An efficient algorithm for generating the internal branches of a Kingman coalescent.

Area of Science:

• Population genetics
• Computational biology
• Evolutionary genetics

Background:

• Coalescent simulations are standard for modeling sample genealogies.
• Full simulations become computationally intensive with large sample sizes.
• Estimating statistics based on internal branch lengths typically requires full simulations.

Purpose of the Study:

• To develop an efficient method for sampling limited portions of genealogies.
• To enable accurate estimation of statistics reliant on internal branch length distributions.
• To overcome the computational burden of full coalescent simulations.

Main Methods:

• Developed a sampling method using analytic equations for internal branch probabilities.
• Equations determine branch number, start, and end, conditional on subtended samples.
• Method avoids direct simulation of coalescent waiting times.

Main Results:

• The new method efficiently generates partial genealogies.
• Achieved equivalent distributions of branch lengths and summary statistics compared to full simulations.
• Demonstrated a speed improvement of at least 10x under various conditions.

Conclusions:

• The proposed analytic sampling method offers a computationally efficient alternative to full coalescent simulations.
• This advancement facilitates the study of complex population genetic models with large datasets.
• The method provides a faster way to estimate statistics crucial for understanding evolutionary processes.