Early warning signals as indicators of cyclostationarity in three-species hierarchies

Predicting stability from current ecosystem performance is theoretically difficult, but early statistical warning signals (EWS) may enable the anticipation of regime shifts. However, little is known regarding the behavior of EWS in shifts with cyclic dynamics. In this study, we use indicators to assess the stability of a three-species system in a competitive loop similar to a rock-paper-scissors (RPS) hierarchy. In two scenarios, the RPS is simulated using a 3-D automaton whose input matrix combines probabilities of pair-wise dominance with differential reaction frequencies. The first scenario uses the data of a microbial experiment in which the RPS hierarchy is characterized by incomplete dominance within species pairs and differences in reaction frequency between species pairs. The input of the second model was chosen to generate a contrasting scenario: a symmetric RPS interaction gradually subjected to a stressor. The reaction frequency of one species pair was modeled to decay linearly over time. The relative species abundances are monitored spatiotemporally. In the first scenario, abundances oscillate stably despite initial large swings, whereas in the second scenario, one species gradually dominates, eventually resulting in transitivity. In both scenarios, species cluster spatially in patches of single species. In scenario 1, the average patch size remains constant throughout the iterations and possibly contributes to the overall stability; however, in the second scenario, a further homogenization takes place. In the first scenario, EWS reflected the system's stability with species abundances settling into a stable basin. In scenario 1 only one of the EWS indicators detected consistently the loss of resilience. Sensitivity analysis revealed excessive variability in dominance resulted in immediate loss of the RPS hierarchy.