The fundamental theorem of natural selection with mutations
Open accessAbstract
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.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Kimura's mutational spectrum implies a fitness decrease over time, in line with Haldane's Dilemma.
“In particular, they showed that Kimura's mutational spectrum implies a fitness decreases over time, in line with the predictions of Haldane's Dilemma.”
From Using statistical methods to model the fine-tuning of molecular machines and systems (2020) · cites this paper as Basener and Sanford (2018)
The Numerical simulations section uses a gamma distribution attributed to Kimura and reports steadily declining fitness in a finite-population simulation. The Discussion likewise reports continuous decline under its modeled deleterious-to-beneficial mutation ratio. Our copy does not connect that result to Haldane’s Dilemma, and the decline is a result under the paper’s modeling conditions rather than an unqualified implication of Kimura’s spectrum. (LLM, conf=0.86)
Experimental — accuracy not yet measuredBasener and Sanford (2018) extended Fisher's Theorem to allow for arbitrary mutational spectra.
“Basener and Sanford (2018) recently extended Fisher's Theorem, allowing for arbitrary mutational spectra.”
From Using statistical methods to model the fine-tuning of molecular machines and systems (2020) · cites this paper as Basener and Sanford (2018)
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
The genetical theory of natural selection
Fisher, R. A. (1930) · doi:10.5962/bhl.title.27468 · Cited by 17,617 · see citing works
An introduction to population genetics theory
Crow, J. F., & Kimura, M. (1970) · Medical Entomology and Zoology · Cited by 4,223 · see citing works
Selforganization of matter and the evolution of biological macromolecules
Eigen, M. (1971) · Die Naturwissenschaften · doi:10.1007/bf00623322 · Cited by 3,788 · see citing works
An Introduction to Population Genetics Theory
J., A., Crow, J. F., & Kimura, M. (1971) · Population · doi:10.2307/1529706 · Cited by 3,523 · see citing works
The relation of recombination to mutational advance
Muller, H. J. (1964) · Mutation Research · doi:10.1016/0027-5107(64)90047-8 · Cited by 2,512 · see citing works
Evolutionary Dynamics: Exploring the Equations of Life
NOWAK, M. A. (2006) · doi:10.2307/j.ctvjghw98 · Cited by 2,438 · see citing works
A principle of natural self-organization: Part A: Emergence of the hypercycle
Eigen, M., & Schuster, P. (1977) · Naturwissenschaften · doi:10.1007/bf00450633 · Cited by 1,752 · see citing works
THE EVOLUTIONARY ADVANTAGE OF RECOMBINATION
Felsenstein, J. (1974) · Genetics · doi:10.1093/genetics/78.2.737 · Cited by 1,711 · see citing works
Mutation Accumulation and the Extinction of Small Populations
Lynch, M. F., Conery, J. S., & Bürger, R. (1995) · The American Naturalist · doi:10.1086/285812 · Cited by 1,110 · see citing works
RNA virus error catastrophe: Direct molecular test by using ribavirin
Crotty, S., Cameron, C. E., & Andino, R. (2001) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.111085598 · Cited by 853 · see citing works
The fate of competing beneficial mutations in an asexual population
Gerrish, P. J., & Lenski, R. E. (1998) · Genetica · doi:10.1023/a:1017067816551 · Cited by 783 · see citing works
The fate of competing beneficial mutations in an asexual population
Gerrish, P. J., & Lenski, R. E. (1998) · Contemporary issues in genetics and evolution · doi:10.1007/978-94-011-5210-5_12 · Cited by 721 · see citing works
Lande, R. (1995) · Conservation Biology · doi:10.1046/j.1523-1739.1995.09040782.x · Cited by 686 · see citing works
The Mutational Meltdown in Asexual Populations
Lynch, M., Bürger, R., Butcher, D. L., & Gabriel, W. (1993) · Journal of Heredity · doi:10.1093/oxfordjournals.jhered.a111354 · Cited by 633 · see citing works
ANTLER SIZE IN RED DEER: HERITABILITY AND SELECTION BUT NO EVOLUTION
Kruuk, L. E. B., Slate, J., Pemberton, J. M., Brotherstone, S., GUINNESS, F. E., & Clutton-Brock, T. H. (2002) · Evolution · doi:10.1111/j.0014-3820.2002.tb01480.x · Cited by 569 · see citing works
Heritability of fitness in a wild mammal population
Kruuk, L. E. B., Clutton-Brock, T. H., Slate, J., Pemberton, J. M., Brotherstone, S., & GUINNESS, F. E. (2000) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.97.2.698 · Cited by 522 · see citing works
The fate of competing beneficial mutations in an asexual population.
