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Generalized measures of population synchrony.

Francis C Motta1, Kevin McGoff2, Breschine Cummins3

  • 1Department of Mathematics and Statistics, Florida Atlantic University, Boca Raton, FL, USA.

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Summary

This study introduces a new, computable measure for quantifying population synchrony using Fréchet variance. This mathematical framework provides rigorous definitions and efficient algorithms for analyzing synchronized behavior in diverse populations.

Keywords:
Biological clocksFréchet varianceOptimal transportPlasmodiumPopulation synchronyWasserstein distance

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Area of Science:

  • Mathematical Biology
  • Population Dynamics
  • Statistical Mechanics

Background:

  • Synchronized behavior is common in populations, but quantifying it rigorously is challenging.
  • Existing measures of synchrony often lack precise definitions or are limited to specific systems.
  • Accurate quantification is crucial for understanding population dynamics and developing predictive models.

Purpose of the Study:

  • To introduce a novel, mathematically rigorous, and computable measure of population synchrony.
  • To establish desirable mathematical properties for this new synchrony measure.
  • To demonstrate its applicability in biological contexts and computational analysis.

Main Methods:

  • Defined population synchrony based on the Fréchet variance of individual distributions in a metric space.
  • Established mathematical properties: continuity and invariance to metric scaling.
  • Developed efficient algorithms for computation across various state spaces, including finite and circular distributions.
  • Provided open-source Python implementations.

Main Results:

  • Introduced a robust measure of population synchrony with desirable mathematical properties.
  • Developed an approximation result for synchrony under state space discretization.
  • Demonstrated computational efficiency for diverse state spaces.
  • Successfully applied the measure to analyze Plasmodium parasite developmental cycles.

Conclusions:

  • The proposed Fréchet variance-based synchrony measure offers a rigorous and broadly applicable tool.
  • This framework facilitates the analysis and modeling of synchronized behaviors in complex populations.
  • The findings have implications for various scientific fields studying collective dynamics.