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This study proposes a new definition of fitness based on population model eigenfunctions. This approach enables adaptive control of life histories, even with environmental changes and population density effects.

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Area of Science:

  • Evolutionary Biology
  • Mathematical Ecology
  • Population Dynamics

Background:

  • Traditional fitness definitions focus on descendant counts, limiting understanding of life history evolution.
  • Existing models struggle to explain continuous life history changes and adaptive strategies in dynamic environments.

Purpose of the Study:

  • To propose a novel, unified definition of fitness using eigenfunctions of age-structured population models.
  • To develop a method for adaptive control of life histories considering density effects and environmental variability.
  • To systematize the understanding of adaptive life histories as a universal fitness candidate.

Main Methods:

  • Utilized the eigenfunction of an age-structured population model as a fitness measure.
  • Derived the Hamilton-Jacobi-Bellman equation for adaptive life history control.
  • Applied a perturbation method to link the solution to the growth rate of stochastic structured populations.
  • Analyzed an optimal foraging problem with heterogeneity in variable environments.

Main Results:

  • The eigenfunction-based fitness measure successfully achieves adaptive control of life histories.
  • The Hamilton-Jacobi-Bellman equation effectively incorporates density-dependent and independent effects.
  • The perturbation method accurately predicts long-term population growth rates.
  • Eigenfunctions were shown to be integral to adaptive strategies across diverse environmental conditions.

Conclusions:

  • The proposed eigenfunction approach offers a universal framework for defining fitness.
  • This method provides a robust tool for understanding and controlling adaptive life histories.
  • The findings have implications for managing populations in complex and changing environments.