Gerrish, P. J., & Lenski, R. E. (1998) · PubMed · Cited by 520 · see citing works
MUTATION LOAD AND THE SURVIVAL OF SMALL POPULATIONS
Lynch, M. F., & Gabriel, W. (1990) · Evolution · doi:10.1111/j.1558-5646.1990.tb05244.x · Cited by 492 · see citing works
The high spontaneous mutation rate: Is it a health risk?
Crow, J. F. (1997) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.94.16.8380 · Cited by 474 · see citing works
PERSPECTIVE: SPONTANEOUS DELETERIOUS MUTATION
Lynch, M., Blanchard, J. L., Houle, D., Kibota, T. T., Schultz, S. T., Vassilieva, L. L., & Willis, J. H. (1999) · Evolution · doi:10.1111/j.1558-5646.1999.tb05361.x · Cited by 454 · see citing works
MUTATIONAL MELTDOWNS IN SEXUAL POPULATIONS
Lynch, M. F., Conery, J. S., & Bürger, R. (1995) · Evolution · doi:10.1111/j.1558-5646.1995.tb04434.x · Cited by 441 · see citing works
How large must populations be to retain evolutionary potential?
Franklin, I. R., & Frankham, R. (1998) · Animal Conservation · doi:10.1111/j.1469-1795.1998.tb00228.x · Cited by 433 · see citing works
Fisher's 'Fundamental Theorem' Made Clear
PRICE, G. R. (1972) · Annals of Human Genetics · doi:10.1111/j.1469-1809.1972.tb00764.x · Cited by 410 · see citing works
MULLER'S RATCHET AND MUTATIONAL MELTDOWNS
Gabriel, W., Lynch, M., & Bürger, R. (1993) · Evolution · doi:10.1111/j.1558-5646.1993.tb01266.x · Cited by 371 · see citing works
Lifetime Reproductive Success and Heritability in Nature
Merilä, J., & Sheldon, B. C. (2000) · The American Naturalist · doi:10.1086/303330 · Cited by 337 · see citing works
Quasispecies theory in the context of population genetics
Wilke, C. O. (2005) · BMC Evolutionary Biology · doi:10.1186/1471-2148-5-44 · Cited by 276 · see citing works
Mathematical Topics in Population Genetics
Kojima, K. (1970) · Springer eBooks · doi:10.1007/978-3-642-46244-3 · Cited by 265 · see citing works
Model of effectively neutral mutations in which selective constraint is incorporated
Kimura, M. (1979) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.76.7.3440 · Cited by 254 · see citing works
Kondrashov, A. S. (1995) · Journal of Theoretical Biology · doi:10.1006/jtbi.1995.0167 · Cited by 237 · see citing works
Viral error catastrophe by mutagenic nucleosides
Anderson, J. P., Daifuku, R., & Loeb, L. A. (2004) · Annual Review of Microbiology · doi:10.1146/annurev.micro.58.030603.123649 · Cited by 221 · see citing works
An interpretation and proof of the fundamental theorem of natural selection
Ewens, W. J. (1989) · Theoretical Population Biology · doi:10.1016/0040-5809(89)90028-2 · Cited by 213 · see citing works
The Reception of Charles Darwin in Europe
(2009) · Choice Reviews Online · doi:10.5860/choice.47-0836 · Cited by 207 · see citing works
Efficiency of truncation selection
Crow, J. F., & Kimura, M. (1979) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.76.1.396 · Cited by 201 · see citing works
TOWARD A REALISTIC MODEL OF MUTATIONS AFFECTING FITNESS
Keightley, P. D., & Lynch, M. F. (2003) · Evolution · doi:10.1111/j.0014-3820.2003.tb01561.x · Cited by 183 · see citing works
The selection mutation equation
Hofbauer, J. (1985) · Journal of Mathematical Biology · doi:10.1007/bf00276557 · Cited by 161 · see citing works
Efficient Virus Extinction by Combinations of a Mutagen and Antiviral Inhibitors
Pariente, N., Sierra, S., Lowenstein, P. R., & Domingo, E. (2001) · Journal of Virology · doi:10.1128/jvi.75.20.9723-9730.2001 · Cited by 151 · see citing works
Grande-Pérez, A., Sierra, S., Castro, M. G., Domingo, E., & Lowenstein, P. R. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.182426999 · Cited by 143 · see citing works
Distribution of fitness effects caused by random insertion mutations in Escherichia coli
Elena, S. F., Ekunwe, L., Hajela, N., Oden, S. A., & Lenski, R. E. (1998) · Contemporary issues in genetics and evolution · doi:10.1007/978-94-011-5210-5_28 · Cited by 138 · see citing works
Distribution of fitness effects caused by random insertion mutations in Escherichia coli
Elena, S. F., Ekunwe, L., Hajela, N., Oden, S. A., & Lenski, R. E. (1998) · Genetica · doi:10.1023/a:1017031008316 · Cited by 129 · see citing works
Muller's ratchet, epistasis and mutation effects.
