecosystem has turned into a matter of grave concern, due to growing threat of land degradation and bioproductivity-loss. Self-organized vegetation patterns are a remarkable characteristic of these ecosystems; apart from being visually captivating, patterns modulate the system-response to increasing environmental stress. Empirical studies hinted that herbivory is one the key regulatory mechanism behind pattern formation and overall ecosystem functioning. However most of the mathematical models have taken a mean-field strategy to grazing; foraging has been considered to be independent of spatial distribution of vegetation. To this end, an extended version of the celebrated plant-water model due to Klausmeier, has been taken as the base here. To encompass the effect of heterogeneous vegetation distribution on foraging intensity and subsequent impact on entire ecosystem, grazing is considered here to depend on spatially weighted average vegetation density, instead of density at a particular point. Moreover, varying influence of vegetation at any location over gazing elsewhere, is incorporated by choosing suitable averaging function. A comprehensive analysis demonstrates that inclusion of spatial non-locality, alters the understanding of system dynamics significantly. The grazing ecosystem is found to be more resilient to increasing aridity than it was anticipated to be in earlier studies on non-local grazing. The system-response to rising environmental pressure is also observed to vary depending on the grazer. Obtained results also suggest possibility of multi-stability due the history-dependence of system-response. Overall, this work indicates that the spatial heterogeneity in grazing intensity has a decisive role to play in the functioning of water-limited ecosystems.