Quasicycles revisited: apparent sensitivity to initial conditions.

Area of Science:

• Ecology
• Dynamical Systems Theory
• Nonlinear Time Series Analysis

Background:

• Environmental noise is recognized for sustaining ecological cycles by perturbing deterministic oscillatory systems.
• Quasicycles, characterized by regular periods and variable amplitudes, were previously proposed to explain natural population fluctuations.
• Nisbet and Gurney first introduced quasicycles as a potential driver of population dynamics.

Purpose of the Study:

• To re-examine quasicyclic dynamics using nonlinear time series analysis.
• To investigate the influence of environmental noise on predator-prey models and population fluctuations.
• To analyze sensitivity to initial conditions in populations exhibiting quasicyclic behavior.

Main Methods:

• Generated time series data from a predator-prey model with environmentally noisy prey growth rates.
• Applied nonlinear time series analysis methods suitable for short and noisy datasets.
• Compared results with previous analyses of quasicycles in individual-based models with spatial heterogeneity.

Main Results:

• Evidence of sensitivity to initial conditions was found, with Lyapunov exponents near zero, indicating dynamics at the 'edge of chaos'.
• Analyses of long time series suggested a finite-dimensional attractor governing the sensitive dynamics.
• Distinguished between phase-forgetting and phase-remembering quasicycles based on sensitivity patterns.

Conclusions:

• Quasicyclic dynamics, driven by environmental noise, can lead to population fluctuations sensitive to initial conditions.
• The 'edge of chaos' dynamics observed may be a common feature in ecological systems exhibiting quasicycles.
• The findings provide a framework for interpreting Lyapunov exponent modes in natural populations.