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In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
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Detecting stabilizing dynamics in biased biodiversity time series using Haar fluctuation analysis.

Wyatt Petryshen1, Pincelli M Hull1, David A Vasseur2

  • 1Department of Earth and Planetary Sciences, Yale University, New Haven, CT 06511, USA.

Proceedings. Biological Sciences
|April 21, 2026
PubMed
Summary
This summary is machine-generated.

Haar fluctuation analysis can reliably detect biodiversity stability, even with biased data. This time-series method offers a robust approach for studying long-term ecological dynamics and macroevolutionary patterns.

Keywords:
Sadler effectmacroecologymacroevolutionnull modelspalaeobiology

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Area of Science:

  • Paleontology
  • Ecology
  • Time-series analysis

Background:

  • Understanding Earth's biodiversity changes and their drivers is a major scientific challenge.
  • Haar fluctuation analysis is a novel time-series method proposed for macroevolutionary inference and stability assessment.
  • Its efficacy with biased time series and ability to identify specific drivers remain unproven.

Purpose of the Study:

  • To evaluate the effectiveness of Haar fluctuation analysis and cross-Haar correlations.
  • To test the method's performance with simulated ecological data incorporating realistic biases.
  • To determine if Haar fluctuation analysis can reliably detect biodiversity dynamics and stability.

Main Methods:

  • Utilized process-based ecological simulations to generate time-series data.
  • Incorporated realistic sampling and depositional biases into simulations.
  • Applied Haar fluctuation analysis and cross-Haar correlations to analyze simulated data.

Main Results:

  • Simpler, neutral mechanisms can generate patterns observed in the Phanerozoic biodiversity record.
  • Sampling biases and sedimentary hiatuses can distort scaling relationships, challenging direct mechanistic interpretations.
  • Haar fluctuation analysis reliably distinguishes stabilizing from non-stabilizing dynamics, even with significant sampling bias.

Conclusions:

  • Haar fluctuation analysis supports the identification of long-term equilibrium in Phanerozoic marine biodiversity.
  • The method is robust for detecting stability when time-series resolution and duration are adequate relative to system dynamics.
  • Time-scale-based approaches are valuable for studying complex biodiversity dynamics.