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Modeling the avoidance behavior of zooplankton on phytoplankton infected by free viruses

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Abstract

In any ecosystem, chaotic situations may arise from equilibrium state for different reasons. To overcome these chaotic situations, sometimes the system itself exhibits some mechanisms of self-adaptability. In this paper, we explore an eco-epidemiological model consisting of three aquatic groups: phytoplankton, zooplankton, and marine free viruses. We assume that the phytoplankton population is infected by external free viruses and zooplankton get affected on consumption of infected phytoplankton; also, the infected phytoplankton do not compete for resources with the susceptible one. In addition, we model a mechanism by which zooplankton recognize and avoid infected phytoplankton, at least when susceptible phytoplankton are present. The zooplankton extinction chance increases on increasing the force of infection or decreasing the intensity of avoidance. Further, when the viral infection triggers chaotic dynamics, high zooplankton avoidance intensity can stabilize again the system. Interestingly, for high avoidance intensity, nutrient enrichment has a destabilizing effect on the system dynamics, which is in line with the paradox of enrichment. Global sensitivity analysis helps to identify the most significant parameters that reduce the infected phytoplankton in the system. Finally, we compare the dynamics of the system by allowing the infected phytoplankton also to share resources with the susceptible phytoplankton. A gradual increase of the virus replication factor turns the system dynamics from chaos to doubling state to limit cycle to stable state and the system finally settles down to the zooplankton-free equilibrium point. Moreover, on increasing the intensity of avoidance, the system shows a transcritical bifurcation from the zooplankton-free equilibrium to the coexistence steady state and remains stable thereafter.

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References

  1. Vaulot, D.: Phytoplankton. In: Encyclopedia of Life Sciences, pp. 1–7. Macmillan Publishers Ltd. (2001)

  2. Evans, C., Pond, D. W., Wilson, W. H.: Changes in Emiliania huxleyi fatty acid profiles during infection with E. huxleyi virus 86: physiological and ecological implications. Aquat. Microb. Ecol. 55, 219–228 (2009)

    Article  Google Scholar 

  3. Gilg, I. C., et al.: Differential gene expression is tied to photochemical efficiency reduction in virally infected Emiliania huxleyi. Mar. Ecol. Prog. Ser. 555, 13–27 (2016)

    Article  ADS  Google Scholar 

  4. Malitsky, S., et al.: Viral infection of the marine alga Emiliania huxleyi triggers lipidome remodeling and induces the production of highly saturated triacylglycerol. New Phytol. 210(1), 88–96 (2016)

    Article  Google Scholar 

  5. Rosenwasser, S., et al.: Rewiring host lipid metabolism by large viruses determines the fate of Emiliania huxleyi, a bloom-forming alga in the ocean. Plant Cell tpc-114 (2014)

  6. Suzuki, T., Yasuo, S.: Virus infection and lipid rafts. Biol. Pharm. Bull. 29 (8), 1538–1541 (2006)

    Article  Google Scholar 

  7. Bratbak, G., Egge, J. K., Heldal, M.: Viral mortality of the marine alga Emiliania huxleyi (Haptophyceae) and termination of algal blooms. Mar. Ecol. Prog. Ser. 93, 39–48 (1993)

    Article  ADS  Google Scholar 

  8. Brussaard, C. P. D., et al.: Virus-like particles in a summer bloom of Emiliania huxleyi in the North Sea. Aquat. Microb. Ecol. 10, 105–113 (1996)

    Article  Google Scholar 

  9. Castberg, T., et al.: Microbial population dynamics and diversity during a bloom of the marine coccolithophorid Emiliania huxleyi (Haptophyta). Mar. Ecol. Prog. Ser. 221, 39–46 (2001)

    Article  ADS  Google Scholar 

  10. Nagasaki, K., et al.: Virus-like particles in Heterosiginu akashiwo (Raphidophyceae): a possible red-tide disintegration mechanism. Mar. Biol. 119(2), 307–312 (1994)

    Article  Google Scholar 

  11. Jacquet, S., et al.: Flow cytometric analysis of an Emiliana huxleyi bloom terminated by viral infection. Aquat. Microb. Ecol. 27, 111–124 (2002)

