Can spatial patterns along climatic gradients predict ecosystem responses to climate change? Experimenting with reactiondiffusion simulations

Abstract

Following a predicted decline in water resources in the Mediterranean Basin, we used reaction-diffusion equations to gain a better understanding of expected changes in properties of vegetation patterns that evolve along the rainfall transition between semi-arid and arid rainfall regions. Two types of scenarios were investigated: the first, a discrete scenario, where the potential consequences of climate change are represented by patterns evolving at discrete rainfall levels along a rainfall gradient. This scenario concerns space-for-time substitutions characteristic of the rainfall gradient hypothesis. The second, a continuous scenario, represents explicitly the effect of rainfall decline on patterns which evolved at different rainfall levels along the rainfall gradient prior to the climate change. The eccentricity of patterns that emerge through these two scenarios was found to decrease with decreasing rainfall, while their solidity increased. Due to their inverse modes of change, their ratio was found to be a highly sensitive indicator for pattern response to rainfall decline. An eccentricity ratio versus rainfall (ER:R) line was generalized from the results of the discrete experiment, where ERs above this line represent developed (recovered) patterns and ERs below this line represent degraded patterns. For the rainfall range of 1.2 to 0.8 mm/day, the continuous rainfall decline experiment with ERs that lie above the ER:R line, yielded patterns less affected by rainfall decline than would be expected according to the discrete representation of ecosystems' response. Thus, for this range, space-for-time substitution represents an overestimation of the consequences of the expected rainfall decline. For rainfall levels below 0.8 mm/day, eccentricity ratios from the discrete and continuous experiments practically converge to the same trend of pattern change along the ER:R line. Thus, the rainfall gradient hypothesis may be valid for regions characterized by this important rainfall range, which typically include desert fringe ecosystems.