Hamilton's rule, gradual evolution, and the optimal (feedback) control of phenotypically plastic traits

Area of Science:

• Evolutionary biology
• Theoretical ecology
• Behavioral ecology

Background:

• Organismal traits, including gene expression and behavior, are often function-valued, changing with age and environmental factors.
• Individuals typically live in populations with limited genetic mixing, leading to interactions with relatives.

Purpose of the Study:

• To formalize selection on genetically determined function-valued traits in group-structured populations.
• To derive a marginal version of Hamilton's rule for function-valued traits.
• To analyze the conditions for invasion and fixation of mutant traits and evolutionary stability.

Main Methods:

• Utilized optimal control theory and differential game theory.
• Derived a marginal version of Hamilton's rule for function-valued traits.
• Compared open-loop (time-dependent) and closed-loop (state-dependent) traits.

Main Results:

• The derived rule provides conditions for trait invasion, fixation, and evolutionary stability.
• Closed-loop traits simplify to open-loop traits under no interaction or interaction with clonal relatives.
• Delineated the influence of state-dependence and inter-individual interdependence on trait evolution.

Conclusions:

• The study provides a framework for understanding the evolution of phenotypic plasticity in social contexts.
• Findings have implications for life-history theory and the study of social evolution.
• Highlights the importance of considering individual interactions and state-dependence in evolutionary models.