    Article  Google Scholar 

  12. Costamagna, A., et al.: A model for the operations to render epidemic-free a hog farm infected by the Aujeszky disease. Appl. Math. Nonlinear Sci. 1(1), 207–228 (2016)

    Article  MathSciNet  Google Scholar 

  13. Venturino, E.: Ecoepidemiology: a more comprehensive view of population interactions. Math. Model. Nat. Phenom. 11(1), 49–90 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  14. Samanta, S., et al.: Effect of enrichment on plankton dynamics where phytoplankton can be infected from free viruses. Nonlinear Stud. 20(2), 223–236 (2013)

    MathSciNet  MATH  Google Scholar 

  15. Bairagi, N., et al.: Virus replication factor may be a controlling agent for obtaining disease-free system in a multi-species eco-epidemiological system. J. Biol. Syst. 13(3), 245–259 (2005)

    Article  MATH  Google Scholar 

  16. Evans, C., Wilson, W. H.: Preferential grazing of Oxyrrhis marina on virus infected Emiliania huxleyi. Limnol. Oceanogr. 53, 2035–2040 (2008)

    Article  ADS  Google Scholar 

  17. Vermont, A., et al.: Virus infection of Emiliania huxleyi deters grazing by the copepod Acartia tonsa. J. Plankton Res. 38(5), 1194–1205 (2016)

    Article  ADS  Google Scholar 

  18. Townsend, D. W., et al.: Blooms of the coccolithophore Emiliania huxleyi with respect to hydrography in the Gulf of Maine. Cont. Shelf Res. 14, 979–1000 (1994)

    Article  ADS  Google Scholar 

  19. Wilson, W. H., et al.: Isolation of viruses responsible for the demise of an Emiliania huxleyi bloom in the English Channel. J. Mar. Biol. Assoc. U.K. 82(3), 369–377 (2002)

    Article  ADS  Google Scholar 

  20. Evans, C.: The Influence of Marine Viruses on the Production of Dimethyl Sulphide (DMS) and Related Compounds from Emiliania Huxleyi. PhD Thesis, University of East Anglia (2005)

  21. Evans, C., et al.: Viral infection of Emiliania huxleyi (Prymnesiophyceae) leads to elevated production of reactive oxygen species. J. Phycol. 42, 1040–1047 (2006)

    Article  Google Scholar 

  22. Poulet, S. A., Ouellet, G.: The role of amino acids in the chemosensory swarming and feeding of marine copepods. J. Plankton Res. 4, 341–361 (1982)

    Article  Google Scholar 

  23. Gill, C. W., Poulet, S. A.: Responses of copepods to dissolved free amino acids. Mar. Ecol. Prog. Ser. 43, 269–276 (1988)

    Article  ADS  Google Scholar 

  24. Demott, W. R., Watson, M. D.: Remote detection of algae by copepods: responses to algal size, odors and motility. J. Plankton Res. 13, 1203–1222 (1991)

    Article  Google Scholar 

  25. Steinke, M., Stefels, J., Stamhuis, E.: Dimethyl sulfide triggers search behavior in copepods. Limnol. Oceanogr. 51, 1925–1930 (2006)

    Article  ADS  Google Scholar 

  26. Floge, S. A.: Virus infections of eukaryotic marine microbes, Electronic Theses and Dissertations. The University of Maine (2014)

  27. Evans, C., et al.: The relative sinificance of viral lysis and microzooplankton grazing as pathways of dimethylsulfoniopropionate (DMSP) cleavage: an Emiliania huxleyi culture study. Limnol. Oceanogr. 52, 1036–1045 (2007)

    Article  ADS  Google Scholar 

  28. Predators in the Plankton, Available at http://oceans.mit.edu/news/featured-stories/predators-in-the-plankton.html

  29. Mukherjee, D.: Persistence in a prey-predator system with disease in the prey. J. Biol. Syst. 11(01), 101–112 (2003)

    Article  MATH  Google Scholar 

  30. Venturino, E.: Epidemics in Predator-Prey Models: Disease in the Prey. In: Arino, O., Axelrod, D., Kimmel, M., Langlais, M. (eds.) Mathematical Population Dynamics: Analysis of Heterogeneity, vol. 1, pp 381–393 (1995)

