“…you can’t have a paradigm shift if there’s no paradigm to be shifted. You can, however, have a paradigm shaft—that’s when people create a false view of the field and claim that new discoveries have overthrown the standard paradigm.”
–Laurence A. Moran (2023), What’s in Your Genome?
Abstract
Fisher’s fundamental theorem of natural selection has haunted theoretical population genetic literature since it was proposed in 1930, leading to numerous interpretations. Most of the confusion stemmed from Fisher’s own obscure presentation. By the 1970s, a clearer view of Fisher’s theorem had been achieved and it was found that, regardless of its utility or significance, it represents a general theorem of evolutionary biology. Basener and Sanford (J Math Biol 76:1589–1622, 2018) writing in JOMB, however, paint a different picture of the fundamental theorem as one hindered by its assumptions and incomplete due to its failure to explicitly incorporate mutational effects. They argue that Fisher saw his theorem as a “mathematical proof of Darwinian evolution”. In this reply, we show that, contrary to Basener and Sanford, Fisher’s theorem is a general theorem that applies to any evolving population, and that, far from their assertion that it needed to be expanded, the theorem already implicitly incorporates ancestor–descendant variation. We also show that their numerical simulations produce unrealistic results. Lastly, we argue that Basener and Sanford’s motivations were in undermining not merely Fisher’s theorem, but the concept of universal common descent itself.
Similar content being viewed by others
References
Basener WF, Sanford JC (2018) The fundamental theorem of natural selection with mutations. J Math Biol 76:1589–1622
Basener WF, Cordova S, Hössjer O, Sanford JC (2021) Dynamics systems and fitness maximization in evolutionary biology. In: Sriraman B (ed) Handbook of the mathematics of the arts and sciences. Springer, Switzerland, pp 2097–2169
Bulmer M (1989) Maintenance of genetic variability by mutation-selection balance: a child’s guide through the jungle. Genome 31:761–767
Bürger R (2000) The mathematical theory of selection, recombination, and mutation. John Wiley and Sons, Chichester
Chou H, Chiu H, Delaney NF, Segrè D, Marx CJ (2011) Diminishing returns epistasis among beneficial mutations decelerates adaptation. Science 332(6034):1190–1192
Coltman DW, O’Donoghue P, Hogg JT, Festa-Bianchet M (2005) Selection and genetic (co)variance in bighorn sheep. Evolution 59(6):1372–1382
Couce A, Magnan M, Lenski RE, Tenaillon O (2022) Predictability shifts from local to globe rules during bacterial adaptation. bioRxiv. https://doi.org/10.1101/2022.05.17.492360
Crow J (1997) The high spontaneous mutation rate: Is it a health risk? PNAS 94(16):8380–8386
Crow J, Kimura M (1970) An introduction to population genetic theory. Harper & Row Publishers, New York
Edwards AWF (1969) Review of Ewens (1969). Heredity 24:672–673
Ewens WJ (1989) An interpretation and proof of the fundamental theorem of natural selection. Theo Pop Biol 36:167–180
Eyre-Walker A, Keightley PD (2007) The distribution of fitness effects of new mutations. Nat Rev Genet 8:610–618
Eyre-Walker A, Woolfit M, Phelps T (2006) The distribution of fitness effects of new deleterious amino acid mutations in humans. Genetics 173:891–900
Fisher RA (1930) The genetical theory of natural selection. Clarendon Press, Oxford
Fleming WH (1979) Equilibrium distributions of continuous polygenic traits. SIAM J App Math 36:148–168
Gillespie JH (1984) A simple stochastic gene substitution model. Theor Popul Biol 23:202–215
Grafen A (2015) Biological fitness and the fundamental theorem of natural selection. Am Nat 186(1):1–14
Gustafsson L (1986) Lifetime reproductive success and heritability: empirical support for Fisher’s fundamental theorem. Am Nat 128(5):761–764
Haller BC, Messer PW (2023) SLiM 4: multispecies eco-evolutionary modeling. Am Nat 201(5):E127–E139
Hamilton WD (1975) Innate social aptitudes of man: an approach from evolutionary genetics. In: Fox R (ed) ASA Studies 4: biological anthropology. Malaby Press, London, pp 133–153
