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Control of Competitive Bioinvasion

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Dispersal, Individual Movement and Spatial Ecology

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2071))

Abstract

The invasion of alien and displacement of indigenous species is a crucial ecological and economical problem of even increasing significance. Measures to control and perhaps to stop and reverse such invasive processes are urgently needed. Mathematical models are a suitable tool to preview the impact of control measures before utilizing them in nature. Here, a reaction-diffusion model is used to describe the competition and dispersal of invasive and native species. Not only the environment is changing but also growth, harvesting and dispersal of the two competitors vary in space and time. Extreme events such as fires or landslides or any other processes yielding bare re-invadable ground lead to temporary extinction of both species at a randomly chosen time and spatial range. The spatiotemporal dimension of these extreme fragmentation events, the ratio of the dispersal rates of the competing species as well as the selective removal of the invader turn out to be the crucial driving forces of the system dynamics. Finally, the controlling effect of a targeted infection of the invasive species with a specific pathogen is studied in an eco-epidemiological competition-diffusion model.

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References

  1. H.M. Alexander, R.D. Holt, The interaction between plant competition and disease. Perspect. Plant Ecol. Evol. Syst. 1/2, 206–220 (1998)

    Google Scholar 

  2. R.M. Anderson, R.M. May, The invasion, persistence and spread of infectious diseases within animal and plant communities. Phil. Trans. R. Soc. Lond. B 314, 533–570 (1986)

    Article  Google Scholar 

  3. W. Bruckart, C. Cavin, L. Vajna, I. Schwarczinger, F.J. Ryan, Differential susceptibility of Russian thistle accessions to Colletotrichum gloeosporioides. Biol. Contr. 30, 306–311 (2004)

    Google Scholar 

  4. J.B. Burie, A. Calonnec, M. Langlais, Modeling of the invasion of a fungal disease over a vineyard, in Mathematical Modeling of Biological Systems, vol. II, ed. by A. Deutsch, R.B. de la Parra, R.J. de Boer, O. Diekmann, P. Jagers, E. Kisdi, M. Kretzschmar, P. Lansky, H. Metz. Epidemiology, Evolution and Ecology, Immunology, Neural Systems and the Brain, and Innovative Mathematical Methods, Modeling and Simulation in Science, Engineering and Technology (Birkhäuser, Boston, 2008), pp. 11–21

    Google Scholar 

  5. J. Cardina, G.A. Johnson, D.H. Sparrow, The nature and consequence of weed spatial distribution. Weed Sci. 45, 364–373 (1997)

    Google Scholar 

  6. R. Cousens, C. Dytham, R. Law, Dispersal in plants. A population perspective, in Oxford Biology (Oxford University Press, Oxford, 2008)

    Google Scholar 

  7. O. Diekmann, J.A.P. Heesterbeck (eds.), Mathematical epidemiology of infectious diseases. Model building, analysis and interpretation, in Wiley Series in Mathematical and Computational Biology (Wiley, Chichester, 2000)

    Google Scholar 

  8. J.A. Drake, H.A. Mooney (eds.), Biological invasions: a global perspective, in SCOPE, vol. 27 (Wiley, Chichester, 1989)

    Google Scholar 

  9. W. Ebeling, L. Schimansky-Geier, Stochastic dynamics of a bistable reaction system. Phys. A 98, 587–600 (1979)

    Article  Google Scholar 

  10. W. Ebeling, C. Ivanov, L. Schimansky-Geier, Stochastic theory of nucleation in bistable reaction systems. Rostocker Phys. Manuskripte 2, 93–103 (1977)

    MathSciNet  Google Scholar 

  11. J. Frantzen, Disease epidemics and plant competition: control of Senecio vulgaris with Puccinia lagenophorae. Basic Appl. Ecol. 1, 141–148 (2000)

    Google Scholar 

  12. H.I. Freedman, A model of predator-prey dynamics as modified by the action of a parasite. Math. Biosci. 99, 143–155 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  13. J.S. Fulda, The logistic equation and population decline. J. Theor. Biol. 91, 255–259 (1981)

    Article  MathSciNet  Google Scholar 

  14. L.Q. Gao, H.W. Hethcote, Disease transmission models with density dependent demographics. J. Math. Biol. 30, 717–731 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  15. K.P. Hadeler, H.I. Freedman, Predator-prey populations with parasitic infection. J. Math. Biol. 27, 609–631 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  16. K. Harley, I.W. Forno, Biological Control of Weeds: A Handbook for Practitioners and Students (Inkata Press, Melbourne, 1992)