  31. Chattopadhyay, J., Arino, O.: A predator-prey model with disease in the prey. Nonlinear Anal. 36, 747–766 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  32. Hethcote, H. W., et al.: A predator-prey model with infected prey. Theor. Popul. Biol. 66(3), 259–268 (2004)

    Article  MathSciNet  Google Scholar 

  33. Beretta, E., Kuang, Y.: Modeling and analysis of a marine bacteriophage infection. Math. Biosci. 149, 57–76 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  34. Siekmann, I., Malchow, H., Venturino, E.: An extension of the Beretta-Kuang model of viral diseases. Math. Biosci. Eng. 5, 549–565 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  35. Hilker, F. M., et al.: Oscillations and waves in a virally infected plankton system Part II: Transition from lysogeny to lysis. Ecol. Compl. 3, 200–208 (2006)

    Article  Google Scholar 

  36. Bhattacharyya, S., Bhattacharya, D. K.: Pest control through viral disease: mathematical modeling and analysis. J. Theor. Biol. 238(1), 177–197 (2006)

    Article  MathSciNet  Google Scholar 

  37. Beltrami, E., Carroll, T. O.: Modeling the role of viral disease in recurrent phytoplankton blooms. J. Math. Biol. 32, 857–863 (1994)

    Article  MATH  Google Scholar 

  38. Gakkhar, S., Negi, K.: A mathematical model for viral infection in toxin producing phytoplankton and zooplankton system. Appl. Math. Comp. 179, 301–313 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  39. Chattopadhyay, J., Pal, S.: Viral infectionon phytoplankton-zooplankton system: a mathematical model. Ecol. Model. 151, 15–28 (2002)

    Article  Google Scholar 

  40. Rhodes, C., Truscott, J., Martin, A.: Viral infection as a regulator of oceanic phytoplankton populations. J. Mar. Syst. 74, 216–226 (2008)

    Article  Google Scholar 

  41. Singh, B. K., Chattopadhyay, J., Sinha, S.: The role of virus infection in a simple phytoplankton-zooplankton system. J. Theor. Biol. 231, 153–166 (2004)

    Article  MathSciNet  Google Scholar 

  42. Rhodes, C. J., Martin, A. P.: The influence of viral infection on a plankton ecosystem undergoing nutrient enrichment. J. Theor. Biol. 265(3), 225–237 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  43. May, R.M.: Chaos and the dynamics of biological populations. Proc. R. Soc. Lond. 413, 27–44 (1987)

    ADS  MathSciNet  MATH  Google Scholar 

  44. Godfray, H.C.J., Grenfell, B.T.: The continuing quest for chaos. Trends Ecol. Evol. 8, 43–44 (1993)

    Article  Google Scholar 

  45. Hastings, A., et al.: Chaos in ecology: is mother nature a strange attractor?. Annu. Rev. Ecol. Syst. 24, 1–33 (1993)

    Article  Google Scholar 

  46. Perry, J.N., Woiwod, I.P., Hanski, I.: Using response-surface methodology to detect chaos in ecological time series. Oikos 68, 329–339 (1993)

    Article  Google Scholar 

  47. Jørgensen, S.E.: The growth rate of zooplankton at the edge of chaos: ecological models. J. Theor. Biol. 175, 13–21 (1995)

    Article  Google Scholar 

  48. Hastings, A., Powell, T.: Chaos in three-species food chain. Ecology 72, 896–903 (1991)

    Article  Google Scholar 

  49. Chattopadhyay, J., Sarkar, R.R.: Chaos to order: preliminary experiments with a population dynamics models of three trophic levels. Ecol. Model. 163, 45–50 (2003)

    Article  Google Scholar 

  50. Peters, R.H.: The Ecological Implications of Body Size. Cambridge University Press, Cambridge (1983)

    Book  Google Scholar 

  51. Mandal, S., et al.: Order to chaos and vice versa in an aquatic ecosystem. Ecol. Model. 197, 498–504 (2006)

    Article  Google Scholar 

  52. Chakraborty, S., et al.: The role of avoidance by zooplankton for survival and dominance of toxic phytoplankton. Ecol. Compl. 11, 144–153 (2012)

