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Simplest Population Models

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Part of the book series: Mathematics and Its Applications ((MASS,volume 22))

Abstract

In this chapter we will show how even simple models, describing the most elementary populational genetic processes, bring us to conclusions, which are interesting due to their biological clearness. Simple models are still better since they are readily verified in experiments, clearly demonstrating their merits and drawbacks and showing to what extent mathematical models may be applied to the analysis of populational genetic processes. A complex model of great generality is hard to apply to concrete biological situations. The arising mathematical complications can totally shade the biological origin of the problem, shifting the basic accent of the study onto the lines of their overcoming.

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Notes and Bibliography

  • Haldane, J. B. S.: 1927, ‘A Mathematical Theory of Natural and Artificial Selection. Part V.’, Proc. Comb. Phil. Soc. 223,607–615.

    Article  Google Scholar 

  • Norton, H. T. J.: 1928, ‘Natural Selection and Mendelian Variation’, Proc. Lond. Math. Soc., Ser. 2, 28, 1, 1-45.

    Article  Google Scholar 

  • Charlesworth, B.: 1972, ‘Selection in Population with Overlapping Generations. III. Conditions for Genetic Equilibrium’, Theor. Pop. Biol. 3,4, 377–395.

    Article  Google Scholar 

  • Smirnov, M. V.: 1980, ‘O polimorfizme v populjacii s učetom vozrastnoi struktury (On Polymorphism in Populations with Age Structure.’ In Russian), Zurnal Obshei Biologii (Journal of General Biology) 41, 1,31–46

    Google Scholar 

  • Charlesworth, B.: 1973, ‘Selection in Populations with Overlapping Generations. V. Natural Selection and Life Histories’, Amer. Natur. 107, 954, 303–311.

    Article  Google Scholar 

  • Smirnov, M. V.: ‘Ob ustoičivosti predelnyh traektoriy dinamiki populjaciy s učetom vozrastnoi struktury (On Stability of Limiting Trajectories for Population Dynamics with Account Taken of the Age-Structure.’ In Russian), Tezisy VII Vsesouznovo soveshanija po problemam upravlenija (Theses of the Seventh All-Union Conference on Problems of Control), Tallin, 716–718

    Google Scholar 

  • May, R. M.: 1975, ‘Biological Populations Obeying Difference Equations: Stable Points, Stable Cycles and Chaos’, Theor. Biol. 51, 2, 522–524

    Article  Google Scholar 

  • Levin, S. A., May, R. M.: 1976, ‘A Note on Dilference-Delay Equations’, Theor. Pop. Biol. 9, 2, 178–187.

    Article  MathSciNet  Google Scholar 

  • Svirezhev, Yu. M. and Timofeeff-Ressovsky, N. V.: 1966, ‘O ravnovesii genotipov v modelnyh populjacijah Drosophila melanogaster (On the Equilibrium of Genotypes in Model Populations of Drosophila Melanogaster.’ In Russian), Problemy Kibernetiki (Problems of Cybernetics) 16, 123–136.

    Google Scholar 

  • Svirezhev, Yu. M. and Timofeelf-Ressovsky, N. W.: 1968, ‘Some Types of Polymorphism in Populations’, In: Haldane and Modern Biology, Hopkins Press, J. Baltimore, 141–168.

    Google Scholar 

  • Lewontin, R. C.: 1974, The Genetic Basis of Evolutionary Change, Columbia Univ. Press, N.Y., L., 346 p.

    Google Scholar 

  • Scudo, F. M. and Ziegler, J. R.: 1978, The Golden Age of Theoretical Ecology: 1923-1940, Springer-Verlag, Berlin Heidelberg, N.Y., 413–438.

    MATH  Google Scholar 

  • Kostitzin, V. A.: 1937, Biologie Mathéimatique, A. Colin, Paris, 204–215.

    Google Scholar 

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© 1990 Kluwer Academic Publishers

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Svirezhev, Y.M., Passekov, V.P. (1990). Simplest Population Models. In: Fundamentals of Mathematical Evolutionary Genetics. Mathematics and Its Applications, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2589-2_3

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  • DOI: https://doi.org/10.1007/978-94-009-2589-2_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7670-8

  • Online ISBN: 978-94-009-2589-2

  • eBook Packages: Springer Book Archive

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