Butcher, D. L. (1995) · Genetics · doi:10.1093/genetics/141.1.431 · Cited by 112 · see citing works
Mutation and Human Exceptionalism: Our Future Genetic Load
Lynch, M. (2016) · Genetics · doi:10.1534/genetics.115.180471 · Cited by 105 · see citing works
ON AN INEQUALITY IN PARTIAL AVERAGES
Kingmán, J. F. C. (1961) · The Quarterly Journal of Mathematics · doi:10.1093/qmath/12.1.78 · Cited by 94 · see citing works
Estimation of spontaneous genome-wide mutation rate parameters: whither beneficial mutations?
Bataillon, T. M. (2000) · Heredity · doi:10.1046/j.1365-2540.2000.00727.x · Cited by 91 · see citing works
Stable cycling in discrete-time genetic models.
Hastings, A. (1981) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.78.11.7224 · Cited by 87 · see citing works
An Inequality Arising in Genetical Theory
Mulholland, H. P., & Smith, C. A. B. (1959) · American Mathematical Monthly · doi:10.1080/00029890.1959.11989387 · Cited by 85 · see citing works
An inequality in population genetics
Scheuer, P. A. G., & Mandel, S. P. H. (1959) · Heredity · doi:10.1038/hdy.1959.52 · Cited by 64 · see citing works
Numerical studies on two-loci selection models with general viabilities
Karlin, S., & Carmelli, D. (1975) · Theoretical Population Biology · doi:10.1016/0040-5809(75)90026-x · Cited by 49 · see citing works
What was Fisher’s fundamental theorem of natural selection and what was it for?
Plutynski, A. (2006) · Studies in History and Philosophy of Science Part C Studies in History and Philosophy of Biological and Biomedical Sciences · doi:10.1016/j.shpsc.2005.12.004 · Cited by 42 · see citing works
Carter, R. W., & Sanford, J. C. (2012) · Theoretical Biology and Medical Modelling · doi:10.1186/1742-4682-9-42 · Cited by 34 · see citing works
Self-citationChanges in Mean Fitness under Natural Selection
TURNER, J. R. G. (1970) · Springer eBooks · doi:10.1007/978-3-642-46244-3_2 · Cited by 20 · see citing works
Using Computer Simulation to Understand Mutation Accumulation Dynamics and Genetic Load
Sanford, J. C., Baumgardner, J. R., Brewer, W., Gibson, P. T., & ReMine, W. J. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-72586-2_55 · Cited by 20 · see citing works
Self-citationFundamental Theorem of Natural Selection
Edwards, A. W. F. (1967) · Nature · doi:10.1038/215537a0 · Cited by 18 · see citing works
Computational Evolution Experiments Reveal a Net Loss of Genetic Information Despite Selection
Nelson, C. W., & Sanford, J. C. (2013) · doi:10.1142/9789814508728_0014 · Cited by 13 · see citing works
Self-citationSelection Threshold Severely Constrains Capture of Beneficial Mutations
Sanford, J. C., Baumgardner, J. R., & Brewer, W. H. (2013) · doi:10.1142/9789814508728_0011 · Cited by 12 · see citing works
Self-citationUsing Numerical Simulation to Test the “Mutation-Count” Hypothesis
Brewer, W. H., Baumgardner, J. R., & Sanford, J. C. (2013) · doi:10.1142/9789814508728_0012 · Cited by 10 · see citing works
Self-citationCan Synergistic Epistasis Halt Mutation Accumulation? Results from Numerical Simulation
Baumgardner, J. R., Brewer, W. H., & Sanford, J. C. (2013) · doi:10.1142/9789814508728_0013 · Cited by 10 · see citing works
Self-citationMutation-Selection Models in Population Genetics and Evolutionary Game Theory
Bürger, R. (1989) · Springer eBooks · doi:10.1007/978-94-009-2358-4_8 · Cited by 10 · see citing works
Can Purifying Natural Selection Preserve Biological Information?
