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  3. Non-ergodicity In Ecology And Evolution.
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  3. Non-ergodicity In Ecology And Evolution.

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Non-ergodicity in ecology and evolution.

Teemu Kuosmanen1, Alexandre Minetto1, Ville Mustonen1

  • 1Department of Computer Science, Organismal and Evolutionary Research Programme, University of Helsinki, Helsinki 00014, Finland.

Proceedings of the National Academy of Sciences of the United States of America
|March 31, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

Biological systems often exhibit non-ergodicity, meaning typical outcomes differ from averages. This study explores how non-ergodicity in ecological and evolutionary dynamics impacts population growth, fitness, and cooperation.

Keywords:
demographic stochasticityenvironmental stochasticityergodicityfitnessmetapopulations

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Area of Science:

  • Ecology and Evolutionary Biology
  • Theoretical Biology
  • Mathematical Biology

Background:

  • Stochasticity is crucial in biological systems, but standard ensemble averaging assumes ergodicity.
  • Ergodicity implies that system trajectories mirror ensemble statistics over time.
  • Non-ergodicity, where trajectories diverge from ensemble averages, may be common in real biological systems.

Purpose of the Study:

  • To investigate the implications of non-ergodicity for eco-evolutionary dynamics.
  • To challenge the assumption of ergodicity in biological modeling.
  • To provide a framework for understanding systems where typical outcomes differ from mean statistics.

Main Methods:

  • Analysis of demographic stochasticity and its impact on growth rates.
  • Modeling of environmental stochasticity and eco-evolutionary feedbacks.
  • Examination of metapopulation dynamics and subpopulation evolutionary trajectories.

    • Main Results:

    • Demographic stochasticity can cause ergodicity breaking, making growth rates dependent on initial conditions and defining a mutant establishment threshold.
    • Eco-evolutionary feedbacks under environmental stochasticity lead to non-ergodic dynamics, precluding simple averaging of genotype fitness.
    • Metapopulation dynamics can exhibit deviations from ensemble averages, explaining cooperation's evolution despite fitness costs.

    Conclusions:

    • Non-ergodicity is prevalent in biological systems and significantly alters eco-evolutionary dynamics.
    • Standard averaging methods may fail to capture typical outcomes in many ecological and evolutionary contexts.
    • Understanding non-ergodicity is essential for accurately modeling population dynamics, fitness landscapes, and the evolution of complex traits like cooperation.