B-tipping points in plankton dynamics: Stochasticity and early warning signals

Near a tipping point, a critical transition occurs when small changes in input conditions lead to abrupt, oftenirreversible shifts in a dynamical system's state. This phenomenon is observed in various biological and physicalsystems, including the collapse of species in ecosystems. Several statistical indicators, known as early warningsignals (EWSs), have been developed to anticipate such collapses, garnering significant attention for theirbroad applicability. This paper investigates the stochastic versions of a bistable algae-zooplankton food-chainmodel under demographic and environmental noise. Our findings show that an increase in the predatory fishpopulation, which consumes zooplankton, triggers a collapse in zooplankton abundance through a saddle-nodebifurcation. Basin stability measure reveals that the resilience of the underexploited steady state significantlydiminishes as the system approaches the collapse point. We evaluate the efficacy of various generic EWSs inpredicting sudden collapses under both types of noise through statistical analysis. The robustness of AR(1) andvariance are assessed through a comprehensive sensitivity analysis of processing parameters. We also calculateconditional heteroskedasticity, which minimizes false positive signals in the time series. Our results indicate thatthe prediction accuracy of variance and conditional heteroskedasticity remains independent of the noise type.However, AR(1) and skewness perform better in the presence of environmental noise.