Exchangeable coalescents beyond the Cannings class

Area of Science:

• Population genetics
• Mathematical biology
• Probability theory

Background:

• The study of population genealogy is crucial for understanding evolutionary dynamics.
• Existing models, like Cannings models, often assume exchangeability of offspring distributions, limiting their applicability.
• A less restrictive framework is needed to analyze a broader range of population structures.

Purpose of the Study:

• To propose a general framework for studying the genealogy of neutral discrete-time populations.
• To relax the standard assumption of exchangeability in offspring distributions.
• To establish criteria for the convergence of genealogies to coalescent processes.

Main Methods:

• Developed a new theoretical framework for population genealogy.
• Introduced the condition of non-heritability of reproductive success.
• Derived a general criterion for weak convergence to $$-coalescents.
• Applied the framework to various population models, including those with asymmetric offspring distributions and bottlenecks.

Main Results:

• Established a general criterion for the weak convergence of population genealogies to $$-coalescents.
• Demonstrated the framework's applicability to populations with non-exchangeable offspring distributions.
• Showcased examples including highly-asymmetric offspring distributions and populations with recurrent bottlenecks.
• Analyzed the limit genealogy of a novel exponential model within the new framework.

Conclusions:

• The proposed framework offers a more flexible approach to studying population genealogy.
• It accommodates a wider range of population structures than traditional models.
• The findings advance our understanding of evolutionary processes in diverse populations.