Tipping points in spatial ecosystems driven by correlated noise

Abstract

Complex spatial systems can experience critical transitions or tippings on crossing a threshold value in their response to stochastic perturbations. Whilst previous studies have well-characterized the impact of white noise on tipping, the effect of correlated noise in spatial ecosystems remains largely unexplored. Here, we investigate the effect of both multiplicative and additive Ornstein-Uhlenbeck (OU) correlated noise on the occurrence of critical transitions in spatial ecosystems. We find that decreasing the noise correlation aggravates the chance of critical transitions - opposite to what is observed previously in temporal systems in the presence of OU-noise with fixed lag-1 correlation. Our results hold good and are supported by the analysis of three well-studied spatial ecological models of varying nonlinearity. We also compute spatial early warning indicators (e.g., spatial variance, spatial skewness, and spatial correlation) to determine their reliability in anticipating tipping points with variations in noise correlation. The indicators of critical transitions exhibit mixed success in forewarning the occurrence of a tipping point, as indicated by the distribution of Kendall's rank correlation.