Oscillations and waves in a virally infected plankton system. Part I: The lysogenic stage

Ecological Complexity

Volumn 1, Issue 3, 2004, Pages 211-223

  Malchow, Horst ^a   Hilker, Frank M ^a   Petrovskii, Sergei V ^b   Brauer, Klaus ^a  

^a UNIVERSITY OF OSNABRÜCK   (Germany)

^b SHIRSHOV INSTITUTE OF OCEANOLOGY   (Russian Federation)

Author keywords

Noise enhanced spatial spread and survival; Plankton; Spatio temporal structures; Stochastic reaction diffusion system; Viral infections

Indexed keywords

EID: 12844270741     PISSN: 1476945X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecocom.2004.03.002     Document Type: Conference Paper

References (53)

1. Abramson, G., Kenkre, V., Yates, T., Parmenter, R., 2003. Traveling waves of infection in the Hantavirus epidemics. Bull. Math. Biol. 65, 519-534.
2. Allen, L., 2003. An Introduction to Stochastic Processes with Applications to Biology. Pearson Education, Upper Saddle River, NJ.
3. Anishenko, V., Astakov, V., Neiman, A., Vadivasova, T., Schimansky-Geier, L., 2003. Nonlinear dynamics of chaotic and stochastic systems. Tutorial and modern developments. Springer Series in Synergetics. Springer, Berlin.
4. Beltrami, E., Carroll, T., 1994. Modelling the role of viral disease in recurrent phytoplankton blooms. J. Math. Biol. 32, 857-863.
5. Chattopadhyay, J., Pal, S., 2002. Viral infection on phytoplankton- zooplankton system - a mathematical model. Ecol. Model. 151, 15-28.
6. Chattopadhyay, J., Sarkar, R., Pal, S., 2003. Dynamics of nutrient-phytoplankton interaction in the presence of viral infection. BioSystems 68, 5-17.
7. Dietz, K., Schenzle, D., 1985. Proportionate mixing models for age-dependent infection transmission. J. Math. Biol. 22, 117-120.
8. Fuhrman, J., 1999. Marine viruses and their biogeochemical and ecological effects. Nature 399, 541-548.
9. Grenfell, B., Bjørnstad, O., Kappey, J., 2001. Travelling waves and spatial hierarchies in measles epidemics. Nature 414, 716-723.
10. Higham, D., 2001. An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43 (3), 525-546.
11. Jacquet, S., Heldal, M., Iglesias-Rodriguez, D., Larsen, A., Wilson, W., Bratbak, G., 2002. Flow cytometric analysis of an Emiliana huxleyi bloom terminated by viral infection. Aquat. Microb. Ecol. 27, 111-124.
12. Jiang, S., Paul, J., 1998. Significance of lysogeny in the marine environment: studies with isolates and a model of lysogenic phage production. Microb. Ecol. 35, 235-243.
13. Kloeden, P., Platen, E., 1992. Numerical Solution of Stochastic Differential Equations. In: Applications of Mathematics, vol. 23. Springer, Berlin.
14. Kuznetsov, Y., Muratori, S., Rinaldi, S., 1992. Bifurcations and chaos in a periodic predator-prey model. Int. J. Bifurcat. Chaos 2, 117-128.
15. Lin, J., Andreasen, V., Casagrandi, R., Levin, S., 2003. Traveling waves in a model of influenza A drift. J. Theor. Biol. 222, 437-445.
16. Malchow, H., 1993. Spatio-temporal pattern formation in nonlinear nonequilibrium plankton dynamics. Proc. R. Soc. Lond. B 251, 103-109.
17. Malchow, H., 1996. Nonlinear plankton dynamics and pattern formation in an ecohydrodynamic model system. J. Mar. Sys. 7 (2-4), 193-202.
18. Malchow, H., 2000a. Motional instabilities in predator-prey systems. J. Theor. Biol. 204, 639-647.
19. Malchow, H., 2000b. Nonequilibrium spatio-temporal patterns in models of nonlinear plankton dynamics. Freshwater Biol. 45, 239-251.
20. Malchow, H., Hilker, F., Petrovskii, S., 2004a. Noise and productivity dependence of spatiotemporal pattern formation in a prey-predator system. Discrete Continuous Dynamical Sys. B 4 (3), 707-713.
21. Malchow, H., Medvinsky, A., Petrovskii, S., 2004b. Patterns in models of plankton dynamics in a heterogeneous environment. In: Seuront, L., Strutton, P. (Eds.), Handbook of Scaling Methods in Aquatic Ecology: Measurement, Analysis, Simulation. CRC Press, Boca Raton, pp. 401-410.
22. Malchow, H., Petrovskii, S., Medvinsky, A., 2002. Numerical study of plankton-fish dynamics in a spatially structured and noisy environment. Ecol. Model. 149, 247-255.
23. Malchow, H., Petrovskii, S., 2002. Dynamical stabilization of an unstable equilibrium in chemical and biological systems. Math. Comput. Model. 36, 307-319.
24. Malchow, H., Petrovskii, S., Hilker, F., 2003. Models of spatiotemporal pattern formation in plankton dynamics. Nova Acta Leopoldina, NF 88 (332), 325-340.
