Skip to main content
SpringerLink
Log in

Changes in Mean Fitness under Natural Selection

  • Chapter
Mathematical Topics in Population Genetics

Part of the book series: Biomathematics ((BIOMATHEMATICS,volume 1))

Abstract

The Reformation in Europe changed Man’s view of his relation with God; no longer dependent on a hierarchy of ordained vicars, the individual must seek God by his own efforts. There grew, particularly in England, the tradition of Natural Theology: not only was God approached through His Works of Nature, but those very Works were held to be evidence of His Divine Wisdom. This idea was applied especially to living organisms, whose adaptations, whose fitness to the ends they served, suggested powerfully that they had been designed by an intelligent, beneficent creator. This “Argument from Design”, a very popular proof of the existence of a Christian God, is well summarized by Robert Boyle (1688):

And I confess, that when I assist at a well-administered Anatomy, I do so wonder at the admirable Contrivance of a Humane Body, that I cannot but somewhat wonder, that there should be found among Philosophers, men that can ascribe it to blind Chance. The Stoick that in Cicero asked an Epicurean, why Chance did not make Palaces and other Buildings, seems not to me to have made an impertinent Question.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Atkinson, F. V., G. A. Watterson, and P. A. P. Moran: A matrix inequality. Quart. J. Math. (Oxford) (2) 11, 137–140 (1960).

    Article  MATH  MathSciNet  Google Scholar 

  • Ayala, F. S.: Evolution of fitness. II. Correlated effects of natural selection on the productivity and size of experimental population of Drosophila serrata. Evolution 22, 55–65 (1968).

    Article  Google Scholar 

  • Beardmore, J. A., Th. Dobzhansky, and O. Pavlovsky: An attempt to compare the fitness of polymorphic and monomorphic experimental populations of Drosophila pseudoobscura. Heredity 14, 19–33 (1960).

    Article  Google Scholar 

  • Bentvelzen, P.: Some interrelations between density and genetic structure of a Drosophila population. Genetica (Netherlands) 34, 229–241 (1963).

    Google Scholar 

  • Blakley, G. R.: Darwinian natural selection acting within populations. J. Theor. Biol. 17, 252–281 (1967).

    Article  Google Scholar 

  • Bodmer, W. F., and J. Felsenstein: Linkage and selection: theoretical analysis of the deterministic two locus random mating model. Genetics 57, 237–265 (1967)

    Google Scholar 

  • Boyle, R.: A Disquisition about the final Causes of natural Things. London: H. C. for John Taylor 1688.

    Google Scholar 

  • Cain, A. J., and P. M. Sheppard: The theory of adaptive polymorphism. Amer. Natur. 88, 321 -326 (1954).

    Article  Google Scholar 

  • - - Adaptive and selective value. Amer. Natur. 90, 202–203 (1956).

    Article  Google Scholar 

  • Campos Rosado, J. M., and A. Robertson: The genetic control of sex ratio. J. Theor. Biol. 13, 324–329 (1966).

    Article  Google Scholar 

  • Cannings, C., and A. W. F. Edwards: Natural selection and the de Finetti diagram. Ann. Hum. Genet. (Lond.) 31, 421–428 (1968).

    Article  Google Scholar 

  • Cockerham, C. C.: An extension of the concept of partitioning hereditary variance for analysis of covariances among relatives when epistasis is present. Genetics 39, 859–882 (1954).

    Google Scholar 

  • * Crow, J. F., and M. Kimura: Some genetic problems in natural populations. Proc. 3rd. Berkeley Symp. Math. Stat. Prob. 4, 1–22 (1956).

    MathSciNet  Google Scholar 

  • Dobzhansky, Th.: Genetic diversity and fitness. Proc. XI Int. Cong. Genet. Hague 3, 541–552 (1965).

    Google Scholar 

  • * Edwards, A. W. F.: Fundamental Theorem of natural selection. Nature (Lond.) 215, 537–538 (1967).

