Skip to main content
SpringerLink
Log in

Introduction

  • Chapter
  • First Online:
The Mathematics Behind Biological Invasions

Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 44))

  • 2018 Accesses

Abstract

We review several notorious cases of biological invasion, starting from a few historical cases and then proceeding to recent and ongoing ones. In doing so, we show that biological invasions often have numerous adverse impacts on ecology, agriculture, human well-being, and society, and hence is a phenomenon of high practical importance. Also, by observing similarity between cases of apparently different origins, we reveal some typical, generic properties of biological invasion. We then raise questions about the invasion dynamics that need to be answered and that will eventually be answered throughout this book.

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 EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 89.99
Price excludes VAT (USA)
  • Durable hardcover 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

Notes

  1. 1.

    Personal communication to one of the authors (S.P.) by Prof. M.E. Vinogradov, the head of the biology department in the Shirshov Institute of Oceanology, Moscow.

References

  1. Andow, D.A., Kareiva, P.M., Levin, S.A., Okubo, A.: Spread of invading organisms. Landsc. Ecol. 4(2–3), 177–188 (1990). doi:10.1007/ bf00132860

    Article  Google Scholar 

  2. Aronson, D.G., Weinberger, H.F.: Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. In: Goldstein, J.A. (ed.) Partial Differential Equations and Related Topics, pp. 5–49. Springer, New York (1975)

    Chapter  Google Scholar 

  3. Atkinson, I.A.E.: The spread of commensal species of Rattus to oceanic islands and their effect on island aviafaunas. In: Moors, P.J. (ed.) Conservation of Island Birds, vol. 3, pp. 35–81. ICBP, Cambridge (1985)

    Google Scholar 

  4. Barenblatt, G.I., Vinogradov, M.E., Gorbunov, A.Y., Petrovskii, S.V.: On the mathematical simulation of impact waves in complex ecological systems. Okeanologiya 33, 5–12 (1993)

    Google Scholar 

  5. Bell, B.D.: The Big South Cape Island rat irruption. In: Dingwall, P.R., Atkinson, I.A.E., Hay, C. (eds.) The Ecology and Control of Rodents in New Zealand Nature Reserves. Information Series, vol. 4, pp. 33–46. Department of Land and Surveys, Wellington (1978)

    Google Scholar 

  6. Bell, S.S., White, A., Sherratt, J.A., Boots, M.: Invading with biological weapons: the role of shared disease in ecological invasion. Theor. Ecol. 2, 53–66 (2009). doi:10.1007/s12080-008-0029-x

    Article  Google Scholar 

  7. Carlton, J.T., Geller, J.B.: Ecological roulette: the global transport of nonindigenous marine organisms. Science 261, 78–82 (1993)

    Article  Google Scholar 

  8. Case, T.J., Bolger, D.T.: The role of introduced species in shaping the distribution and abundance of island reptiles. Evol. Ecol. 5, 272–290 (1991). doi:10.1007/bf02214232

    Article  Google Scholar 

  9. Case, T.J., Bolger, D.T., Richman, A.D.: Reptilian extinctions: the last ten thousand years. In: Fielder, P.L., Subodh, K.J. (eds.) Conservation Biology: The Theory and Practice of Nature Conservation, Preservation and Management, pp. 91–125. Chapman and Hall, London (1992)

    Chapter  Google Scholar 

  10. Chapuis, J.L.: Alien mammals in the French Subantarctic Islands. In: Dingwall, P.R. (ed.) Progress in Conservation of the Subantarctic Islands. Conservation of the Southern Polar Region, vol. 2, pp. 127–132. IUCN, Paimpont (1995)

    Google Scholar 

  11. Child, L.E., Wade, M.: The Japanese Knotweed Manual. Packard, Chichester (2000)

    Google Scholar 

  12. Courchamp, F., Langlais, M., Sugihara, G.: Cats protecting birds: modelling the mesopredator release effect. J. Anim. Ecol. 68, 282–292 (1999)

    Article  Google Scholar 

  13. Courchamp, F., Langlais, M., Sugihara, G.: Control of rabbits to protect island birds from cat predation. Biol. Conserv. 89, 219–225 (1999). doi:10.1016/s0006-3207(98)00131-1

    Article  Google Scholar 

  14. Davis, H.G., Taylor, C.M., Civille, J.C., Strong, D.R.: An Allee effect at the front of a plant invasion: spartina in a Pacific estuary. J. Ecol. 92, 321–327 (2004)

    Article  Google Scholar 

  15. Diamond, J.: Overview of recent extinctions. In: Western, D., Pearl, M.C. (eds.) Conservation for the Twenty-First Century, pp. 37–41. Oxford University Press, Oxford (1989)

    Google Scholar 

  16. Drake, J.A., Mooney, H.A., di Castri, F., Groves, R.H., Kruger, F.J.: Biological Invasions: A Global Perspective. Wiley, Chichester (1989)