Gibson, P. T., Baumgardner, J. R., Brewer, W. H., & Sanford, J. C. (2013) · doi:10.1142/9789814508728_0010 · Cited by 8 · see citing works
Self-citationChanges in ribosomes from neonatal animal lung following 98% oxygen exposure
Durbridge, T. C., Bieber, M. M., Cogan, M. G., & Rosan, R. C. (1971) · Die Naturwissenschaften · doi:10.1007/bf00624623 · Cited by 8 · see citing works
Limits of Chaos and Progress in Evolutionary Dynamics
Basener, W. (2013) · doi:10.1142/9789814508728_0004 · Cited by 8 · see citing works
Self-citationMultiple Overlapping Genetic Codes Profoundly Reduce the Probability of Beneficial Mutation
Montañez, G. D., Marks, R. J., Fernandez, J., & Sanford, J. C. (2013) · doi:10.1142/9789814508728_0006 · Cited by 7 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Convergent Evolution, Evolving Evolvability, and the Origins of Lethal Cancer
Pienta, K. J., Hammarlund, E. U., Axelrod, R., Amend, S. R., & Brown, J. S. (2020) · Molecular Cancer Research · doi:10.1158/1541-7786.mcr-19-1158 · Cited by 82 · see citing works
Wang, Y., Nie, F., Shahid, M. Q., & Baloch, F. S. (2020) · BMC Plant Biology · doi:10.1186/s12870-020-02461-w · Cited by 45 · see citing works
Baverstock, K. F. (2021) · Progress in Biophysics and Molecular Biology · doi:10.1016/j.pbiomolbio.2021.04.005 · Cited by 38 · see citing works
Engineering and Expression Strategies for Optimization of L-Asparaginase Development and Production
Shishparenok, A. N., Gladilina, Y. A., & Zhdanov, D. D. (2023) · International Journal of Molecular Sciences · doi:10.3390/ijms242015220 · Cited by 36 · see citing works
Genetic trajectory and immune microenvironment of lung-specific oligometastatic colorectal cancer
Ottaiano, A., Circelli, L., Lombardi, A., Scala, S., Martucci, N., Galon, J., Buonanno, M., Scognamiglio, G., Botti, G., Hermitte, F., et al. (2020) · Cell Death and Disease · doi:10.1038/s41419-020-2480-6 · Cited by 31 · see citing works
Smirnov, E., Chmúrčiaková, N., Liška, F., Bažantová, P., & Cmarko, D. (2021) · Cells · doi:10.3390/cells10020196 · Cited by 30 · see citing works
Origin of Life: The Point of No Return
Kunnev, D. (2020) · Life · doi:10.3390/life10110269 · Cited by 21 · see citing works
A life history model of the ecological and evolutionary dynamics of polyaneuploid cancer cells
Bukkuri, A., Pienta, K. J., Austin, R. H., Hammarlund, E. U., Amend, S. R., & Brown, J. S. (2022) · Scientific Reports · doi:10.1038/s41598-022-18137-4 · Cited by 18 · see citing works
Using statistical methods to model the fine-tuning of molecular machines and systems
Thorvaldsen, S., & Hössjer, O. (2020) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2020.110352 · Cited by 15 · see citing works
“Basener and Sanford (2018) recently extended Fisher’s Theorem, allowing for arbitrary mutational spectra.”
