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This study introduces a new model combining replicator dynamics with age-structured populations to analyze strategy evolution across life cycles. The model simplifies complex population dynamics, offering insights into frequency-dependent selection in aging populations.

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Population Dynamics

Background:

  • Frequency-dependent selection is typically modeled using replicator dynamics.
  • Standard models often do not account for age structure within populations.
  • Integrating age structure is crucial for understanding life-cycle dependent strategy evolution.

Purpose of the Study:

  • To develop a novel modeling framework that integrates replicator dynamics with age-structured population models.
  • To analyze how competing strategies evolve in populations where individuals change throughout their life cycle.
  • To provide a simplified and timescale-independent mathematical representation of these dynamics.

Main Methods:

  • Discretization of the McKendrick-von Foerster model for age-structured populations.
  • Application of multipopulation game theory to derive coupled systems of equations.
  • Formulation of a mixed ordinary differential equation-partial differential equation (ODE-PDE) system for strategy dynamics.
  • Validation using a sex ratio model with differential mortality rates.

Main Results:

  • The new framework successfully models populations with competing strategies across different life stages.
  • The derived ODE-PDE system simplifies the analysis of evolutionary dynamics in age-structured populations.
  • The sex ratio model example demonstrates that deviations in mortality can lead to a 0.5 sex ratio, but Fisher's mechanism may not reach equilibrium.

Conclusions:

  • The integrated model offers a powerful tool for studying evolutionary dynamics in age-structured populations.
  • The simplified ODE-PDE system provides a more tractable approach compared to traditional matrix methods.
  • The findings highlight the importance of considering age-specific mortality and reproductive values in evolutionary models.