Evolution of cooperation in a finite homogeneous graph

Area of Science:

• Evolutionary biology
• Theoretical ecology
• Population genetics

Background:

• Theoretical studies of selection in finite structured populations often use fixation probability or inclusive fitness.
• These measures, while analytically distinct, can yield equivalent results under specific assumptions.
• Population structure is frequently modeled as a graph in continuous-time evolutionary models.

Purpose of the Study:

• To derive a simple analytical condition for the selective advantage of a cooperative allele in structured populations.
• To extend inclusive fitness analysis to a broader range of population structures, including those previously intractable for fixation probability calculations.
• To investigate the impact of population regulation on the invasion of cooperative alleles.

Main Methods:

• Utilized an inclusive fitness analysis within a continuous-time evolutionary model.
• Focused on population structures represented by graphs satisfying a general symmetry condition (bi-transitivity).
• Derived an analytical condition for the selective advantage of a cooperative allele.

Main Results:

• A surprisingly simple analytical condition for cooperative allele advantage was derived for bi-transitive graphs.
• The results apply to a wide array of population structures, including previously challenging ones.
• Under certain population regulation types, invasion of cooperation is independent of population structure, mirroring unstructured populations.
• Under other regulation types, cooperation invades when partners are chosen via high-weight edges.

Conclusions:

• Inclusive fitness analysis provides a powerful and simplified approach to understanding selection in structured populations.
• The derived condition offers a unified framework for analyzing cooperation across diverse population structures.
• Population regulation mechanisms critically influence whether and how cooperation evolves in structured populations.