BackgroundBaverstock, K. F. (2023) · Progress in Biophysics and Molecular Biology · doi:10.1016/j.pbiomolbio.2023.11.001 · Cited by 16 · see citing works
Protocell Effects on RNA Folding, Function, and Evolution
Saha, R., Choi, J., & Chen, I. A. (2024) · Accounts of Chemical Research · doi:10.1021/acs.accounts.4c00174 · Cited by 13 · see citing works
Universal constraint on nonlinear population dynamics
Adachi, K., Iritani, R., & Hamazaki, R. (2022) · Communications Physics · doi:10.1038/s42005-022-00912-4 · Cited by 12 · see citing works
Venegas-Aravena, P., & Cordaro, E. G. (2024) · Fractal and Fractional · doi:10.3390/fractalfract8010035 · Cited by 13 · see citing works
Sonowal, S., Pathak, K., Das, D., Buragohain, K., Gogoi, A., Borah, N., Das, A., & Nath, R. (2024) · Advanced Therapeutics · doi:10.1002/adtp.202400156 · Cited by 11 · see citing works
Bukkuri, A., Andersson, S., Mazariegos, M. S., Brown, J. S., Hammarlund, E. U., & Mohlin, S. (2024) · iScience · doi:10.1016/j.isci.2024.111433 · Cited by 12 · see citing works
The contribution of evolvability to the eco‐evolutionary dynamics of competing species
Bukkuri, A., Pienta, K. J., Amend, S. R., Austin, R. H., Hammarlund, E. U., & Brown, J. S. (2023) · Ecology and Evolution · doi:10.1002/ece3.10591 · Cited by 10 · see citing works
A percolation model of natural selection
Sidorova, A., Levashova, N. T., Гараева, А. С., & Tverdislov, V. A. (2020) · Biosystems · doi:10.1016/j.biosystems.2020.104120 · Cited by 8 · see citing works
Active Information Requirements for Fixation on the Wright-Fisher Model of Population Genetics
Marks, R., & Pachón, D. A. D. (2020) · BIO-Complexity · doi:10.5048/bio-c.2020.4 · Cited by 8 · see citing works
Geometric speed limit for acceleration by natural selection in evolutionary processes
Hoshino, M., Nagayama, R., Yoshimura, K., Yamagishi, J. F., & Ito, S. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023127 · Cited by 8 · see citing works
Chhina, A. K., Abhari, N., Mooers, A. Ø., & Lewthwaite, J. M. M. (2024) · Genome · doi:10.1139/gen-2024-0036 · Cited by 7 · see citing works
Modeling stress-induced responses: plasticity in continuous state space and gradual clonal evolution
Bukkuri, A. (2024) · Theory in Biosciences · doi:10.1007/s12064-023-00410-3 · Cited by 7 · see citing works
Limits on the evolutionary rates of biological traits
García-Pintos, L. P. (2024) · Scientific Reports · doi:10.1038/s41598-024-61872-z · Cited by 9 · see citing works
Biomarkers or biotargets? Using competition to lure cancer cells into evolutionary traps
Bukkuri, A., & Adler, F. R. (2023) · Evolution Medicine and Public Health · doi:10.1093/emph/eoad017 · Cited by 6 · see citing works
Escala, A. (2023) · Theoretical Ecology · doi:10.1007/s12080-023-00565-1 · Cited by 6 · see citing works
Responses to commentaries on “The gene: An appraisal”
Baverstock, K. F. (2024) · Progress in Biophysics and Molecular Biology · doi:10.1016/j.pbiomolbio.2024.02.002 · Cited by 5 · see citing works
Dynamical Systems and Fitness Maximization in Evolutionary Biology
Basener, W., Cordova, S., Hössjer, O., & Sanford, J. C. (2021) · Springer eBooks · doi:10.1007/978-3-319-57072-3_121 · Cited by 5 · see citing works
Self-citationGenerators, Harmonics and Evolutionary Emergence
Furze, J. N., & Mayad, E. H. (2022) · Springer eBooks · doi:10.1007/978-3-030-85829-2_1 · Cited by 4 · see citing works
The fundamental theorem of natural selection in optimization and games
Jaćimović, V. (2023) · Biosystems · doi:10.1016/j.biosystems.2023.104956 · Cited by 3 · see citing works
Alternate mutation modalities in models of population dynamics
Bartlett, J. (2024) · Academia Biology · doi:10.20935/acadbiol7432 · Cited by 3 · see citing works
Flores, L. A. M., Porras-Loaiza, A. P., Watters, C. E., & Skadron, S. (2026) · Sustainability · doi:10.3390/su18083720 · Cited by 2 · see citing works
Natural Selection as a Percolation System