Hartl DL, Taubes CH (1996) Compensatory nearly neutral mutations: Selection without adaptation. J Theor Biol 192:303–309
Hirsch CN, Flint-Garcia SA, Beissinger TM, Eichten SR, Deshpande S, Barry K, McMullen MD, Holland JB, Buckler ES, Springer N, Buell CR, de Leon N, Kaeppler SM (2014) Insights into the effects of long-term artificial selection on seed size in maize. Genetics 198(1):409–421
Houle D (1992) Comparing evolvability and variability of quantitative traits. Genetics 130(1):195–204
Houle D, Morikawa B, Lynch M (1996) Comparing mutational variabilities. Genetics 143(3):1467–1483
Huber CD, Durvasula A, Hancock AM, Lohmueller KE (2018) Gene expression drives the evolution of dominance. Nat Comm 9(2750):1–11
Istock CA (1978) Fitness variation in a natural population. In: Dingle H (ed) Evolution of insect migration and diapause. Springer-Verlag, New York, pp 171–190
Keightley PD, Lynch M (2003) Toward a realistic model of mutations affecting fitness. Evolution 57(3):683–685
Kempthorne O (1957) An introduction to genetical statistics. Chapman and Hall, London
Kimura M (1964) Diffusion models in population genetics. J App Prob 1:177–232
Kimura M (1979) Model of effectively neutral mutations in which selective constraint is incorporated. Proc Natl Acad Sci USA 76(7):3440–3444
Kimura M (1983) The neutral theory of molecular evolution. Cambridge Univ Press, Cambridge
Kingman JFC (1978) Simple model for balance between selection and mutation. J Appl Probab 15:1–12
Kondrashov AS (1995) Contamination of the genome by very slightly deleterious mutations: why have we not died 100 times over? J Theo Biol 175(4):583–594
Kruuk LEB, Clutton-Brock TH, Slate J, Pemberton JM, Brotherstone S, Guinness FE (2000) Heritability of fitness in a wild mammal population. PNAS 97(2):698–703
Lande R (1975) The maintenance of genetic variability by mutation in a polygenic character with linked loci. Gen Res 26:221–235
Lande R (1976) Natural selection and random genetic drift in phenotypic evolution. Evolution 30:314–334
Lederberg J, Lederberg E (1952) Replica plating and indirect selection of bacterial mutants. J Bacteriol 63(3):399–406
Leigh EG (1987) Ronald Fisher and the development of evolutionary theory. II. Influences of new variation on evolutionary process. Oxford Surv Evol Biol 4:212–264
Luque VJ (2017) One equation to rule them all: a philosophical analysis of the Price equation. Biol Philos 32:97–125
Lynch M (2016) Mutation and human exceptionalism: our future genetic load. Genetics 202(3):869–875
Lynch M, Hill W (1986) Phenotypic evolution by neutral mutation. Evolution 40:915–935
MacLean RC, Buckling A (2009) The distribution of fitness effects of beneficial mutations in Pseudomonas aeruginosa. PLoS Genet 5(3):e1000406
Manalil S, Busi R, Renton M, Powles SB (2011) Rapid evolution of herbicide resistance by low herbicide dosages. Weed Sci 59(2):210–217
Maynard Smith J (1962) The scientist speculates: an anthology of partly-baked ideas. Ed. Good IJ, Basic Books, NY, pp 252–256
McCleery RH, Pettifor RA, Armbruster P, Meyer K, Sheldon BC, Perrins CM (2004) Components of variance underlying fitness in a natural population of the Great Tit Parus major. Am Nat 164(3):E63–E72
Merilä J, Sheldon C (1999) Lifetime reproductive success and heritability in nature. Am Nat 155(3):301–310
Messina FJ (1993) Heritability and ‘evolvability’ of fitness components in Callosobruchus maculatus. Heredity 71:623–629
Muller HJ (1950) Our load of mutations. Am J Hum Genet 2(2):111–176
Mustonen V, Lässig M (2009) From fitness landscapes to seascapes: non-equilibrium dynamics of selection and adaptation. Trends Genet 25(3):111–119
Ohta T (1977) Molecular evolution and polymorphism. Natl Inst Genet Mishima Japan 76:148–167
Ohta T, Tachida H (1990) Theoretical study of near neutrality. I. Heterozygosity and rate of mutation substitution. Genetics 126:219–229
Orr HA (1998) The population genetics of adaptation: the distribution of factors fixed during adaptive evolution. Evolution 52(4):935–949
