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, often irreversible shifts in a dynamical system's state. This phenomenon is observed in various biological and physical systems, including the collapse of species in ecosystems. Several statistical indicators, known as early warning signals (EWSs), have been developed to anticipate such collapses, garnering significant attention for their broad applicability. This paper investigates the stochastic versions of a bistable algae-zooplankton food-chain model under demographic and environmental noise. Our findings show that an increase in the predatory fish population, which consumes zooplankton, triggers a collapse in zooplankton abundance through a saddle-node bifurcation. Basin stability measure reveals that the resilience of the underexploited steady state significantly diminishes as the system approaches the collapse point. We evaluate the efficacy of various generic EWSs in predicting sudden collapses under both types of noise through statistical analysis. The robustness of AR(1) and variance are assessed through a comprehensive sensitivity analysis of processing parameters. We also calculate conditional heteroskedasticity, which minimizes false positive signals in the time series. Our results indicate that the 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.