Journal
MATHEMATICS
Volume 10, Issue 24, Pages -Publisher
MDPI
DOI: 10.3390/math10244818
Keywords
adaptive dynamics; replicator-mutator equation; mutation rate evolution
Categories
Funding
- Dartmouth Fellowship
- Bill & Melinda Gates Foundation [OPP1217336]
- NIH COBRE Program [1P20GM130454]
- Neukom CompX Faculty Grant
- Dartmouth Faculty Startup Fund
- Walter & Constance Burke Research Initiation Award
- Bill and Melinda Gates Foundation [OPP1217336] Funding Source: Bill and Melinda Gates Foundation
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This study explores the evolution of mutation rates in different models and finds that it can be more complicated than previously expected. By using adaptive dynamics and the replicator-mutator equation, the study demonstrates the possibility of reverse evolution of mutation rates even in relatively simple models.
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore, it is reasonable to expect that mutation rates will evolve downwards. However, we find that this need not be the case, examining several models of mutation. While upwards evolution of the mutation rate has been found with frequency- or time-dependent fitness, we demonstrate its possibility in a much simpler context. This work uses adaptive dynamics to study the evolution of the mutation rate, and the replicator-mutator equation to model trait evolution. Our approach differs from previous studies by considering a wide variety of methods to represent mutation. We use a finite string approach inspired by genetics as well as a model of local mutation on a discretization of the unit intervals, handling mutation beyond the endpoints in three ways. The main contribution of this work is a demonstration that the evolution of the mutation rate can be significantly more complicated than what is usually expected in relatively simple models.
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