    Google Scholar 

  17. R. Hengeveld (ed.), Dynamics of Biological Invasions (Chapman and Hall, London, 1989)

    Google Scholar 

  18. F.M. Hilker, Spatiotemporal Patterns in Models of Biological Invasion and Epidemic Spread (Logos, Berlin, 2005)

    Google Scholar 

  19. F.M. Hilker, H. Malchow, Strange periodic attractors in a prey-predator system with infected prey. Math. Popul. Stud. 13(3), 119–134 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  20. M. Julien, G. White, Biological control of weeds: theory and practical application, in ACIAR Monograph Series, vol. 49 (Australian Centre for International Agricultural Research, Bruce ACT, 1997)

    Google Scholar 

  21. R.M. Keane, M.J. Crawley, Exotic plant invasions and the enemy release hypothesis. Trends Ecol. Evol. 17(4), 164–170 (2002)

    Article  Google Scholar 

  22. B.W. Kooi, M.P. Boer, S.A.L.M. Kooijman, On the use of the logistic equation in models of food chains. Bull. Math. Biol. 60, 231–246 (1998)

    Article  MATH  Google Scholar 

  23. E. Kuno, Some strange properties of the logistic equation defined with r and K: inherent effects or artefacts? Res. Popul. Ecol. 33, 33–39 (1991)

    Article  Google Scholar 

  24. H. Malchow, L. Schimansky-Geier, Noise and diffusion in bistable nonequilibrium systems, in Teubner-Texte zur Physik, vol. 5 (Teubner, Leipzig, 1985)

    Google Scholar 

  25. H. Malchow, B. Radtke, M. Kallache, A.B. Medvinsky, D.A. Tikhonov, S.V. Petrovskii, Spatio-temporal pattern formation in coupled models of plankton dynamics and fish school motion. Nonlinear Anal. Real World Appl. 1, 53–67 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  26. H. Malchow, S.V. Petrovskii, E. Venturino, Spatiotemporal patterns in ecology and epidemiology: theory, models, simulations, in CRC Mathematical and Computational Biology Series (CRC Press, Boca Raton, 2008)

    Google Scholar 

  27. H. Malchow, A. James, R. Brown, Competitive and diffusive invasion in a noisy environment. Math. Med. Biol. 28, 153–163 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. M. Matsumoto, T. Nishimura, Mersenne Twister: a 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)

    Article  MATH  Google Scholar 

  29. H. McCallum, N. Barlow, J. Hone, How should pathogen transmission be modelled? Trends Ecol. Evol. 16(6), 295–300 (2001)

    Article  Google Scholar 

  30. P.B. McEvoy, E.M. Coombs, Biological control of plant invaders: regional patterns, field experiments, and structured population models. Ecol. Appl. 9(2), 387–401 (1999)

    Article  Google Scholar 

  31. D. Mollison, Modelling biological invasions: chance, explanation, prediction. Phil. Trans. R. Soc. Lond. B 314, 675–693 (1986)

    Article  Google Scholar 

  32. D. Mollison (ed.), Epidemic models. Their structure and relation to data, in Publications of the Newton Institute, vol. 5 (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

  33. R. Nathan, F.M. Schurr, O. Spiegel, O. Steinitz, A. Trakhtenbrot, A. Tsoar, Mechanisms of long-distance seed dispersal. Trends Ecol. Evol. 23, 638–647 (2008)

    Article  Google Scholar 

  34. A. Nitzan, P. Ortoleva, J. Ross, Nucleation in systems with multiple stationary states. Faraday Symp. Chem. Soc. 9, 241–253 (1974)

    Article  Google Scholar 

  35. S.V. Petrovskii, B.L. Li, Exactly solvable models of biological invasion, in CRC Mathematical Biology and Medicine Series (CRC Press, Boca Raton, 2006)

    Google Scholar 

  36. D. Pimentel (ed.), Biological invasions, in Economic and Environmental Costs of Alien Plant, Animal, and Microbe Species (CRC Press, Boca Raton, 2002)

    Google Scholar 

  37. E.N. Rosskopf, R. Charudattan, J.B. Kadir, Use of plant pathogens in weed control, in Handbook of Biological Control. Principles and Applications of Biological Control, ed. by T.S. Bellows, T.W. Fisher, L.E. Caltagirone, D.L. Dahlsten, G. Gordh, C.B. Huffaker (Academic, San Diego, 1999), pp. 891–918

    Google Scholar 

  38. L. Sattenspiel, The geographic spread of infectious diseases, in Princeton Series in Theoretical and Computational Biology (Princeton University Press, Princeton, 2009)

