Towards a general theory of group selection.

Area of Science:

• Evolutionary biology
• Theoretical biology
• Mathematical modeling

Background:

• The importance of group selection in evolution is debated due to a lack of formal models.
• Existing models often lack explicit descriptions of selection events at multiple levels.

Purpose of the Study:

• To develop a general class of models for two-level evolutionary processes.
• To provide a formal mathematical framework for distinguishing individual- and group-level selection events.
• To offer a new, intuitive definition of group selection.

Main Methods:

• Developed continuous-time Markov chain and partial differential equation (PDE) models for two-level systems.
• Incorporated state-dependent birth and death rates at both individual and group levels.
• Analyzed the mathematical structure of the PDE to differentiate event types.

Main Results:

• The PDE's mathematical structure is consistent across various two-level population models.
• A clear distinction between individual- and group-level events is established.
• Group selection, as defined by this framework, is not mathematically equivalent to individual (kin) selection.

Conclusions:

• The proposed mathematical framework offers a robust method for analyzing multilevel selection.
• The new definition of group selection provides clarity and aids in understanding evolutionary dynamics.
• The findings have implications for understanding the evolution of cooperation and multicellularity.