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

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.