    Google Scholar 

  39. D.F. Sax, J.J. Stachowicz, S.D. Gaines (eds.), Species invasions, in Insights into Ecology, Evolution, and Biogeography (Sinauer, Sunderland, 2005)

    Google Scholar 

  40. J. Segarra, M.J. Jeger, F. van den Bosch, Epidemic dynamics and patterns of plant diseases. Phytopathology 91(10), 1001–1010 (2001)

    Article  Google Scholar 

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

    Google Scholar 

  42. N. Shigesada, K. Kawasaki, Y. Takeda, Modeling stratified diffusion in biological invasions. Am. Nat. 146(2), 229–251 (1995)

    Article  Google Scholar 

  43. I. Siekmann, Mathematical Modelling of Pathogen-Prey-Predator Interactions (Verlag Dr. Hut, München, 2009)

    Google Scholar 

  44. J. Suszkiw, Fungus unleashed to combat yellow starthistle. Agric. Res. Mag. 52(8), 20–22 (2004)

    Google Scholar 

  45. P. van den Driessche, M.L. Zeeman, Disease induced sscillations between two competing species. SIAM J. Appl. Dynam. Syst. 3(4), 601–619 (2004)

    Article  MATH  Google Scholar 

  46. J.E. van der Plank, Host-pathogen interactions in plant disease (Academic, New York, 1982)

    Google Scholar 

  47. E. Venturino, The influence of diseases on Lotka-Volterra systems. Rocky Mt. J. Math. 24, 381–402 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  48. E. Venturino, The effect of diseases on competing species. Math. Biosci. 174, 111–131 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  49. L.J. Wiles, G.W. Oliver, A.C. York, H.C. Gold, G.G. Wilkerson, Spatial distribution of broadleaf weeds in North Carolina soybean (Glycine max) field. Weed Sci. 40, 554–557 (1992)

    Google Scholar 

  50. M. Williamson, Biological invasions, in Population and Community Biology Series, vol. 15 (Chapman & Hall, London, 1996)

    Google Scholar 

  51. C.L. Wilson, Use of plant pathogens in weed control. Annu. Rev. Phytopathol. 7(1), 411–434 (1969)

    Article  Google Scholar 

  52. L.M. Wilson, C. Jette, J. Connett, J.P. McCaffrey, Biology and biological control of yellow starthistle, in FHTET Technology Transfer Series 17-1998 (Forest Health Technology Enterprise Team, Morgantown WV, 2003)

    Google Scholar 

  53. D.M. Woods, W.L. Bruckart III, M. Pitcairn, V. Popescu, J. O’Brien, Susceptibility of yellow starthistle to Puccinia jaceae var. solstitialis and greenhouse production of inoculum for classical biological control programs. Biol. Contr. 50, 275–280 (2009)

    Google Scholar 

  54. M. Yokozawa, Y. Kubota, T. Hara, Effects of competition mode on spatial pattern dynamics in plant communities. Ecol. Model. 106, 1–16 (1998)

    Article  Google Scholar 

  55. R.L. Zimdahl, Weed-Crop Competition. A review (Blackwell Publishing, Oxford, 2004)

    Google Scholar 

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Acknowledgements

H.M. would like to dedicate this paper to his academic teacher and friend Werner Ebeling (Berlin) on occasion of his 75th birthday on 15 September 2011. Furthermore, he is thankful to the Erskine Foundation at the University of Canterbury at Christchurch, New Zealand, for a Visiting Erskine Fellowship.

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Authors and Affiliations

  1. Institute of Environmental Systems Research, University of Osnabrück Barbarastr. 12, 49076, Osnabrück, Germany

    Horst Malchow

  2. Department of Mathematics and Statistics, University of Canterbury, 4800, Christchurch, New Zealand

    Alex James & Richard Brown

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  1. Horst Malchow
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  2. Alex James
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Correspondence to Horst Malchow .

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Editors and Affiliations

  1. Mathematical & Statistical Sciences, University of Alberta, Central Academic Building 632, Edmonton, T6G 2G1, Alberta, Canada

    Mark A. Lewis

  2. Mathematical Institute, Centre for Mathematical Biology, University of Oxford, St. Giles Street 24-29, Oxford, OX1 3LB, United Kingdom

    Philip K. Maini

  3. Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

    Sergei V. Petrovskii

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Malchow, H., James, A., Brown, R. (2013). Control of Competitive Bioinvasion. In: Lewis, M., Maini, P., Petrovskii, S. (eds) Dispersal, Individual Movement and Spatial Ecology. Lecture Notes in Mathematics(), vol 2071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35497-7_10

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