Adaptive walks on changing landscapes: Levins' approach extended

Area of Science:

• Evolutionary biology
• Population genetics
• Quantitative genetics

Background:

• Trade-offs are fundamental in evolutionary theory.
• Levins graphical method analyzes evolution of two quantitative traits but excludes density- and frequency-dependent selection.
• Fitness landscapes can change with population state.

Purpose of the Study:

• To extend Levins graphical method to include density- and frequency-dependent selection.
• To develop a framework for analyzing evolutionary endpoints and bifurcations in dynamic fitness landscapes.
• To provide a priori predictions for evolutionary trajectories.

Main Methods:

• Utilizing trade-off curves and fitness contours, similar to Levins method.
• Modifying fitness contours to be dependent on resident traits, defining invasion boundaries.
• Applying the extended approach to analyze evolutionary endpoints and bifurcations.

Main Results:

• The extended method successfully incorporates density- and frequency-dependent selection.
• Fitness contours are shown to be dynamic, influenced by resident traits.
• The approach allows for a priori predictions of evolutionary endpoints and their bifurcations.
• Illustrative examples from recent literature demonstrate the method's applicability.

Conclusions:

• The developed graphical approach provides a powerful tool for analyzing evolutionary trade-offs under complex selection regimes.
• This extension of Levins method enhances our understanding of evolutionary dynamics in changing environments.
• The framework facilitates predictions of evolutionary endpoints and critical transitions (bifurcations).