25. Malchow, H., Petrovskii, S., Medvinsky, A., 2001. Pattern formation in models of plankton dynamics. A synthesis. Oceanol. Acta 24 (5), 479-487.
26. McCallum, H., Barlow, N., Hone, J., 2001. How should pathogen transmission be modelled? TREE 16 (6), 295-300.
27. McDaniel, L., Houchin, L., Williamson, S., Paul, J., 2002. Lysogeny in Synechococcus. Nature 415, 496.
28. Medvinsky, A., Petrovskii, S., Tikhonova, I., Malchow, H., Li, B.-L., 2002. Spatiotemporal complexity of plankton and fish dynamics. SIAM Rev. 44 (3), 311-370.
29. Medvinsky, A., Tikhonov, D., Enderlein, J., Malchow, H., 2000. Fish and plankton interplay determines both plankton spatio-temporal pattern formation and fish school walks. A theoretical study. Nonlinear Dynamics, Psychol. Life Sci. 4 (2), 135-152.
30. Menzinger, M., Rovinsky, A., 1995. The differential flow instabilities. In: Kapral, R., Showalter, K. (Eds.), Chemical Waves and Patterns. Understanding Chemical Reactivity, vol. 10. Kluwer Academic Publishers, Dordrecht, pp. 365-397.
31. Nold, A., 1980. Heterogeneity in disease-transmission modeling. Math. Biosci. 52, 227-240.
32. Ortmann, A., Lawrence, J., Suttle, C., 2002. Lysogeny and lytic viral production during a bloom of the cyanobacterium Synechococcus spp. Microb. Ecol. 43, 225-231.
33. Pascual, M., 1993. Diffusion-induced chaos in a spatial predator-prey system. Proc. R. Soc. Lond. B 251, 1-7.
34. Petrovskii, S., Malchow, H., 1999. A minimal model of pattern formation in a prey-predator system. Math. Comput. Model. 29, 49-63.
35. Petrovskii, S., Malchow, H., 2000. Critical phenomena in plankton communities: KISS model revisited. Nonlinear Anal. Real World Appl. 1, 37-51.
36. Petrovskii, S., Malchow, H., 2001. Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics. Theor. Popul. Biol. 59 (2), 157-174.
37. Rinaldi, S., Muratori, S., Kuznetsov, Y., 1993. Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities. Bull. Math. Biol. 55, 15-35.
38. Sarkar, R., Chattopadhyay, J., 2003. Occurence of planktonic blooms under environmental fluctuations and its possible control mechanism - mathematical models and experimental observations. J. Theor. Biol. 224, 501-516.
39. Satnoianu, R., Menzinger, M., 2000. Non-Turing stationary patterns in flow-distributed oscillators with general diffusion and flow rates. Phys. Rev. E 62 (1), 113-119.
40. Satnoianu, R., Menzinger, M., Maini, P., 2000. Turing instabilities in general systems. J. Math. Biol. 41, 493-512.
41. Scheffer, M., 1991a. Fish and nutrients interplay determines algal biomass: a minimal model. OIKOS 62, 271-282.
42. Scheffer, M., 1991b. Should we expect strange attractors behind plankton dynamics - and if so, should we bother? J. Plankton Res. 13, 1291-1305.
43. Scheffer, M., Rinaldi, S., Kuznetsov, Y., van Nes, E., 1997. Seasonal dynamics of daphnia and algae explained as a, periodically forced predator-prey system. OIKOS 80, 519-532.
44. Sherratt, J., Lewis, M., Fowler, A., 1995. Ecological chaos in the wake of invasion. Proc. Natl. Acad. Sci. USA 92, 2524-2528.
45. Steele, J., Henderson, E., 1992. A simple model for plankton patchiness. J. Plankton Res. 14, 1397-1403.
46. Steffen, E., Malchow, H., Medvinsky, A., 1997. Effects of seasonal perturbation on a model plankton community. Environ. Model. Assess. 2, 43-48.
47. Suttle, C., 2000. Ecological, evolutionary, and geochemical consequences of viral infection of cyanobacteria and eukaryotic algae. In: Hurst, C. (Ed.), Viral Ecology. Academic Press, San Diego, pp. 247-296.
48. Suttle, C., Chan, A., Cottrell, M., 1990. Infection of phytoplankton by viruses and reduction of primary productivity. Nature 347, 467-469.
49. Thomas, J., 1995. Numerical partial differential equations: finite difference methods. In: Texts in Applied Mathematics, vol. 22. Springer, New York.
50. Truscott, J., Brindley, J., 1994. Ocean plankton populations as excitable media. Bull. Math. Biol. 56, 981-998.
51. Wilcox, R., Fuhrman, J., 1994. Bacterial viruses in coastal sea, water: lytic rather than lysogenic production. Max. Ecol. Prog. Ser. 114, 35-45.
52. Wommack, K., Colwell, R., 2000. Virioplankton: viruses in aquatic ecosystems. Microb. Molec. Biol. Rev. 64 (1), 69-114.
53. Zhdanov, V., 2003. Propagation of infection and the prey-predator interplay. J. Theor. Biol. 225, 489-492.