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Models and Analyses of Dispersal Patterns

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Mathematical Topics in Population Genetics

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

Abstract

For a given set of gametes, population structure is the controlling factor determining the array of genotypes exposed to selective forces. This array reflects the combined effects of genotype frequencies, mating preferences, and mate availability, as well as any changes in age distributions of fertile adults or availability of breeding sites. Because the extent of the array of genotypes may either enhance or render ineffective a particular mode of selection, population genetic theory always incorporates a statement specifying the population structure. Models developed from “conditions of random pairing of gametes” are useful as a first step for understanding selection forces, but ultimately such oversimplifications of population structure must be revised to better agree with the complexities of actual situations in nature. Evidence available from a variety of sources indicates that existing theory does not adequately account for non-random mating of several forms.

This paper is dedicated to Professor Th. Dobzhansky in honor of his long leadership in evolutionary genetics and of his pioneering efforts in ecological genetics of Drosophila.

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References

  • Bateman, A. J.: Contamination of seed crops. II. Wind pollination. Heredity 1, 235–246 (1947a).

    Article  Google Scholar 

  • - Contamination of seed crops. III. Relation with isolation distance. Heredity 1, 303–336 (1947b).

    Article  Google Scholar 

  • - Contamination of seed crops. I. Insect pollination. J. Genet. 48, 257–275 (1948).

    Google Scholar 

  • - Is gene dispersion normal? Heredity 4, 253–263 (1951).

    Google Scholar 

  • Blair, W. F.: The Rusty Lizard. Austin: University of Texas Press 1960.

    Google Scholar 

  • Brownlee, J.: The mathematical theory of random migration and epidemic distribution. Proc. Roy. Soc. Edinburgh 31, 262–289 (1911).

    MATH  Google Scholar 

  • Dobzhansky, Th., and S. Wright: Genetics of natural populations. X. Dispersion rates in Drosophila pseudoobscura. Genetics 28, 304–340 (1943).

    Google Scholar 

  • - - Genetics of natural populations. XV. Rate of diffusion of a mutant gene through a population of Drosophila pseudoobscura. Genetics 32, 303–339 (1947).

    Google Scholar 

  • Ehrman, L.: Mating success and genotype frequency in Drosophila. Anim. Behav. 14, 332–339 (1966).

    Article  Google Scholar 

  • Feller, W.: An introduction to probability theory and its applications. Vol. II. New York: John Wiley & Sons 1966.

    MATH  Google Scholar 

  • - An introduction to probability theory and its applications. Vol. I. 3 rd ed. New York: John Wiley & Sons 1968.

    Google Scholar 

  • Frampton, V. L., M. B. Linn, and E. D. Hansing: The spread of virus diseases of the yellows type under field conditions. Phytopathology 32, 799–808 (1942).

    Google Scholar 

  • Glasstone, S., and A. Sesonske: Nuclear reactor engineering. Princeton, N. J.: D. van Nostrand Co. 1963.

    Google Scholar 

  • Hamilton, T. H., and I. Rubinoff: Isolation, endemism, and multiplication of species in the Darwin finches. Evolution 17, 388–403 (1963).

    Article  Google Scholar 

  • Heed, W. B., J. S. Russell, and B. L.Ward: Host specificity of cactiphilic Drosophila in the Sonoran Desert. Drosophila Information Service 43, 94 (1968).

    Google Scholar 

  • Papoulis, A.: Probability, random variables, and stochastic processes. New York: McGraw Hill Co. 1965.

    MATH  Google Scholar 

  • Reimer, J. D., and M. L. Petras: Breeding structure of the house mouse, Mus musculus, in a population cage. J. Mammalogy 48, 88–99 (1967).

    Article  Google Scholar 

  • Richardson, R. H.: Migration, and enzyme polymorphism in natural populations of Drosophila. Jap. J. Genet. Suppl. 1, 172–179 (1969a).

    Google Scholar 

  • -, R. J. Wallace, Jr., S. J. Gage, G. D. Bouchey, and M. Denell: Neutron activation techniques for labeling Drosophila in natural populations. In: Studies in genetics. Ed. by M. R. Wheeler. Austin: University of Texas Press 1969b.

    Google Scholar 

  • Skellam, J. G.: Random dispersal in theoretical populations. Biometrika 38, 196–218 (1951).

    MATH  MathSciNet  Google Scholar 

  • Stern, V. M., and A. Mueller: Techniques of marking insects with micronized fluorescent dust with especial emphasis on marking millions of Lygus hesperus for dispersal studies. J. Econ. Ento. 61, 1232–1237 (1968).

    Google Scholar 

  • Timofeeff-Ressovsky, N. W., and E. A. Timofeeff-Ressovsky: Populationsgenetische Versuche an Drosophila Z. indukt. Abstamm.- u. Vererblehre 79, 28–49 (1940).

    Article  Google Scholar 

  • Wallace, B.: On the dispersal of Drosophila. Amer. Natur. 100, 551–563 (1966).

    Article  Google Scholar 

  • - Topics in population genetics. New York: W. W. Norton Co. 1968a.

    Google Scholar 

  • - On the dispersal of Drosophila. Amer. Natur. 102, 85–87 (1968b).

    Article  Google Scholar 

  • Wolfenbarger, D. O.: Dispersion of small organisms. Amer. Midland Natur. 35, 1–152 (1946).

    Article  Google Scholar 

  • Wright, S.: Evolution and the genetics of populations. Vol. I. Genetic and biometric foundations. Chicago: University of Chicago Press 1968a.

    Google Scholar 

  • - Dispersion of Drosophila pseudoobscura. Amer. Natur. 102, 81–84 (1968b).

    Article  Google Scholar 

  • - Evolution and the genetics of populations. Vol. II. The theory of gene frequencies. Chicago: University of Chicago Press 1969.

    Google Scholar 

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Authors

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Ken-ichi Kojima

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© 1970 Springer-Verlag Berlin · Heidelberg

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Richardson, R.H. (1970). Models and Analyses of Dispersal Patterns. 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_3

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  • DOI: https://doi.org/10.1007/978-3-642-46244-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-46246-7

  • Online ISBN: 978-3-642-46244-3

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