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A branching-process model for the evolution of transposable elements incorporating selection

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Abstract

We have formulated a very general mathematical model to analyze the evolution of transposable genetic elements in prokaryotic populations. Transposable genetic elements are DNA sequences able to replicate and insert copies of themselves at new locations in the genome. This work characterizes the equilibrium distribution of copy number under the influence of copy number-dependent selection, transposition and deletion. Our principal results concern the equilibrium distribution of copy number in response to various selective regimes. For particular transposition patterns (e.g. unregulated transposition or copy number-dependent transposition), equilibrium distributions are calculated numerically for a variety of specific selection patterns. Selection is quantified through specification of the expected number of offspring for individuals of each type, which is generally a non-increasing function of copy number, in accord with the usual evolutionary speculations.

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References

  1. Asmussen, S., Hering, H.: Branching Processes. Boston Basel Stuttgart: Birkhäuser 1983

    Google Scholar 

  2. Athreya, K. B., Ney, P. E.: Branching Processes. Berlin Heidelberg New York: Springer 1972

    Google Scholar 

  3. Brookfield, J. F. Y.: Interspersed repetitive DNA sequences are unlikely to be parasitic. J. Theor. Biol. 92, 281–299 (1982)

    Google Scholar 

  4. Brookfield, J. F. Y.: A model for DNA sequence evolution within transposable element families. Genetics 112, 396–407 (1986)

    Google Scholar 

  5. Campbell, A.: Some general questions about movable elements and their implications. Cold Spring Harbor Symp. Quant. Biol. 45, 1–10 (1981)

    Google Scholar 

  6. Campbell, A.: Transposons and their evolutionary significance. In: Nei, M., Koehn, R. K. (eds.) Evolution of Genes and Proteins, pp. 258–279. Sunderland, MA: Sinauer Associates, Inc. 1983

    Google Scholar 

  7. Cavalier-Smith, T.: How selfish is DNA? Nature 285, 617–618 (1980)

    Google Scholar 

  8. Chao, L., McBroom, S. M.: Evolution of transposable elements: An IS10 insertion increases fitness in Escherichia coli. Mol. Biol. Evol. 2, 359–369 (1985)

    Google Scholar 

  9. Chao, L., Vargas, C., Spear, B. B., Cox, E. C.: Transposable elements as mutator genes in evolution. Nature 303, 633–635 (1983)

    Google Scholar 

  10. Charlesworth, B.: Genetic divergence between transposable elements. Genet. Res. 48, 111–118 (1986)

    Google Scholar 

  11. Charlesworth, B., Charlesworth, D.: The population dynamics of transposable elements. Genet. Res. 42, 1–27 (1983)

    Google Scholar 

  12. Charlesworth, B., Langley, C. H.: The evolution of self-regulated transposition of transposable elements. Genetics 112, 359–383 (1986)

    Google Scholar 

  13. Condit, R.: The evolution of transposable elements: conditions for establishment in bacterial populations. Evolution 44, 347–359 (1990)

    Google Scholar 

  14. Condit, R., Stewart, F. M., Levin, B. R.: The population biology of bacterial transposons: a priori conditions for maintenance as parasitic DNA. Am. Nat. 132, 129–147 (1988)

    Google Scholar 

  15. Cox, E. C.: Bacterial mutator genes and control of spontaneous mutation. Annu. Rev. Genet. 10, 135–156 (1976)

    Google Scholar 

  16. Davidson, E. H., Britten, R. J.: Regulation of gene expression: possible role of repetitive sequences. Science 204, 1052–1059 (1979)

    Google Scholar 

  17. Doolittle, W. F., Sapienza, C.: Selfish genes, the phenotype paradigm and genome evolution. Nature 284, 601–604 (1980)

    Google Scholar 

  18. Dover, G.: Ignorant DNA? Nature 285, 618–620 (1980)

    Google Scholar 

  19. Dover, G., Doolittle, W. F.: Modes of genome evolution. Nature 288, 646–647 (1980)

    Google Scholar 

  20. Engels, W. R.: Hybrid dysgenesis in Drosophila, and the stochastic loss hypothesis. Cold Spring Harbor Symp. Quant. Biol. 45, 561–566 (1981)

    Google Scholar 

  21. Ginzburg, L. R., Bingham, P. M., Yoo, S.: On the theory of speciation induced by transposable elements. Genetics 107, 331–341 (1984)

    Google Scholar 

  22. Harris, T. E.: The Theory of Branching Processes. Berlin Heidelberg New York: Springer 1963

    Google Scholar 

  23. Hartl, D. L., Dykhuizen, D. E., Miller, R. D., Green, L., de Framond, J.: Transposable element IS50 improves growth rate of E. coli cells without transposition. Cell 35, 503–510 (1983)

    Google Scholar 

  24. Hartl, D. L., Sawyer, S. A.: Why do unrelated insertion sequences occur together in the genome of Escherichia coli? Genetica 118, 537–541 (1988)

    Google Scholar 

  25. Hickey, D. A.: Selfish DNA: A sexually transmitted nuclear parasite. Genetics 101, 519–531(1982)

    Google Scholar 

  26. Hudson, R. R., Kaplan, N. L.: On the divergence of members of a transposable element family. J. Math. Biol. 24, 207–215 (1986)

    Google Scholar 

  27. Jagers, P.: Branching Processes with Biological Applications. Chichester London New York Sydney Toronto: Wiley 1975

    Google Scholar 

  28. Jain, H. K.: Incidental DNA. Nature 288, 647–648 (1980)

    Google Scholar 

  29. Joffe, A., Ney, P.: Branching Processes. New York: Dekker 1978

    Google Scholar 

  30. Johnson, R. C., Reznikoff, W. S.: Copy number control of TN5 transposition. Genetics 107, 9–18 (1984)

    Google Scholar 

  31. Kaplan, N., Darden, T., Langley, C. H.: Evolution and extinction of transposable elements in Mendelian populations. Genetics 109, 459–480 (1985)