    Article  Google Scholar 

  • - On the fundamental theorem of natural selection. Duplicated paper available from the author at Gonville & Caius College, Cambridge (1968).

    Google Scholar 

  • Ehrlich, P. R., and L. C. Birch: The “balance of nature” and “population control”. Amer. Natur. 101, 97–107 (1967).

    Article  Google Scholar 

  • Ellegård, A.: Darwin and the general reader. The reception of Darwin’s theory of evolution in the British periodical press, 1859–1872. Gothenberg Studies in English VIII Ed. F. Behre. Göteberg 1958.

    Google Scholar 

  • Falconer, D. S.: Introduction to quantitative genetics. Edinburgh-London: Oliver and Boyd 1961.

    Google Scholar 

  • - Genetic consequences of selection pressure. In Genetic and environmental factors in human ability. pp. 219–232. Ed. by J. E. Meade and A. S. Parkes. Edinburgh — London: Oliver and Boyd 1966.

    Google Scholar 

  • Feller, W.: On fitness and the cost of natural selection. Genet. Res. (Camb.) 9, 1–15 (1967).

    Article  Google Scholar 

  • Fisher, R. A.: The genetical theory of natural selection. Oxford: Clarendon Press 1930.

    MATH  Google Scholar 

  • - Average excess and average effect of a gene substitution. Ann. Eugen. (Lond.) 11, 53–63 (1941).

    Article  Google Scholar 

  • - The genetical theory of natural selection. 2nd ed. New York: Dover Books 1958.

    Google Scholar 

  • Ford, E. B.: Ecological genetics. London: Methuen; New York: John Wiley & Sons 1964.

    Google Scholar 

  • Harper, J. L.: The nature and consequence of interference amongst plants. Proc. XI Int. Cong. Genet. Hague 2, 465–482 (1965).

    Google Scholar 

  • Hasofer, A. M.: A continuous-time model in population genetics. J. Theor. Biol. 11, 150–163 (1966).

    Article  Google Scholar 

  • Jain, S. K., and P. L. Workman: Generalized F-statistics and the theory of inbreeding and selection. Nature (Lond.) 214, 674–678 (1967).

    Article  Google Scholar 

  • Kempthorne, O.: An introduction to genetic statistics. New York: John Wiley & Sons 1957.

    MATH  Google Scholar 

  • Kimura, M.: On the change of population fitness by natural selection. Heredity 12, 145–167 (1958).

    Article  Google Scholar 

  • - Shudan iden-gaku gairon (Introduction to population genetics). Tokyo: Baihukan 1960.

    Google Scholar 

  • - Attainment of quasi linkage equilibrium when gene frequencies are changing by natural selection. Genetics 52, 875–890 (1965).

    Google Scholar 

  • - Two loci polymorphism as a stationary point. Ann. Rep. Natl. Inst. Genet. Japan 17, 65–67 (1966).

    Google Scholar 

  • Kingman, J. F. C.: On an inequality in partial averages. Quart. J. Math. (Oxford) (2) 12, 78–80 (1961).

    Article  MATH  MathSciNet  Google Scholar 

  • Kojima, K.: Role of epistasis and overdominance in stability of equilibrium with selection. Proc. Natl. Acad. Sci. (Wash.) 45, 984–989 (1959).

    Article  MATH  Google Scholar 

  • -, and T. M. Kelleher: Changes of mean fitness in random mating populations when epistasis and linkage are present. Genetics 46, 527–540 (1961).

    Google Scholar 

  • - and K. M. Yarbrough: Frequency-dependent selection at the esterase 6 locus in Drosophila melanogaster. Proc. Natl. Acad. Sci. (Wash.) 57, 645–649 (1967).

    Article  Google Scholar 

  • Lerner, I. M.: Ecological genetics-synthesis. Proc. XI Int. Cong. Genet. Hague 2, 489–494 (1965).

