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Fixation probabilities and hitting times for low levels of frequency-dependent selection
P Pfaffelhuber1, A Wakolbinger2
1Albert-Ludwigs University of Freiburg, Ernst-Zermelo-Str. 1, 79104 Freiburg, Germany.
Theoretical Population Biology
|October 2, 2018
Summary
This study models allele frequency changes using diffusion approximations. We derive new formulas for fixation probabilities and expected frequencies under frequency-dependent selection, extending existing evolutionary game theory rules.
Area of Science:
- Population genetics
- Mathematical biology
- Evolutionary dynamics
Background:
- Allele frequency dynamics are crucial in population genetics.
- Diffusion processes on the unit interval model these dynamics.
- Frequency-dependent selection influences evolutionary trajectories.
Purpose of the Study:
- Derive approximations for fixation probabilities.
- Calculate expected hitting times for allele frequencies.
- Analyze the expected frequency spectrum under low frequency-dependent selection.
Main Methods:
- Utilizing diffusion approximations on the unit interval.
- Extending the one-third rule from evolutionary game theory.
- Analyzing effects of stochastic slowdown in evolutionary models.
Main Results:
- New approximations for fixation probabilities derived.
- Expected hitting times and frequency spectrum analyzed.
- Results reformulated for general one-dimensional diffusions.
Conclusions:
- The study provides analytical tools for frequency-dependent selection.
- Extends foundational concepts in evolutionary game theory.
- Applicable to broader fields modeling one-dimensional diffusion processes.
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