    Google Scholar 

  32. Kaplan, N. L., Brookfield, J. F. Y.: The effect of homozygosity of selective differences between sites of transposable elements. Theor. Popul. Biol. 23, 273–280 (1983)

    Google Scholar 

  33. Kleckner, N.: Transposable elements in prokaryotes. Annu. Rev. Genet. 15, 341–404 (1981)

    Google Scholar 

  34. Langley, C. H., Brookfield, J. F. Y., Kaplan, N.: Transposable elements in Mendelian populations. I. A Theory. Genetics 104, 457–471 (1983)

    Google Scholar 

  35. Langley, C. H., Montgomery, E., Hudson, R., Kaplan, N., Charlesworth, B.: On the role of unequal exchange in the containment of transposable element copy number. Genet. Res. 52, 223–236 (1988)

    Google Scholar 

  36. Mode, C. J.: Multitype Branching Processes. New York: American Elsevier 1971

    Google Scholar 

  37. Moody, M. E.: A branching process model for the evolution of transposable elements. J. Math. Biol. 26, 347–357 (1988)

    Google Scholar 

  38. Nanjundiah, V.: Transposable element copy number and stable polymorphisms. J. Genet. 64, 127–134 (1985)

    Google Scholar 

  39. Ohta, T.: A model of duplicative transposition and gene conversion for repetitive DNA families. Genetics 110, 513–524 (1985)

    Google Scholar 

  40. Ohta, T.: Population genetics of an expanding family of mobile genetic elements. Genetics 113, 145–159 (1986)

    Google Scholar 

  41. Ohta, T.: Population genetics of selfish DNA. Nature 292, 648–649 (1981)

    Google Scholar 

  42. Ohta, T.: Population genetics of transposable elements. IMA J. Math. Appl. Med. Biol. 1, 17–29 (1984)

    Google Scholar 

  43. Ohta, T.: Theoretical study on the accumulation of selfish DNA. Genet. Res. 41, 1–15 (1983)

    Google Scholar 

  44. Ohta, T., Kimura, M.: Some calculations on the amount of selfish DNA. Proc. Natl. Acad. Sci. USA 78, 1129–1132 (1981)

    Google Scholar 

  45. Orgel, L. E., Crick, F. H.: Selfish DNA: the ultimate parasite. Nature 284, 604–607 (1980)

    Google Scholar 

  46. Orgel, L. E., Crick, F. H., Sapienza, C.: Selfish DNA. Nature 288, 645–646 (1980)

    Google Scholar 

  47. Reid, R. A.: Selfish DNA in “Petite” mutants. Nature 285, 620 (1980)

    Google Scholar 

  48. Rose, M. R.: The contagion mechanism for the origin of sex. J. Theor. Biol. 101, 137–146 (1983)

    Google Scholar 

  49. Rose, M. R., Doolittle, W. F.: Molecular biological mechanisms of speciation. Science 220, 157–161 (1983)

    Google Scholar 

  50. Rubin, G. M., Kidwell, M. G., Bingham, P. M.: The molecular basis of P-M hybrid dysgenesis: The nature of induced mutations. Cell 29, 987–994 (1982)

    Google Scholar 

  51. Sapienza, C., Doolittle, W. F.: Genes are things you have whether you want them or not. Cold Spring Harbor Symp. Quant. Biol. 45, 177–182 (1981)

    Google Scholar 

  52. Sawyer, S., Hartl, D.: Distribution of transposable elements in prokaryotes. Theor. Popul. Biol. 30, 1–16 (1986)

    Google Scholar 

  53. Sevast'yanov, B. A.: Vetvyaščiesya Processy. Moscow: Mir 1971

    Google Scholar 

  54. Shapiro, J. A.: Mobile Genetic Elements. New York: Academic Press 1983

    Google Scholar 

  55. Slatkin, M.: Genetic differentiation of transposable elements under mutation and unbiased gene conversion. Genetics 110, 145–158 (1985)

    Google Scholar 

  56. Smith, T. F.: Occam's razor. Nature 285, 620 (1980)

    Google Scholar 

  57. Stanley, S. M.: A theory of evolution above the species level. Proc. Natl. Acad. Sci. USA 72, 646–650 (1975)

    Google Scholar 

  58. Syvanen, M.: The evolutionary implications of mobile genetic elements. Annu. Rev. Genet. 18, 271–293 (1984)

    Google Scholar 

  59. Uyenoyama, M. K.: Quantitative models of hybrid dysgenesis: Rapid evolution under transposition, extrachromosomal inheritance, and fertility selection. Theor. Popul. Biol. 27, 176–201 (1985)

    Google Scholar 

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  1. Christopher J. Basten

    Present address: National Institute of Genetics, Yata 1-111, 411, Mishima-shi, Shizuoka-ken, Japan

Authors and Affiliations

  1. Program in Genetics and Cell Biology, Washington State University, 99164-4234, Pullman, WA, USA

    Christopher J. Basten

  2. Department of Pure and Applied Mathematics and Program in Genetics and Cell Biology, Washington State University, 99164-4234, Pullman, WA, USA

    Michael E. Moody

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  1. Christopher J. Basten
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  2. Michael E. Moody
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Basten, C.J., Moody, M.E. A branching-process model for the evolution of transposable elements incorporating selection. J. Math. Biol. 29, 743–761 (1991). https://doi.org/10.1007/BF00160190

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  • DOI: https://doi.org/10.1007/BF00160190

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