Sidorova, A. E., Levashova, N. T., Tverdislov, V. A., & Garaeva, A. Y. (2019) · Moscow University Physics Bulletin · doi:10.3103/s0027134919050151 · Cited by 2 · see citing works
Dynamical Systems and Fitness Maximization in Evolutionary Biology
Basener, W., Cordova, S., Hössjer, O., & Sanford, J. C. (2021) · Springer eBooks · doi:10.1007/978-3-319-70658-0_121-1 · Cited by 2 · see citing works
Self-citationThe evolution of E. coli is NOT driven by genetic variance but by thermodynamics.Preprint
Baverstock, K. F., & Annila, A. (2023) · Qeios · doi:10.32388/nlisv5 · Cited by 2 · see citing works
Back to the fundamentals: a reply to Basener and Sanford 2018
Hancock, Z. B., & Cardinale, D. S. (2024) · Journal of Mathematical Biology · doi:10.1007/s00285-024-02077-w · Cited by 1 · see citing works
Intra-specific diversity and adaptation modify regime shifts dynamics under environmental change
Imbert, T., Poggiale, J., & Gauduchon, M. (2024) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2024342 · Cited by 1 · see citing works
Fisher’s Fundamental Theorem of Natural Selection Isn’t Fundamental After All
Cordova, S. (2020) · Communications of the Blyth Institute · doi:10.33014/issn.2640-5652.2.2.cordova.1 · Cited by 1 · see citing works
Geometry of Fitness Surfaces and Dynamics of Replicator Systems
Bratus, A. S., Novozhilov, A. S., & Yakushkina, T. (2021) · Springer eBooks · doi:10.1007/978-3-030-73241-7_5 · Cited by 1 · see citing works
On a general Wright-Fisher modelPreprint
Roitershtein, A., Rastegar, R., Chapkin, R. S., & Ivanov, I. V. (2019) · arXiv (Cornell University)
Extinction scenarios in evolutionary processes: a multinomial Wright–Fisher approach
Roitershtein, A., Rastegar, R., Chapkin, R. S., & Ivanov, I. V. (2023) · Journal of Mathematical Biology · doi:10.1007/s00285-023-01993-7
Flannery, M. A. (2020) · Metascience · doi:10.1007/s11016-020-00523-1
Do We Understand Heredity and Evolution? NoPreprint
Baverstock, K. F. (2025) · Qeios · doi:10.32388/hhqbio
Gibbon, S. R., Conover, J. L., Barker, M. S., & Gutenkunst, R. N. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.08.28.672890
A Discrete-Time Predator-Prey Model with Selection and Mutation in the Predator Population
Ackleh, A. S., Sikder, S., & Veprauskas, A. (2026) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-032-25494-8_9
Evolution expresses the second law of thermodynamics in action
Annila, A., & Baverstock, K. F. (2026) · Journal of The Royal Society Interface · doi:10.1098/rsif.2026.0430
Dynamical Systems and Fitness Maximization in Evolutionary Biology
Basener, W., Córdova, S., Hössjer, O., & Sanford, J. (2026) · Springer eBooks · doi:10.1007/978-3-319-70658-0_121-2
Self-citation
- Authors
- Basener, W. F., & Sanford, J. C.
- Affiliations
- Rochester Institute of Technology (US)
- Corresponding author
- Basener, William F.
- Venue
- Journal of Mathematical Biology
- Published
- 2017-11-07
- Volume
- 76
- Issue
- 7
- Pages
- 1589-1622
- ISSN
- 0303-6812 (ISSN-L)
- 1432-1416
- PMC
- PMC5906570
- OpenAlex
- W2767985017
- Cited by
- 46
- References
- 61
- Citations by year
- 2026: 4 · 2025: 2 · 2024: 11 · 2023: 9 · 2022: 3 · 2021: 6 · 2020: 9 · 2019: 2
- FWCI
- 2.00
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Journal of Mathematical Biology (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, other-oa)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Keywords
- fundamental theorem of natural selection, mutation-selection balance, mean fitness, genetic variance, mutation effects, neo-Darwinian theory, evolutionary dynamics, differential equation model
- MeSH terms
- Animals, Computer Simulation, Genetics, Population, Humans, Models, Genetic, Mutation, Population Dynamics, Selection, Genetic, Systems Analysis, Time Factors, Genetic Variation, Normal Distribution, Computational Biology, Genetic Determinism, Mathematical Concepts, Genetic Fitness
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