    Google Scholar 

  • Levins, R.: Theory of fitness in a heterogeneous environment. I. The fitness set and adaptive function. Amer. Natur. 96, 361–373 (1962).

    Article  Google Scholar 

  • Lewontin, R. C.: The effects of population density and composition on viability in Drosophila melanogaster. Evolution 9, 27–41 (1955).

    Article  Google Scholar 

  • - Selection in and of populations. Ideas in modern biology. Proc. XVI Int. Cong. Zool. 6, 299–311 (1965).

    Google Scholar 

  • -, and J. L. Hubby: A molecular approach to the study of genetic heterozygosity in natural populations. II. Amount of variation and degree of heterozygosity in natural populations of Drosophila pseudoobscura. Genetics 54, 595–609 (1966).

    Google Scholar 

  • -, and K. Kojima: The evolutionary dynamics of complex polymorphisms. Evolution 14, 458–472 (1960).

    Article  Google Scholar 

  • -, and M. J. D. White: Interaction between inversion polymorphisms of two chromosome pairs in the grasshopper, Moraba scurra. Evolution 14, 116–129 (1960).

    Article  Google Scholar 

  • Li, C. C.: The stability of an equilibrium and the average fitness of a population. Amer. Natur. 89, 281–295 (1955a).

    Article  Google Scholar 

  • - Population genetics. Chicago-London: Chicago Univ. Press 1955b.

    Google Scholar 

  • - Fundamental theorem of natural selection. Nature (Lond.) 214, 505–506 (1967a).

    Article  Google Scholar 

  • - Genetic equilibrium under selection. Biometrics 23, 397–484 (1967b).

    Article  MathSciNet  Google Scholar 

  • - The maximization of average fitness by natural selection for a sex-linked locus. Proc. Natl. Acad. Sci. (Wash.) 57, 1260–1261 (1967c).

    Article  Google Scholar 

  • - Increment of average fitness for multiple alleles. Proc. Natl. Acad. Sci. (Wash.) 62, 395–398 (1969).

    Article  Google Scholar 

  • MacArthur, R. H.: Some generalized theorems of natural selection. Proc. Natl. Acad. Sci. (Wash.) 48, 1893–1897 (1962).

    Article  MATH  Google Scholar 

  • Mandel, S. P. H.: Fundamental theorem of natural selection. Nature (Lond.) 220, 1251–1252 (1968).

    Article  Google Scholar 

  • * Mode, C. J.: A stochastic calculus and its application to some fundamental theorems of natural selection. J. Appl. Prob. 3, 327–352 (1966).

    Article  MATH  MathSciNet  Google Scholar 

  • Moran, P. A. P.: The statistical processes of evolutionary theory. Oxford: Clarendon Press 1962.

    MATH  Google Scholar 

  • - On the nonexistence of adaptive topographies. Ann. Hum. Genet. (Lond.) 27, 383–393 (1964).

    Article  MATH  Google Scholar 

  • Mulholland, H. P., and C. A. B. Smith: An inequality arising in genetical theory. Am. Math. Monthly 66, 673–683 (1959).

    Article  MathSciNet  Google Scholar 

  • Nei, M.: Effects of selection on the components of genetic variance. In: Statistical genetics and plant breeding, pp. 501–515. Ed. by W. A. Hansen and H. F. Robinson. Washington, D. C.: Natl. Acad. Sci. — Natl. Res. Council, Publ. 982, 1963.

    Google Scholar 

  • Peckham, M.: The origin of species, by Charles Darwin. A variorum text. Philadelphia: Univ. Penna. Press 1959.

    Google Scholar 

  • Pimentel, D.: Population ecology and the genetic feedback mechanism. Proc. XI Int. Cong. Genet. Hague 2, 483–488 (1965).

    Google Scholar 

  • Roy, Subodh Kumar: Intra-specific interaction in rice. Proc. XI Int. Cong. Genet., Hague 7, 145 (1963).

