SpringerLink
Log in

Modelling parasitism and predation of mosquitoes by water mites

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

Parasitism and predation are two ecological interactions that can occur simultaneously between two species. This is the case of Culicidae (Insecta: Diptera) and water mites (Acari: Hydrachnidia). The larva mites are~parasites of aquatic and semiaquatic insects, and deutonymphs and adults are predators of insect larvae and eggs. Since several families of water mites are associated with mosquitoes there is an interest in the potential use of these mites as biological control agents. The aim of this paper is to use mathematical modelling and analysis to assess the impact of predation and parasitism in the mosquito population. We propose a system of ordinary differential equations to model the interactions among the larval and adult stages of mosquitoes and water mites. The model exhibits three equilibria: the first equilibrium point corresponds to the state where the two species are absent, the second one to the state where only mosquitoes are present (water mites need insects to complete their life cycle), and the third one is the coexistence equilibrium. We analyze conditions for the asymptotic stability of equilibria, supported by analytical and numerical methods. We discuss the different scenarios that appear when we change the parasitism and predation parameters. High rates of parasitism and moderate predation can drive two species to a stable coexistence.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bader C. (1980) Some biological and ecological data on water mites, mainly some significant data on the life-duration. Int. J. Acar. 6(3): 239–243

    Article  Google Scholar 

  2. Berding C., Keymer A.E., Murray J.D., Slater A.F.G. (1987) The population dynamics of aquired immunity to helminth infection: experimental and natural transmission. J. Theor. Biol. 126, 167–182

    Article  MathSciNet  Google Scholar 

  3. Davids C. (1997) The influence of larval parasitism on life history strategies. in water mites (Acari: Hydrachnidia). Arch. Hydrobiol. 141(1): 35–43

    Google Scholar 

  4. Dixon A.F.G. (2000) Insect Predator-Prey Dynamics. Cambridge University Press, Cambridge

    Google Scholar 

  5. Gubler D.J.: Dengue. In: Monath T.P. (ed.) The Arbovirus: Epidemiology and Ecology, vol. II, pp. 213–261. CRC Press, Florida (1986)

  6. Hale J.K. (1969) Ordinary Differential Equations. Wiley, New York

    MATH  Google Scholar 

  7. Hassell M.P. (1980) Foraging strategies, population models, and biological control: a case of study. J. Anim. Ecol. 49, 603–628

    Article  Google Scholar 

  8. Hassell M.P., May R.M. (1973) Stability in insect host-parasite models. J. Anim. Ecol. 42, 693–726

    Article  Google Scholar 

  9. Laird M. (1947) Some natural enemies of mosquitoes in the vicinity of Palmalmal, New Britain. Trans. R. Soc. N.Z. 76, 453–476

    Google Scholar 

  10. Lanciani C.A., Boyt A.D. (1977) The effect of a parasitic water mite, Arrenurus pseudotenuicollis (Acari: Hydrachnellae), on the survival and reproduction of the mosquito Anopheles crucians (Diptera: Culicidae). J. Med. Entomol. 14, 10–15

    Google Scholar 

  11. Mullen G. (1975) Acarine parasites of mosquitoes I A critical review of all know records of mosquitoes parasitized by mites (Acarina: Hydrachnellae). Proc. N.J. Mosq. Exterm. Assoc. 61, 90–94

    Google Scholar 

  12. Murdoch W., Briggs Ch.J., Swarbrick S. (2005) Host suppression and stability in a parasitoid-host system: experimental demonstration. Science 309, 610–613

    Article  Google Scholar 

  13. Nicholson A.J., Bailey V.A. (1954) An outline of the dynamics of animal population. Aust J. Zool. 2, 9–65

    Article  Google Scholar 

  14. Roberts M.G. (1995) A pocket guide to host-parasite models. Parasitol. Today 11(5): 172–177

    Article  Google Scholar 

  15. Smith B.P. The potential of mites as biological control agents of mosquitoes. In: Hoy M., Cunnigham G., Knutson L. (eds.) Research needs for development of biological control of pest by mites, pp. 79–85. Agric. Exp. Stn. Univ. Calif., USA (1983)

  16. Smith B.P., McIver S.B (1984) Factors influencing host selection and successful parasitism of Aedes spp. mosquitoes by Arrenurus spp. mites. Can J. Zool. 62, 1114–1120

    Article  Google Scholar 

  17. Smith B.P. (1988) Host-parasite interaction and impact of larval water mites on insects. Ann. Rev. Entomol. 33, 487–507

    Article  Google Scholar 

  18. Smith I.M., Cook D.R. Water mites. In: Thorp and Covich (eds.) Freshwater invertebrates from North American, pp. 470–492, Academic, USA (1991)

  19. Stechmann D.H. (1980) Zum Wirtskreis synopischer Arrenurus-Arten (Hydrachnellae, Acari) mit parasitischer Entwicklung an Nematocera (Diptera). Z. Parasitekd. 62, 267–283

    Article  Google Scholar 

  20. Verhulst F. (1990) Nonlinear Differential Equations and Dynamical Systems. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facultad de Ciencias, UNAM, 04510, México, D.F., Mexico

    Lourdes Esteva & Gerardo Rivas

  2. Departamento de Matemática Aplicada, UNICAMP – IMECC, Caixa Postal 6065, CEP: 13081-970, Campinas, Brazil

    Hyun Mo Yang

Authors
  1. Lourdes Esteva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerardo Rivas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hyun Mo Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lourdes Esteva.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Esteva, L., Rivas, G. & Yang, H.M. Modelling parasitism and predation of mosquitoes by water mites. J. Math. Biol. 53, 540–555 (2006). https://doi.org/10.1007/s00285-006-0020-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-006-0020-3

Keywords

Search

Navigation