    Google Scholar 

  17. Editorial: Japanese beetle ravages. Reading Eagle (July 22), 26 (1923)

    Google Scholar 

  18. Elton, C.S.: The Ecology of Invasions by Animals and Plants. Methuen, London (1958)

    Book  Google Scholar 

  19. Fisher, R.A.: The wave of advance of advantageous genes. Ann. Eugen. 7, 355–369 (1937)

    Article  MATH  Google Scholar 

  20. Hengeveld, R.: Dynamics of Biological Invasions. Chapman and Hall, London (1989)

    Google Scholar 

  21. Johnson, D.M., Liebhold, A.M., Tobin, P.C., Bjørnstad, O.N.: Allee effects and pulsed invasion by the gypsy moth. Nature 444(7117), 361–363 (2006). doi:10.1038/nature05242

    Article  Google Scholar 

  22. Keller, R.P., Lodge, D.M., Lewis, M.A., Shogren, J.F.: Bioeconomics of Invasive Species: Integrating Ecology, Economics, Policy, and Management. Oxford University Press, Oxford (2009)

    Google Scholar 

  23. Keondzhan, V.P., Kudin, A.M., Terekhin, Y.V. (eds.): Applied Ecology of Sea Regions: The Black Sea. Naukova Dumka, Kiev (1990)

    Google Scholar 

  24. Kideys, A.E.: Fall and rise of the Black Sea ecosystem. Science 297, 1482–1484 (2002). doi:10.1126/science.1073002

    Article  Google Scholar 

  25. Kolmogorov, A.N., Petrovskii, I.G., Piskunov, N.S.: A study of the diffusion equation with increase in the quantity of matter, and its application to a biological problem. Bull. Moscow Univ. Math. Ser. A 1, 1–25 (1937)

    Google Scholar 

  26. Kurose, D., Renals, T., Shaw, R., Furuya, N., Takagi, M., Evans, H.: Fallopia japonica, an increasingly intractable weed problem in the UK: can fungi help cut through this gordian knot? Mycologist 20(4), 126–129 (2006). doi:10.1016/j.mycol.2006.07.021

    Article  Google Scholar 

  27. Liebhold, A.M., Halverson, J.A., Elmes, G.A.: Gypsy moth invasion in North America: a quantitative analysis. J. Biogeogr. 19, 513–520 (1992). doi:10.2307/2845770

    Article  Google Scholar 

  28. Middleton, A.D.: The ecology of the American gray squirrel (Sciurus carolinensis Gmelin) in the British Isles. Proc. Zool. Soc. Lond. 3, 809–843 (1930)

    Google Scholar 

  29. Mohr, E., Hollister, M.P.: The muskrat, Ondatra zibethica (Linnaeus), in Europe. J. Mammal. 14(1), 58–63 (1933). doi:10.2307/1374037

    Article  Google Scholar 

  30. Mooney, H.A., Drake, J.A.: Ecology of Biological Invasions of North America and Hawaii. Springer, New York (1986)

    Book  Google Scholar 

  31. Moors, P.J., Atkinson, I.A.E.: Predation on seabirds by introduced animals, and factors affecting its severity. In: Croxall, J.P., Evans, P.G.H., Schreiber, R.W. (eds.) Status and Conservation of the World’s Seabirds, vol. 2, pp. 667–690. ICBP, Cambridge (1984)

    Google Scholar 

  32. Mutlu, E.: Distribution and abundance of ctenophores and their zooplankton food in the Black Sea. II. Mnemiopsis leidyi. Mar. Biol. 135, 603–613 (1999). doi:10.1007/s002270050661

    Google Scholar 

  33. Okubo, A.: Diffusion and Ecological Problems: Mathematical Models. Springer, Berlin (1980)

    MATH  Google Scholar 

  34. Okubo, A., Maini, P.K., Williamson, M.H., Murray, J.D.: On the spatial spread of the grey squirrel in Britain. Proc. R. Soc. B 238, 113–125 (1989). doi:10.1098/rspb.1989.0070

    Article  Google Scholar 

  35. Oliveira, O.M.P.: The presence of the ctenophore Mnemiopsis leidyi in the Oslofjorden and considerations on the initial invasion pathways to the North and Baltic Seas. Aquat. Invasions 2(3), 185–189 (2007). doi:10.3391/ai.2007.2.3.5

    Article  Google Scholar 

  36. Parker, I.M.: Mating patterns and rates of biological invasion. Proc. Natl. Acad. Sci. U. S. A. 101, 13,695–13,696 (2004)

    Google Scholar 

  37. Perrings, C., Williamson, M., Dalmazzone, S.: The Economics of Biological Invasions. Edward Elgar, Cheltenham (2000)

    Book  Google Scholar 

  38. Petrovskii, S., Shigesada, N.: Some exact solutions of a generalized Fisher equation related to the problem of biological invasion. Math. Biosci. 172, 73–94 (2001). doi:10.1016/s0025-5564(01)00068-2