    Google Scholar 

  • Sacks, J. M.: A stable equilibrium with minimum average fitness. Genetics 56, 705–708 (1967).

    Google Scholar 

  • Scheuer, P. A. G., and S. P. H. Mandel: An inequality in population genetics. Heredity 13, 519–524 (1959).

    Article  Google Scholar 

  • Slobodkin, L. B.: The strategy of evolution. Amer. Sci. 52, 342–357 (1964).

    Google Scholar 

  • Sokal, R. R.: Some stages in the development of the concept of natural selection. Univ. Kansas Sci. Bull. Supp. 42, 129–151 (1962).

    Google Scholar 

  • -, and I. Huber: Competition among genotypes in Tribolium castaneum at varying densities and gene frequencies (the sooty locus). Amer. Natur. 97, 169–184 (1963).

    Article  Google Scholar 

  • -, and I. Karten: Competition among genotypes in Tribolium castaneum at varying densities and gene frequencies (the black locus). Genetics 49, 195–211 (1964).

    Google Scholar 

  • Thoday, J. M.: Correlation between gene frequency and population size. Amer. Natur. 97, 409–412 (1963).

    Article  Google Scholar 

  • Turner, J. R. G.: On supergenes. I. The evolution of supergenes. Amer. Natur. 101, 195–221 (1967a).

    Article  Google Scholar 

  • - Mean fitness and the equilibria in multilocus polymorphisms. Proc. Roy. Soc. London B 169, 31–58 (1967b).

    Article  Google Scholar 

  • - Why does the genotype not congeal? Evolution 21, 645–656 (1967c).

    Article  Google Scholar 

  • - The effect of mutation on fitness in a system of two coadapted loci. Ann. Hum. Genet. (Lond.) 30, 329–334 (1967d).

    Article  Google Scholar 

  • * - Fundamental theorem of natural selection. Nature (Lond.) 215, 1080 (1967e).

    Article  Google Scholar 

  • - Natural selection for and against a polymorphism which interacts with sex. Evolution 22, 481–495 (1968).

    Article  Google Scholar 

  • - The basic theorems of natural selection: a naive approach. Heredity 24, 75–84 (1969).

    Article  Google Scholar 

  • -, and M. H. Williamson: Population size, natural selection, and the genetic load. Nature (Lond.) 218, 700 (1968).

    Article  Google Scholar 

  • Warburton, F. E.: Increase in the variance of fitness due to selection. Evolution 21, 197–198 (1967).

    Article  Google Scholar 

  • Williamson, M. H.: An elementary theory of interspecific competition. Nature (Lond.) 180, 422–425 (1957).

    Article  MATH  Google Scholar 

  • Wright, S.: The roles of mutation, inbreeding, crossbreeding, and selection in evolution. Proc. 6th Int. Cong. Genet. 1, 356–366 (1932).

    Google Scholar 

  • - Adaptation and selection. In: Genetics, palaeontology and evolution,, pp. 365–389. Ed. by G. L. Jepsen, G. G. Simpson, and E. Mayr. Princeton, N. J.: Princeton Univ. Press 1949.

    Google Scholar 

  • - Classification of the factors of evolution. Cold Spr. Harb. Symp. Quant. Biol. 20, 16–24 D (1955).

    Article  Google Scholar 

  • - Stochastic process in evolution. In: Symposium on stochastic models in medicine and biology, pp. 199–244. Ed. by J. Gurland. Madison: The University of Wisconsin Press 1964.

    Google Scholar 

Download references

Authors
  1. J. R. G. Turner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ken-ichi Kojima

Rights and permissions

Reprints and permissions

Copyright information

© 1970 Springer-Verlag Berlin · Heidelberg

About this chapter

Cite this chapter

Turner, J.R.G. (1970). Changes in Mean Fitness under Natural Selection. In: Kojima, Ki. (eds) Mathematical Topics in Population Genetics. Biomathematics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46244-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-46244-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-46246-7

  • Online ISBN: 978-3-642-46244-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation