Memory, chaos, and noise in ecological forecasting

Ecological populations fluctuate for reasons that are often ascribed—separately—to historical legacies, intrinsic nonlinear dynamics, or stochastic noise. Yet these forces rarely act in isolation. We assembled a global database of 302 abundance time series spanning birds, mammals, fishes, insects, and plankton to ask how memory, nonlinearity, and dynamical stability interact to shape predictability. We used empirical dynamic modeling to estimate the memory length and classified time series stability via effective Lyapunov exponents. We also examined the degree to which incorporating memory and nonlinearity reduce apparent noise and improve prediction. We found that memory length was greatest in neutrally stable series and proportional to the Lyapunov horizon in chaotic series. Both memory and nonlinearity improved forecasts, but gains were largest in series exhibiting positive Lyapunov exponents (oscillations and chaos). By contrast, populations with strongly stable dynamics are well captured by low dimensional linear models. Hence, nonlinearity and memory are both important components of ecological dynamics and the effective Lyapunov exponent is a useful prognosticator of predictability.