The effect of seasonal strength and abruptness on predator-prey dynamics

Stochastic resonance in climate reddening increases the risk of cyclic ecosystem extinction via phase-tipping

Human activity is leading to changes in the mean and variability of climatic parameters in most locations around the world. The changing mean has received considerable attention from scientists and climate policy makers. However, recent work indicates that the changing variability, that is, the amplitude and the temporal autocorrelation of deviations from the mean, may have greater and more imminent impact on ecosystems. In this paper, we demonstrate that changes in climate variability alone could drive cyclic predator-prey ecosystems to extinction via so-called phase-tipping (P-tipping), a new type of instability that occurs only from certain phases of the predator-prey cycle. We construct a mathematical model of a variable climate and couple it to two self-oscillating paradigmatic predator-prey models. Most importantly, we combine realistic parameter values for the Canada lynx and snowshoe hare with actual climate data from the boreal forest. In this way, we demonstrate that critically important species in the boreal forest have increased likelihood of P-tipping to extinction under predicted changes in climate variability, and are most vulnerable during stages of the cycle when the predator population is near its maximum. Furthermore, our analysis reveals that stochastic resonance is the underlying mechanism for the increased likelihood of P-tipping to extinction.

Effectiveness of phase synchronization in chaotic food chain model with refugia and Allee effects during seasonal fluctuations

Seasonal effects powerfully shape the population dynamics with periodic climate changes because species naturally adjust their dynamics with seasonal variations. In response to these effects, sometimes population dynamics exhibit synchrony or generate chaos. However, synchronized dynamics enhance species' persistence in naturally unstable environments; thus, it is imperative to identify parameters that alter the dynamics of an ecosystem and bring it into synchrony. This study examines how ecological parameters enable species to adapt their dynamics to seasonal changes and achieve phase synchrony within ecosystems. For this, we incorporate seasonal effects as a periodic sinusoidal function into a tri-trophic food chain system where two crucial bio-controlling parameters, Allee and refugia effects, are already present. First, it is shown that the seasonal effects disrupt the limit cycle and bring chaos to the system. Further, we perform rigorous mathematical analysis to perform the dynamical and analytical properties of the nonautonomous version of the system. These properties include sensitive dependence on initial condition (SDIC), sensitivity analysis, bifurcation results, the positivity and boundedness of the solution, permanence, ultimate boundedness, and extinction scenarios of species. The SDIC characterizes the presence of chaotic oscillations in the system. Sensitivity analysis determines the parameters that significantly affect the outcome of numerical simulations. The bifurcation study concerning seasonal parameters shows a higher dependency of species on the frequency of seasonal changes than the severity of the season. The bifurcation study also examines the bio-controlling parameters and reveals various dynamic states within the system, such as fold, transcritical branch points, and Hopf points. Moreover, the mathematical analysis of our seasonally perturbed system reveals the periodic coexistence of all species and a globally attractive solution under certain parametric constraints. Finally, we examine the role of essential parameters that contribute to phase synchrony. For this, we numerically investigate the defining role of the coupling dimension coefficient, bio-controlling parameters, and other parameters associated with seasonality. This study infers that species can tune their dynamics to seasonal effects with low seasonal frequency, whereas the species' tolerance for the severity of seasonal effects is relatively high. The research also sheds light on the correlation between the degree of phase synchrony, prey biomass levels, and the severity of seasonal forcing. This study offers valuable insights into the dynamics of ecosystems affected by seasonal perturbations, with implications for conservation and management strategies.

Intermittent instability is widespread in plankton communities

Chaotic dynamics appear to be prevalent in short-lived organisms including plankton and may limit long-term predictability. However, few studies have explored how dynamical stability varies through time, across space and at different taxonomic resolutions. Using plankton time series data from 17 lakes and 4 marine sites, we found seasonal patterns of local instability in many species, that short-term predictability was related to local instability, and that local instability occurred most often in the spring, associated with periods of high growth. Taxonomic aggregates were more stable and more predictable than finer groupings. Across sites, higher latitude locations had higher Lyapunov exponents and greater seasonality in local instability, but only at coarser taxonomic resolution. Overall, these results suggest that prediction accuracy, sensitivity to change and management efficacy may be greater at certain times of year and that prediction will be more feasible for taxonomic aggregates.

Rethinking the Prevalence and Relevance of Chaos in Ecology

Chaos was proposed in the 1970s as an alternative explanation for apparently noisy fluctuations in population size. Although readily demonstrated in models, the search for chaos in nature proved challenging and led many to conclude that chaos is either rare or nigh impossible to detect. However, in the intervening half-century, it has become clear that ecosystems are replete with the enabling conditions for chaos. Chaos has been repeatedly demonstrated under laboratory conditions and has been found in field data using updated detection methods. Together, these developments indicate that the apparent rarity of chaos was an artifact of data limitations and overreliance on low-dimensional population models. We invite readers to reevaluate the relevance of chaos in ecology, and we suggest that chaos is not as rare or undetectable as previously believed.

Phase tipping: how cyclic ecosystems respond to contemporary climate

We identify the phase of a cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. As an example, we consider how contemporary climate variability induces tipping from a predator–prey cycle to extinction in two paradigmatic predator–prey models with an Allee effect. Our analysis of these examples uncovers a counterintuitive behaviour, which we call phase tipping or P-tipping, where tipping to extinction occurs only from certain phases of the cycle. To explain this behaviour, we combine global dynamics with set theory and introduce the concept of partial basin instability for attracting limit cycles. This concept provides a general framework to analyse and identify easily testable criteria for the occurrence of phase tipping in externally forced systems, and can be extended to more complicated attractors.