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Ecological Disturbance02:26

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Integrating Remote Sensing with Species Distribution Models; Mapping Tamarisk Invasions Using the Software for Assisted Habitat Modeling (SAHM)
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Memory, chaos, and noise in ecological forecasting.

Stephan B Munch1,2, Tanya L Rogers1

  • 1Southwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, Santa Cruz, CA 95060.

Proceedings of the National Academy of Sciences of the United States of America
|June 1, 2026
PubMed
Summary

Ecological population fluctuations are shaped by memory, nonlinearity, and stability. Incorporating these factors improves ecological forecasting, especially for chaotic systems, revealing key drivers of population dynamics.

Keywords:
Lyapunov exponentempirical dynamic modelingnonlinearitystabilitytime series

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Area of Science:

  • Ecology
  • Population Dynamics
  • Ecological Forecasting

Background:

  • Ecological population fluctuations are often attributed to historical factors, nonlinear dynamics, or random noise, but these rarely operate independently.
  • Understanding the interplay of these forces is crucial for predicting population dynamics across diverse taxa.

Purpose of the Study:

  • To investigate how ecological memory, nonlinearity, and dynamical stability interact to influence population predictability.
  • To assess the impact of incorporating memory and nonlinearity on reducing apparent noise and enhancing forecast accuracy.

Main Methods:

  • Assembled a global database of 302 abundance time series from various taxa (birds, mammals, fishes, insects, plankton).
  • Employed empirical dynamic modeling to quantify memory length.
  • Classified time series stability using effective Lyapunov exponents to identify oscillations and chaos.

Main Results:

  • Memory length correlated positively with neutral stability and Lyapunov horizon in chaotic series.
  • Both memory and nonlinearity improved population forecasts, with the most significant gains observed in series with positive Lyapunov exponents (oscillations and chaos).
  • Highly stable populations were accurately modeled using low-dimensional linear models.

Conclusions:

  • Nonlinearity and memory are integral components of ecological population dynamics.
  • The effective Lyapunov exponent serves as a valuable indicator for predicting the predictability of ecological time series.
  • Integrating memory and nonlinear dynamics enhances the accuracy of ecological forecasts.