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PhaseGen: exact solutions for time-inhomogeneous multivariate coalescent distributions under diverse demographies
Janek Sendrowski1, Asger Hobolth2
1Bioinformatics Research Center, Aarhus University, Aarhus 8000, Denmark.
Genetics
|July 22, 2025
Summary
Phase-type theory now models complex population histories exactly. This new method, using time-inhomogeneous phase-type theory, enables precise calculations for population genetics, including expansions and bottlenecks.
Area of Science:
- Population genetics
- Mathematical modeling
- Computational biology
Background:
- Phase-type theory offers exact computations for coalescent processes.
- Previous applications were limited to time-homogeneous population models.
- Complex demographic histories require more flexible modeling frameworks.
Purpose of the Study:
- To extend phase-type theory to time-inhomogeneous settings.
- To enable exact computation of moments under piecewise-constant demographies.
- To develop a software tool for demographic model fitting.
Main Methods:
- Application of time-inhomogeneous phase-type theory.
- Exact computation of arbitrary order moments and reward structures.
- Development of the PhaseGen software package for numerical stability and gradient-based estimation.
Main Results:
- Enables exact computation of moments for complex demographic scenarios (expansions, contractions, bottlenecks, splits).
- Supports gradient-based optimization for fitting demographic models to data.
- PhaseGen provides numerically stable computations for diverse scenarios.
Conclusions:
- Time-inhomogeneous phase-type theory significantly expands the scope of exact coalescent modeling.
- PhaseGen facilitates the analysis of realistic, complex population genetic histories.
- This framework advances the ability to infer demographic parameters from genetic data.
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