Detecting stochasticity in population time series using a non‐parametric test of intrinsic predictability

Author:

Şen Bilgecan123ORCID,Che‐Castaldo Christian4ORCID,Lynch Heather J.12ORCID,Ventura Francesco5ORCID,LaRue Michelle A.67ORCID,Jenouvrier Stéphanie5ORCID

Affiliation:

1. Institute for Advanced Computational Science Stony Brook University Stony Brook New York USA

2. Department of Ecology and Evolution Stony Brook University Stony Brook New York USA

3. Appalachian Laboratory University of Maryland Center for Environmental Science Frostburg Maryland USA

4. U.S. Geological Survey, Wisconsin Cooperative Wildlife Research Unit, Department of Forest and Wildlife Ecology University of Wisconsin‐Madison Madison Wisconsin USA

5. Biology Department Woods Hole Oceanographic Institution Woods Hole Massachusetts USA

6. School of Earth and Environment University of Canterbury Christchurch New Zealand

7. Department of Earth and Environmental Sciences University of Minnesota Minneapolis Minnesota USA

Abstract

Abstract Many ecological systems dominated by stochastic dynamics can produce complex time series that inherently limit forecast accuracy. The ‘intrinsic predictability’ of these systems can be approximated by a time series complexity metric called weighted permutation entropy (WPE). While WPE is a useful metric to gauge forecast performance prior to model building, it is sensitive to noise and may be biased depending on the length of the time series. Here, we introduce a simple randomized permutation test (rWPE) to assess whether a time series is intrinsically more predictable than white noise. We apply rWPE to both simulated and empirical data to assess its performance and usefulness. To do this, we simulate population dynamics under various scenarios, including a linear trend, chaotic, periodic and equilibrium dynamics. We further test this approach with observed abundance time series for 932 species across four orders of animals from the Global Population Dynamics Database. Finally, using Adélie (Pygoscelis adeliae) and emperor penguin (Aptenodytes forsteri) time series as case studies, we demonstrate the application of rWPE to multiple populations for a single species. We show that rWPE can determine whether a system is significantly more predictable than white noise, even with time series as short as 10 years that show an apparent trend under biologically realistic stochasticity levels. Additionally, rWPE has statistical power close to 100% when time series are at least 30 time steps long and show chaotic or periodic dynamics. Power decreases to ~10% under equilibrium dynamics, irrespective of time series length. Among four classes of animal taxa, mammals have the highest relative frequency (28%) of time series that are both longer than 30 time steps and indistinguishable from white noise in terms of complexity, followed by insects (16%), birds (16%) and bony fishes (11%). rWPE is a straightforward and useful method widely applicable to any time series, including short ones. By informing forecasters of the inherent limitations to a system's predictability, it can guide a modeller's expectations for forecast performance.

Funder

National Aeronautics and Space Administration

National Science Foundation

Publisher

Wiley

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