The coalescent in two colonies with symmetric migration

Area of Science:

• Population Genetics
• Mathematical Biology
• Evolutionary Biology

Background:

• Kingman's coalescent model is a fundamental tool in population genetics.
• Understanding gene coalescence in structured populations is crucial for evolutionary inference.

Purpose of the Study:

• To extend Kingman's coalescent process to model gene coalescence in two symmetric colonies with migration.
• To analyze waiting times for common ancestors in this two-colony system.

Main Methods:

• Mathematical modeling using Kingman's coalescent theory.
• Derivation of analytical expressions for waiting times.
• Analysis of limiting behaviors as migration rates approach zero.

Main Results:

• The mean waiting time for a common ancestor in two colonies was derived.
• The distribution of the final waiting time converges to the single-population case as migration tends to zero, but the mean does not.
• Waiting times for two common ancestors were modeled as a function of migration rate.

Conclusions:

• The study provides a detailed mathematical framework for coalescent processes in two-colony systems.
• Migration significantly impacts gene coalescence dynamics, with distinct behaviors for waiting time distributions and means.
• The findings offer insights into inferring population structure and history from genetic data.