    Article  Google Scholar 

  53. Holmes, J. C., Bethel, W. M.: Modification of intermediate host behavior by parasites. In: Canning, E.V., Wright, C.A. (eds.) Behavioral Aspects of Parasite Transmission, vol. 51, pp 123–149. Suppl. I to Zool. F. Linnean Soc. (1972)

  54. Lafferty, K. D.: Foraging on prey that are modified by parasites. Am. Nat. 140, 854–867 (1992)

    Article  Google Scholar 

  55. Hamilton, W. D., Axelrod, R., Tanese, R.: Sexual reproduction as an adaptation to resist parasites: a review. Proc. Natl Acad. Sci. USA 87, 3566–3573 (1990)

    Article  ADS  Google Scholar 

  56. Uhlig, G., Sahling, G.: Long-term studies on Noctiluca scintillans in the German Bight population dynamics and red tide phenomena 1968–1988. Neth. J. Sea Res. 25, 101–112 (1992)

    Article  Google Scholar 

  57. Lakshmikantham, V., Leela, S., Martynyuk, A. A.: Stability analysis of nonlinear systems. Marcel Dekker, Inc, New York/Basel (1989)

  58. Smith, H.L.: The Rosenzweig-MacArthur predator-prey model. https://math.la.asu.edu/halsmith/Rosenzweig.pdf

  59. Li, Y., Muldowney, J. S.: On Bendixson’s criterion. J. Diff. Eqn. 106, 27–39 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  60. Marino, S., et al.: A methodology for performing global uncertainty and sensitivity analysis in systems biology. J. Theor. Biol. 254(1), 178–196 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  61. Rosenzweig, M. L.: Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171, 385 (1971)

    Article  ADS  Google Scholar 

  62. Linhart, S. B., et al.: Avoidance of prey by captive coyotes punished with electric shock. In: Proceedings of the Vertebrate Pest Conference, vol. 7, pp. 302–330 (1976)

  63. Lebedeva, L.P.: A model of the latitudinal distribution of the numbers of species of phytoplankton in the sea. J. Cons. Int. Explor. Mer. 34, 341–350 (1972)

    Article  Google Scholar 

  64. Jørgensen, S.E., et al.: Improved calibration of a eutrophication model by use of the size variation due to succession. Ecol. Model. 153, 269–277 (2002)

    Article  Google Scholar 

  65. Odum, H.T.: Self organization, transformity, and information. Science 242, 1132–1139 (1988)

    Article  ADS  Google Scholar 

  66. Kauffman, S.A.: Anti-chaos and adaptation. Sci. Am. 265(2), 78–84 (1991)

    Article  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the anonymous referees for their careful reading, valuable comments, and helpful suggestions, which have contributed to improve the presentation of this work significantly. The authors are grateful to Prof. Guido Badino, DBIOS, University of Turin, Italy, for his valuable suggestions.

Funding

The research work of Saswati Biswas is supported by Council of Scientific and Industrial Research, Government of India, New Delhi in the form of Senior Research Fellowship (Ref. No. 20/12/2015(ii)EU-V). Pankaj Kumar Tiwari is thankful to University Grants Commissions, New Delhi, India for providing financial support in form of D. S. Kothari post-doctoral fellowship (No. F.4-2/2006 (BSR)/MA/17-18/0021). Research of Samares Pal is supported by DST-FIST programme of University of Kalyani (474 (Sanc.)/ST/P/S & T/16 G-22/2018). Ezio Venturino has been partially supported by the project “Metodi numerici e computazionali per le scienze applicate” of the Dipartimento di Matematica “Giuseppe Peano”.

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  1. Department of Mathematics, University of Kalyani, Kalyani, 741235, India

    Saswati Biswas, Pankaj Kumar Tiwari & Samares Pal

  2. DBIOS, University of Turin, via Accademia Albertina 13, 10123, Turin, Italy

    Francesca Bona

  3. Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, via Carlo Alberto 10, 10123, Turin, Italy

    Ezio Venturino

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  1. Saswati Biswas
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Correspondence to Ezio Venturino.

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Biswas, S., Tiwari, P.K., Bona, F. et al. Modeling the avoidance behavior of zooplankton on phytoplankton infected by free viruses. J Biol Phys 46, 1–31 (2020). https://doi.org/10.1007/s10867-020-09538-5

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