Rising relative fluctuation as a warning indicator of discontinuous transitions in symbiotic metapopulations

• An interplay of seasonal and stochastic variabilities in metapopulation models is discussed.
• Using the mean-field approach noise-induced discontinuous transitions are demonstrated.
• Sign reversals in time of the autocorrelation function of population sizes are found.
• An increase of relative fluctuation prior to abrupt shifts is shown.

The long-time limit behavior of the stochastic Lotka–Volterra model of a symbiotic metapopulation subjected to generalized Verhulst self-regulation is considered. The influence of a time-variable environment on the carrying capacities of subpopulations is modeled as a periodic deterministic part and a symmetric dichotomous noise. Relying on the mean-field approach it is established that at certain parameter regimes the mean field (average subpopulations size) exhibits hysteresis in respect to the noise correlation time, manifested in the appearance of colored-noise-induced discontinuous transitions. Especially, it is shown that the relative fluctuation of the subpopulation sizes exhibits accelerated increase prior to abrupt transitions of the metapopulation state. Moreover, in certain cases the autocorrelation function of the population sizes demonstrates anticorrelation at some values of the lag time.