Orr HA (2000) Adaptation and the cost of complexity. Evolution 54:13–20
Orr HA (2005) The genetic theory of adaptation: a brief history. Nat Rev Genet 6:119–127
Palmer AC, Kishony R (2013) Understanding, predicting and manipulating the genotypic evolution of antibiotic resistance. Nat Rev Genet 14:243–248
Price GR (1970) Selection and covariance. Nature 227:520–521
Price GR (1972a) Extension of covariance selection mathematics. Ann Hum Genet Lond 35:485–490
Price GR (1972b) Fisher’s ‘fundamental theorem’ made clear. Ann Hum Genet Lond 36:129–140
Provine WB (1971) The origins of theoretical population genetics. University of Chicago Press, Chicago
Queller DC (2017) Fundamental theorems of evolution. Am Nat 189(4):345–353
Rice S (1990) A geometric model for the evolution of development. J Theo Biol 143(3):319–342
Rice S (2004) Evolutionary theory: mathematical and conceptual foundations. Sinauer Associates, Oxford University Press, Oxford
Robertson A (1955) Selection in animals: synthesis. Cold Spring Harbor Symp Quant Biol 20:225–229
Roth FP, Wakeley J (2016) Taking exception to human eugenics. Genetics 204(2):821–823
Rupe CL, Sanford JC (2013) Using numerical simulation to better understand fixation rates, and establishment of a new principle: Haldane’s ratchet. Proc Int Conf Creat 7(1):32
Sanford JC (2005) Genetic entropy and the mystery of the genome. Elim Publishing, NY
Sanford JC, Carter RW, Brewer W, Baumgardner J, Potter B, Potter J (2018) Adam and eve, designed diversity, and allele frequencies. Proc Int Conf Creat 8(1):8
Sanjuán R, Moya A, Elena SF (2004) The distribution of fitness effects caused by single-nucleotide substitutions in an RNA virus. PNAS 101(22):8396–8401
Schrempf A, Giehr J, Röhrl R, Steigleder S, Heinze J (2017) Royal Darwinian demons: enforced changes in reproductive efforts do not affect the life expectancy of ant queens. Am Nat 189(4):436–442
Stuart YE, Campbell TS, Hohenlohe PA, Reynolds RG, Revell LJ, Losos JB (2014) Rapid evolution of a native species following invasion by a congener. Science 346(6208):463–466
Svensson EI, Connallon T (2019) How frequency-dependent selection affects population fitness, maladaptation and evolutionary rescue. Evol Appl 12(7):1243–1258
Tataru P, Mollion M, Glémin S, Bataillon T (2017) Inference of distribution of fitness effects and proportion of adaptive substitutions from polymorphism data. Genetics 207(3):1103–1119
Teplitsky C, Mills JA, Yarrall JW, Merilä J (2009) Heritability of fitness components in a wild bird population. Evolution 63(3):716–726
Thatcher JW, Shaw JM, Dickinson WJ (1998) Marginal fitness contributions of nonessential genes in yeast. PNAS 95(1):253–257
Turelli M (1984) Heritable genetic-variation via mutation selection balance: Lerch’s zeta meets the abdominal bristle. Theo Pop Biol 25:138–193
Van Noordwijk AJ, Balen JH, Scharloo W (1980) Heritability of ecological important traits in the great tit Parus major. Ardea 68:193–203
Wade MJ (1985) Soft selection, hard selection, kin selection, and group selection. Am Nat 125:61–73
Walsh B, Lynch M (2018) Evolution and selection of quantitative traits. Oxford University Press, Oxford
Wright S (1937) The distribution of gene frequencies in populations. PNAS 23(6):307–320
Wright S (1978) Evolution and the genetics of populations. Vol. 4, Variability within and among natural populations. University of Chicago Press, Chicago
Wright SI, Bi IV, Schroeder SG, Yamasaki M, Doebley JF, McMullen MD, Gaut BS (2005) The effects of artificial selection on the maize genome. Science 308(5726):1310–1314
Acknowledgements
We thank Jonathan L. Baker for helpful comments on this manuscript. We also thank Donny Budinsky and Paul Price for bringing B&S to our attention, as well as their continued encouragement in addressing confusion in the field.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Hancock, Z.B., Cardinale, D.S. Back to the fundamentals: a reply to Basener and Sanford 2018. J. Math. Biol. 88, 54 (2024). https://doi.org/10.1007/s00285-024-02077-w
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00285-024-02077-w