Skip to main content

Advertisement

Log in

Ecological conditions that favor the evolution of intermediate-virulence in an environmentally transmitted parasite

Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

In this paper we develop and analyze several populaion-dynamic models of an environmentally transmitted symbiotic parasite infecting an isolated population of susceptible hosts. In our most basic model infection acts only to decrease the average lifetime of the infected host, parasites are only transmitted to uninfected hosts, there is no recovery from infection, and the rate of parasite transmission is an increasing function of the level of parasite virulence. It is shown that invasion of the parasite-free equilibrium cannot occur for virulence levels that are either too high or too low. We then incorporate a number of modifications to the model, among them the possibility that host fertility is reduced by infection, and that transmission rate depends additionally on susceptible host density. It is shown that the essential nature of the conditions for invasion are preserved. Thus, natural selection for intermediate virulence is a generic property of a broad class of population models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anderson, R.M., May, R.M.: Population biology of infectious diseases I. Nature 280, 361–367 (1979)

    Article  PubMed  Google Scholar 

  2. Anderson, R.M., May, R.M.: The population biology of microparasites and their invertebrate hosts. Phil. Trans. R. Soc. London B291, 451–524 (1981)

    Google Scholar 

  3. Anderson, R.M., May, R.M.: Coevolution of hosts and parasites. Parasitology 85, 411–426 (1982)

    PubMed  Google Scholar 

  4. Bary, A. de: Comparative Morphology and Biology of the Fungi, Mycetozoa and Bacteria. Clarendon Press, Oxford, 1887

  5. Boucher, D.H., James, S., Keller, K.H.: The Ecology of Mutualism. A. Rev. Ecol. Syst. 13, 315–347 (1982)

    Article  Google Scholar 

  6. Crawford, J.D.: Introduction to bifurcation theory. Rev. Mod. Phys. 63, 991–1037 (1991)

    Article  Google Scholar 

  7. Clayton, D.H., Tompkins, D.M.: Comparative effects of mites and lice on the reproductive success of rock doves (Columba livia). Parasitology 110, 195–206 (1994)

    Google Scholar 

  8. Diekmann, O., Heesterbeek, J.A.P., Metz, J.A.J.: On the definition and the computation of the basic reproductive ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990)

    Article  PubMed  MathSciNet  Google Scholar 

  9. Dietz, K.: Transmission and control of arbovirus diseases. In: Ludwig, D., Cooke, K.L. (eds.), Epidemiology (Society for Industrial and Applied Mathematics, Philadelphia 1974) pp. 104–121

  10. Dodds, W.K.: Interspecific interactions: Constructing a general neutral model for interaction type. Oikos 78, 377–383 (1997)

    Google Scholar 

  11. Douglas, A.E.: Symbiotic Interactions. Oxford University Press, Oxford, U.K., 1994

  12. Ebert, D., Weisser, W.W.: Optimal killing for obligate killers: the evolution of life histories and virulence of semeloparous parasites. Proc. R. Soc. London B264, 985–991 (1997)

    Google Scholar 

  13. Ewald, P.W.: Host-parasite relations, vectors, and the evolution of disease severity. A. Rev. Ecol. Syst. 14, 465–485 (1983)

    Article  Google Scholar 

  14. Ewald, P.W.: Transmission modes and evolution of the parasitism-mutualism continuum. Ann. N.Y. Acad. Sci. 503, 295–306 (1987)

    PubMed  Google Scholar 

  15. Fisher, R.A.: The Genetical Theory of Natural Selection, 2nd ed. Dover, New York, 1958

  16. Frank, S.A.: Models of parasite virulence. Q. Rev. Biol. 71, 37–78 (1996)

    Article  PubMed  Google Scholar 

  17. Genkai-Kato, M., Yamamura, N.: Evolution of Mutualistic Symbiosis without Vertical Transmission. Theor. Pop. Biol. 55, 309–323 (1999)

    Article  Google Scholar 

  18. Hastings, A., Godfrey, H.C.J.: Learning, host fidelity, and the stability of host-parasitoid communities. Am. Nat. 153, 295–301 (1999)

    Article  Google Scholar 

  19. Holldobler, B., Wilson, E.O.: The Ants. Springer-Verlag, 1990

  20. Kakehashi, M., Yoshinaga, F.: Evolution of airborne infectious diseases according to changes in characteristics of the host population. Ecol. Res. 7, 235–243 (1992)

    Google Scholar 

  21. Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. London A115, 700–721 (1927)

  22. Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. London A138, 55–83 (1932)

  23. Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. London A141, 94–122 (1933)

  24. Lenski, R., May, R.M.: The evolution of virulence in parasites and pathogens: Reconciliation between two competing hypothesis. J. Theor. Biol. 169, 253–265 (1994)

    Article  PubMed  Google Scholar 

  25. Levin, B.R., Lenski, R.E.: Coevolution in bacteria and their viruses and plasmids. In: D.J. Futuyma, M. Slatkin (eds.), Coevolution (Sinauer Associates, Sunderland, Mass., 1983), pp. 99–129

  26. Levin, B.R., Eden Svanborg, C.: Selection and the evolution of virulence in bacteria: an ecumenical excursion and modest suggestion. Parisitology 100, S103–S115 (1990)

  27. Lipsitch, M., Nowak, M.A., Ebert, D., May, R.M.: The population dynamics of vertically and horizontally transmitted parasites. Proc. R. Soc. London B260, 321–327 (1995)

    Google Scholar 

  28. Lipsitch, M., Stiller, S., Nowak, M.A.: The evolution of virulence in pathogens with vertical and horizontal transmission. Evolution 50, 1729–1741 (1996)

    Google Scholar 

  29. Matsuda, H., Shimada, M.: Cost-benefit model for the evolution of symbiosis. In: H. Kawanabe, J.E. Cohen, K. Iwasaki (eds.), Mutualism and Community Organization: Behavioral, Theoretical and Food Web Approaches (Oxford University Press, Oxford U.K., 1992), pp. 215–230

  30. May, R.M., Anderson, R.M.: Epidemiology and genetics in the coevolution of parasites and hosts. Proc. R. Soc. London B219, 281–313 (1983)

    Google Scholar 

  31. May, R.M., Anderson, R.M.: Parasite-host coevolution. In: D.J. Futuyma, M. Slatkin (eds.), Coevolution (Sinauer Associates, Sunderland, Mass., 1983), pp. 186–206

  32. May, R.M., Anderson, R.M.: Parasite-host coevolution. Parasitology 100, S89–S101 (1990)

    Google Scholar 

  33. Maynard Smith, J., Szathmary, E.: The major transitions in evolution. W.H. Freeman Press, 1995

  34. Starr, M.P.: A generalized scheme for classifying organismic associations. Sympos. Soc. Exper. Biol. 29, 1–20 (1975)

    Google Scholar 

  35. Wilkonson, W.M.: Horizontally acquired mutualisms, an unsolved problem in ecology? Oikos 92, 377–383 (2001)

    Google Scholar 

  36. Williams, P.D., Day, T.: Interactions between sources of mortality and the evolution of parasite virulence. Proc. R. Soc. London B268, 2331–2337 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mary Ballyk.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Golinski, M., Barany, E. & Ballyk, M. Ecological conditions that favor the evolution of intermediate-virulence in an environmentally transmitted parasite. J. Math. Biol. 51, 389–402 (2005). https://doi.org/10.1007/s00285-005-0326-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-005-0326-6

Key words or phrases

Navigation