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Moran-type bounds for the fixation probability in a frequency-dependent Wright-Fisher model
Timothy Chumley1, Ozgur Aydogmus2, Anastasios Matzavinos3,4
1Department of Mathematics and Statistics, Mount Holyoke College, South Hadley, MA, 01075, USA.
Journal of Mathematical Biology
|May 17, 2017
Summary
This study explores evolutionary game dynamics in finite populations, providing bounds for advantageous mutant fixation probability and time. Results show a single advantageous mutant can invade an infinite population with positive probability.
Area of Science:
- Evolutionary game theory
- Population genetics
- Mathematical biology
Background:
- Stochastic evolutionary game dynamics are crucial for understanding population evolution.
- Finite populations introduce unique dynamics compared to infinite models.
- Group structure and frequency-dependent fitness significantly impact evolutionary trajectories.
Purpose of the Study:
- To analyze stochastic evolutionary game dynamics in finite populations.
- To derive bounds for fixation probability and fixation time of advantageous mutants.
- To investigate the invasion dynamics of advantageous mutants in infinite populations.
Main Methods:
- Utilizing a Wright-Fisher type Markov chain model.
- Applying mathematical analysis for frequency-dependent fitness.
- Deriving analytical bounds in strong selection regimes.
- Investigating the infinite population limit.
Main Results:
- Qualitatively matching lower and upper bounds for fixation probability were obtained.
- An exact result demonstrates positive invasion probability for a single advantageous mutant in an infinite population.
- Asymptotically sharp bounds for fixation time distribution were established.
Conclusions:
- The study provides a comprehensive analysis of evolutionary game dynamics in finite populations.
- The findings offer insights into the conditions favoring the spread of advantageous traits.
- The derived bounds and exact results contribute to theoretical population genetics.
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