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Path probability selection in nature and path integral.

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Biological evolution is newly understood through path probability, not just fitness advantage. This approach explains diverse evolutionary paths and species diversity, incorporating environmental feedback for a dynamic view.

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Area of Science:

  • Evolutionary biology
  • Theoretical biology
  • Mathematical biology

Background:

  • Biological evolution, including speciation and biodiversity, is traditionally explained by fitness and natural selection.
  • Existing models, like the Price equation, often neglect environmental feedback and intergenerational effects, limiting understanding of global evolutionary dynamics.

Purpose of the Study:

  • To introduce a novel framework for understanding biological evolution by incorporating path integrals from modern physics.
  • To replace the concept of stationary fitness with path probability in evolutionary models.
  • To explore how this new framework can explain complex evolutionary phenomena like diversified fitness and species diversity.

Main Methods:

  • Iteratively applying the Price equation to introduce path integral concepts.
  • Developing a mathematical framework where evolutionary selection depends on path probability.
  • Analyzing evolutionary paths that do not necessarily lead to a fitness-maximizing equilibrium.

Main Results:

  • Evolutionary selection is redefined as dependent on path probability rather than solely on fitness advantage.
  • The model demonstrates that intermediate evolutionary stages may not always optimize fitness.
  • Multiple evolutionary paths can coexist without requiring a fitness advantage.

Conclusions:

  • The path integral approach offers a more comprehensive understanding of evolutionary dynamics by including environmental feedback.
  • This framework provides a potential explanation for the coexistence of diverse strategies (e.g., altruism and selfishness) within populations.
  • The proposed mechanism may elucidate the generation and maintenance of species diversity through varied evolutionary trajectories.