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Exact numerical calculation of fixation probability and time on graphs
Laura Hindersin1, Marius Möller2, Arne Traulsen1
1Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, D-24306 Plön, Germany.
Bio Systems
|August 25, 2016
Summary
This study introduces a new algorithm for calculating evolutionary fixation probabilities and times on graphs. The method uses a transition matrix approach, offering a faster and more efficient alternative to traditional simulations for studying spatial population dynamics.
Area of Science:
- Evolutionary dynamics
- Theoretical ecology
- Computational biology
Background:
- The Moran process models evolution in structured populations.
- Analytical solutions for fixation probability/time are limited to specific graph types.
- Simulations are computationally expensive due to high variance in fixation times.
Purpose of the Study:
- To develop a numerical algorithm for computing fixation probability and time on arbitrary graphs.
- To provide a faster and more efficient alternative to simulations.
- To enable interactive studies of graph structures' impact on evolutionary dynamics.
Main Methods:
- Algorithm based on the transition matrix approach.
- Automated construction of the transition matrix.
- Numerical computation of fixation probability and time.
Main Results:
- The algorithm computes fixation probability and time for arbitrary small graphs.
- The method is significantly faster than traditional simulations.
- The approach allows for interactive analysis of different graph structures.
Conclusions:
- The developed algorithm provides an efficient and flexible tool for studying evolutionary dynamics on graphs.
- The method supports various update mechanisms (Birth-Death, Death-Birth) and graph types (directed/undirected).
- This facilitates a deeper understanding of how spatial structure influences evolutionary outcomes.
