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On the establishment of a mutant
Jeremy Baker1, Pavel Chigansky2, Peter Jagers3
1School of Mathematics, Monash University, Monash, VIC, 3800, Australia.
Journal of Mathematical Biology
|February 28, 2020
Summary
This study models how quickly advantageous mutants establish in populations using the Bare Bones evolution model. Establishment time is proportional to the inverse of successful mutant division probability, influencing population composition.
Area of Science:
- Evolutionary biology
- Mathematical modeling
- Population dynamics
Background:
- Understanding the establishment time and population composition of advantageous mutants is crucial in evolutionary biology.
- The Bare Bones evolution model offers a simplified framework for studying adaptive population dynamics in binary splitting cells.
Purpose of the Study:
- To determine the time required for an initially advantageous mutant to establish within a resident population.
- To analyze the resulting population composition after mutant establishment.
- To investigate the conditions under which a mutant can successfully coexist with a resident population.
Main Methods:
- Utilizing the Bare Bones evolution model for adaptive population dynamics of binary splitting cells.
- Assuming resident populations start with sizes proportional to a large carrying capacity (K).
- Analyzing the stochastic nonlinear dynamics and their asymptotic behavior to define and calculate establishment time.
Main Results:
- The time for a mutant to establish is found to be proportional to 1/p_s, where p_s is the probability of successful mutant division.
- Conditions for successful mutant establishment alongside residents were identified.
- At later times, population densities closely follow a deterministic two-dimensional nonlinear dynamic model with a random initial condition.
Conclusions:
- The establishment time of an advantageous mutant is directly related to its successful division probability.
- The deterministic approximation with a random initial condition accurately describes population dynamics asymptotically.
- This model provides insights into the dynamics of adaptive evolution in microbial populations.
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