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Adaptive Dynamics models for the evolution of class-structured populations in stable systems.

Michael H Cortez1

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Summary

Adaptive Dynamics models predict evolutionary change in structured populations. This study reveals the determinant-form selection gradient represents indirect effects and provides methods to compute reproductive values, aiding evolutionary analysis.

Keywords:
LysogenyParasiteReproductive valueSelection gradientStage-structureVirulence

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Area of Science:

  • Evolutionary Biology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Individuals face varied selective pressures across different life stages or classes.
  • Adaptive Dynamics models are used for long-term evolutionary predictions in structured populations.
  • Existing selection gradient forms present a trade-off between interpretability and explicit calculation.

Purpose of the Study:

  • To elucidate the biological interpretation of the determinant-form selection gradient in class-structured populations.
  • To develop methods for computing reproductive values in these models.
  • To apply these advancements to models of parasite virulence and viral evolution.

Main Methods:

  • Interpreting the determinant-form selection gradient as a sum of class-mediated indirect selection effects.
  • Deriving formulas to compute reproductive values from minors of the transition rate matrix.
  • Analyzing life cycle graphs to visualize inter-class effects.
  • Applying the framework to specific evolutionary models (virulence, lysis/lysogeny).

Main Results:

  • The determinant-form selection gradient quantifies indirect selection effects mediated by class transitions.
  • Reproductive values can be computed using minors of the transition rate matrix, representing total inter-class effects.
  • Visualizations of life cycle graphs aid in understanding these effects.
  • Novel predictions are generated for parasite virulence and viral evolution.

Conclusions:

  • This work bridges the gap between interpretable and calculable forms of the selection gradient in population dynamics.
  • The developed methods enhance the analytical power of Adaptive Dynamics models for structured populations.
  • The findings offer new insights into the evolution of virulence and viral life-history strategies.