The coalescent in finite populations with arbitrary, fixed structure

Area of Science:

• Population Genetics
• Theoretical Biology
• Mathematical Modeling

Background:

• The coalescent process models neutral genetic drift in populations.
• Existing coalescent models are limited to well-mixed populations.
• Real populations exhibit complex structures (spatial, age, sex, class).

Purpose of the Study:

• To formulate a generalized coalescent process for diverse, fixed population structures.
• To extend coalescent theory to arbitrary spatial, age, sex, and class configurations.
• To analyze genetic dissimilarity measures under varying population structures.

Main Methods:

• Representing the coalescent as a random sequence of mappings between population sites.
• Defining and analyzing coalescence time, branch length, and mutation effects.
• Developing a computational approach for identity-by-descent and identity-by-state probabilities.

Main Results:

• A generalized coalescent framework applicable to complex population structures.
• Formulas for analyzing coalescence time, branch length, and mutation impacts.
• Identified that genetic dissimilarity scales with the population's sex ratio (4r(1-r)).

Conclusions:

• The generalized coalescent provides a flexible tool for studying diverse populations.
• Population structure, particularly sex ratio, significantly impacts genetic dissimilarity.
• The findings offer a method to compute genetic identity probabilities in structured populations.