The fundamental theorem of natural selection with mutations

The mutation–selection process is the most fundamental mechanism of evolution. In 1935, R. A. Fisher proved his fundamental theorem of natural selection, providing a model in which the rate of change of mean fitness is equal to the genetic variance of a species. Fisher did not include mutations in h...

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Bibliographic Details
Published in:Journal of mathematical biology 2018-06, Vol.76 (7), p.1589-1622
Main Authors: Basener, William F., Sanford, John C.
Format: Article
Language:English
Subjects:
Animals
Applications of Mathematics
Biological effects
Computational Biology
Computer Simulation
Differential equations
First principles
Fitness
Genetic Determinism
Genetic diversity
Genetic Fitness
Genetic variance
Genetic Variation
Genetics, Population - statistics & numerical data
Humans
Mathematical and Computational Biology
Mathematical Concepts
Mathematical models
Mathematics
Mathematics and Statistics
Models, Genetic
Mutation
Natural selection
Normal Distribution
Population Dynamics - statistics & numerical data
Reproductive fitness
Selection, Genetic
Systems Analysis
Theorems
Time Factors
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Summary:The mutation–selection process is the most fundamental mechanism of evolution. In 1935, R. A. Fisher proved his fundamental theorem of natural selection, providing a model in which the rate of change of mean fitness is equal to the genetic variance of a species. Fisher did not include mutations in his model, but believed that mutations would provide a continual supply of variance resulting in perpetual increase in mean fitness, thus providing a foundation for neo-Darwinian theory. In this paper we re-examine Fisher’s Theorem, showing that because it disregards mutations, and because it is invalid beyond one instant in time, it has limited biological relevance. We build a differential equations model from Fisher’s first principles with mutations added, and prove a revised theorem showing the rate of change in mean fitness is equal to genetic variance plus a mutational effects term. We refer to our revised theorem as the fundamental theorem of natural selection with mutations. Our expanded theorem, and our associated analyses (analytic computation, numerical simulation, and visualization), provide a clearer understanding of the mutation–selection process, and allow application of biologically realistic parameters such as mutational effects. The expanded theorem has biological implications significantly different from what Fisher had envisioned.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-017-1190-x