Ecological systems such as lakes and vegetation in semi-arid ecosystems can undergo rapid transition from one state to an alternative stable state often leading to severe ecological and economic consequences. They are referred to as catastrophic regime shifts. Recently, several studies have suggested leading indicators which can serve as an early warning signal of an impending transition (Carpenter et al, 2006, Ecology letters, Vol. 9, 311-318; van Nes et al, Am Nat 2007. Vol. 169, pp. 738747; Guttal and Jayaprakash, 2008, Ecology Letters, in press). These studies do not include spatial fluctuations in ecological systems and a reliable evaluation of these indicators often require long time series data, thus undermining their practical utility. Aim of this research work is to develop indicators of regime shifts in spatial ecological models and study their practical utility.
Results/Conclusions
We show from studies of spatial ecological models that spatial variance and spatial skewness determined from snapshots of spatial data of an ecological system can be robust indicators of proximity to a transition. Moreover, spatial data can be used reliably even with much shorter length of time series thus substantially enhancing the predictive capabilities. Novel feature of these indicators is that they are derived from nonlinearity and external fluctuations which drive the regime shifts. These results are shown to hold for various kernels of spatial interactions such as local (Gaussian), fat tailed and heavily fat tailed kernels and hence they are potentially applicable across wide variety of ecological systems. Applications to real systems where data availability is sparse will be discussed.