Geographical invariance and the strong-migration limit in subdivided populations

Area of Science:

• Population genetics
• Evolutionary biology
• Mathematical modeling

Background:

• Understanding genetic variation requires models accounting for population structure.
• Neutral models are crucial for studying evolutionary processes without selection.
• Population subdivision and migration significantly impact genetic drift and coalescence.

Purpose of the Study:

• Investigate invariance properties under population subdivision in digenic neutral models.
• Analyze the strong-migration limit for genetic samples.
• Determine how population structure and migration affect genetic coalescence and diversity.

Main Methods:

• Developed mathematical models for monoecious, diploid populations.
• Utilized a finite number of panmictic colonies with gamete exchange.
• Employed an arbitrary, time-independent, and ergodic backward migration matrix.

Main Results:

• Derived the distribution of coalescence place and time.
• Calculated the probability of identity in the infinite-alleles model.
• Determined the distribution of nucleotide differences in the infinite-sites model without recombination.

Conclusions:

• Population subdivision and migration patterns are key factors in digenic neutral models.
• The derived results provide insights into genetic diversity and evolutionary history.
• This work offers a framework for analyzing genetic data in structured populations.