    Article  MathSciNet  MATH  Google Scholar 

  39. Petrovskii, S.V., Li, B.L.: Exactly Solvable Models of Biological Invasion. Chapman & Hall/CRC, Boca Raton (2006)

    MATH  Google Scholar 

  40. Pimentel, D. (ed.): Biological Invasions: Economic and Environmental Costs of Alien Plant, Animal, and Microbe Species. CRC Press, Boca Raton (2002)

    Google Scholar 

  41. Richardson, D.M. (ed.): Fifty Years of Invasion Ecology: The Legacy of Charles Elton. Wiley, Chichester (2011)

    Google Scholar 

  42. Richardson, D.M., Pysek, P.: Fifty years of invasion ecology: the legacy of Charles Elton. Divers. Distrib. 14(2), 161–168 (2008)

    Article  Google Scholar 

  43. Russell, J.C., Towns, D.R., Clout, M.N.: Review of Rat Invasion Biology: Implications for Island Biosecurity. New Zealand Department of Conservation, Wellington (2008)

    Google Scholar 

  44. Sandlund, O.T., Schei, P.J., Viken, A.: Invasive Species and Biodiversity Management. Kluwer Academic, Dordrecht (2001)

    Google Scholar 

  45. Seebens, H., Gastner, M.T., Blasius, B.: The risk of marine bioinvasion caused by global shipping. Ecol. Lett. 16, 782–790 (2013). doi:10.1111/ ele.12111

    Article  Google Scholar 

  46. Sharov, A.A., Liebhold, A.M.: Model of slowing the spread of gypsy moth (Lepidoptera: Lymantriidae) with a barrier zone. Ecol. Appl. 8(4), 1170–1179 (1998). doi:10.2307/2640970

    Article  Google Scholar 

  47. Shiganova, T.A., Mirzoyan, Z.A., Studenikina, E.A., Volovik, S.P., Siokou-Frangou, I., Zervoudaki, S., Christou, E.D., Skirta, A.Y., Dumont, H.J.: Population development of the invader ctenophore Mnemiopsis leidyi, in the Black Sea and in other seas of the Mediterranean basin. Mar. Biol. 139, 431–445 (2001). doi:10.1007/ s002270100554

    Article  Google Scholar 

  48. Shigesada, N., Kawasaki, K.: Biological Invasions: Theory and Practice. Oxford University Press, Oxford (1997)

    Google Scholar 

  49. Shorten, M.: Squirrels in England, Wales and Scotland, 1955. J. Anim. Ecol. 26(2), 287–294 (1957). doi:10.2307/1748

    Article  Google Scholar 

  50. Skellam, J.G.: Random dispersal in theoretical populations. Biometrika 38(1–2), 196–218 (1951). doi:10.2307/2332328

    Article  MathSciNet  MATH  Google Scholar 

  51. Storer, T.I.: The muskrat as native and alien. J. Mammal. 18(4), 443–460 (1937). doi:10.2307/1374334

    Article  Google Scholar 

  52. Taylor, C.M., Hastings, A.: Finding optimal control strategies for invasive species: a density-structured model for Spartina alterniflora. J. Appl. Ecol. 41, 1049–1057 (2004)

    Google Scholar 

  53. Tompkins, D.M., White, A.R., Boots, M.: Ecological replacement of native red squirrels by invasive greys driven by disease. Ecol. Lett. 6, 189–196 (2003). doi:10.1046/j.1461-0248.2003.00417.x

    Article  Google Scholar 

  54. United States Bureau of Entomology and Plant Quarantine: Japanese beetle. In: Insect Pest Surv. Bull., vol. 21, pp. 801–802 (1941)

    Google Scholar 

  55. Vinogradov, M.E., Shushkina, E.A., Musayeva, E.I., Sorokin, P.Y.: A newly acclimated species in the Black Sea: the ctenophore Mnemiopsis leidyi (Ctenophora: Lobata). Okeanologiya 29(2), 220–224 (1989)

    Google Scholar 

  56. Williamson, M.: Biological Invasions. Chapman & Hall, London (1996)

    Google Scholar 

  57. Williamson, M.H., Brown, K.C.: The analysis and modelling of British invasions. Philos. Trans. R. Soc. Lond. B 314, 505–522 (1986)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics & Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada

    Mark A. Lewis

  2. Department of Mathematics, University of Leicester, Leicester, UK

    Sergei V. Petrovskii

  3. School of Mathematics & Statistics, University of Sheffield, Sheffield, UK

    Jonathan R. Potts

Authors
  1. Mark A. Lewis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergei V. Petrovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jonathan R. Potts
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Lewis, M.A., Petrovskii, S.V., Potts, J.R. (2016). Introduction. In: The Mathematics Behind Biological Invasions. Interdisciplinary Applied Mathematics, vol 44. Springer, Cham. https://doi.org/10.1007/978-3-319-32043-4_1

Download citation

Publish with us

Policies and ethics

Search

Navigation