ArticleJournal of mathematical biology2018
The fundamental theorem of natural selection with mutations.
Article in Journal of mathematical biology, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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14 citing papers in PubMed, 47 citations in OpenAlex.
- Evolution expresses the second law of thermodynamics in action.Journal of the Royal Society, Interface · 2026Article
- Bistable Mutation-Selection Equilibria and Violations of Fisher's Theorem in Tetraploids: Insights from Nonlinear Dynamics.bioRxiv : the preprint server for biology · 2025Article
- Protocell Effects on RNA Folding, Function, and Evolution.Accounts of chemical research · 2024Article
- Limits on the evolutionary rates of biological traits.Scientific reports · 2024Article
- Modeling stress-induced responses: plasticity in continuous state space and gradual clonal evolution.Theory in biosciences = Theorie in den Biowissenschaften · 2024Article
- Engineering and Expression Strategies for Optimization of L-Asparaginase Development and Production.International journal of molecular sciences · 2023Review
- The contribution of evolvability to the eco-evolutionary dynamics of competing species.Ecology and evolution · 2023Article
- Extinction scenarios in evolutionary processes: a multinomial Wright-Fisher approach.Journal of mathematical biology · 2023Article
- Biomarkers or biotargets? Using competition to lure cancer cells into evolutionary traps.Evolution, medicine, and public health · 2023Article
- A life history model of the ecological and evolutionary dynamics of polyaneuploid cancer cells.Scientific reports · 2022Article
- Variability of Human rDNA.Cells · 2021Review
- Origin of Life: The Point of No Return.Life (Basel, Switzerland) · 2020Article
- Molecular footprints of selection effects and whole genome duplication (WGD) events in three blueberry species: detected by transcriptome dataset.BMC plant biology · 2020Article
- Convergent Evolution, Evolving Evolvability, and the Origins of Lethal Cancer.Molecular cancer research : MCR · 2020Review
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Authors and funding
2 authors at 1 institution in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
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.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.