Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-19T16:53:37.249Z Has data issue: false hasContentIssue false
  • English
  • Français

THE PARADOX OF ENRICHMENT, SPATIAL HETEROGENEITY, COMMUNITY EFFECTS AND THE PHENOMENON OF APPARENT DISAPPEARANCE IN THE MARINE BACTERIOPHAGE DYNAMICS

Part of: Qualitative theory

Published online by Cambridge University Press:  22 June 2020

ANDREI KOROBEINIKOV Open the ORCID record for ANDREI KOROBEINIKOV [Opens in a new window] ,
ELENA SHCHEPAKINA Open the ORCID record for ELENA SHCHEPAKINA [Opens in a new window]  and
VLADIMIR SOBOLEV Open the ORCID record for VLADIMIR SOBOLEV [Opens in a new window]
ANDREI KOROBEINIKOV*
Affiliation:
School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, China
ELENA SHCHEPAKINA
Affiliation:
Department of Differential Equations and Control Theory, Samara National Research University, Moskovskoye shosse 34, Samara443086, Russian Federation; e-mail: shchepakina@yahoo.com, hsablem@gmail.com
VLADIMIR SOBOLEV
Affiliation:
Department of Differential Equations and Control Theory, Samara National Research University, Moskovskoye shosse 34, Samara443086, Russian Federation; e-mail: shchepakina@yahoo.com, hsablem@gmail.com
*
e-mail: akorobeinikov777@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

In aquatic microbial systems, high-magnitude variations in abundance, such as sudden blooms alternating with comparatively long periods of very low abundance (“apparent disappearance”), are relatively common. We suggest that in order for this to occur, such variations in abundance in microbial systems and, in particular, the apparent disappearance of species do not require seasonal or periodic forcing of any kind or external factors of any other nature. Instead, such variations can be caused by internal factors and, in particular, by bacteria–phage interaction. Specifically, we suggest that the variations in abundance and the apparent disappearance phenomenon can be a result of phage infection and the lysis of infected bacteria. To illustrate this idea, we consider a reasonably simple mathematical model of bacteria–phage interaction based on the model suggested by Beretta and Kuang, which assumes neither periodic forcing nor action of other external factors. The model admits a loss of stability via Andronov–Hopf bifurcation and exhibits dynamics which explains the phenomenon. These properties of the model are especially distinctive for spatially nonhomogeneous biosystems as well as biosystems with some sort of cooperation or community effects.

Keywords

mathematical modelbacterioplanktonphagehost–parasite systemHopf bifurcationstabilitylimit cycleself-sustained oscillationskill the winner hypothesisparadox of enrichmentspatial heterogeneitycommunity effectscooperation

MSC classification

Primary: 92D25: Population dynamics (general)
Secondary: 34C23: Bifurcation
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 4 , October 2020 , pp. 453 - 468
Check for updates
Copyright
© Australian Mathematical Society 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abedon, S. T., “Phage evolution and ecology”, Adv. Appl. Microbiol. 67 (2009) 1–45; doi:10.1016/S0065-2164(08)01001-0.Google Scholar
Alldredge, A. L., Cole, J. J. and Caron, D. A., “Production of heterotrophic bacteria inhabiting macroscopic organic aggregates (marine snow) from surface waters”, Limnol. Oceanogr. 31 (1986) 68–78; doi:10.1088/1742-6596/55/1/008.Google Scholar
Allee, W. C. and Bowen, E., “Studies in animal aggregations: mass protection against colloidal silver among goldfishes”, J. Exp. Zool. 61 (1932) 185–207; doi:10.1002/jez.1400610202.Google Scholar
Anderson, R. M. and May, R. M., “The population dynamics of microparasites and their invertebrate hosts”, Philos. Trans. R. Soc. Lond. Ser. B 291 (1981) 451–524; doi:10.1098/rstb.1981.0005.Google Scholar
Azam, F., “Microbial control of oceanic carbon flux: the plot thickens”, Science 280 (1998) 694–696; doi:10.1126/science.280.5364.694.Google Scholar
Beretta, E. and Kuang, Y., “Modeling and analysis of a marine bacteriophage infection”, Math. Biosci. 149 (1998) 57–76; doi:10.1016/s0025-5564(97)10015-3.Google Scholar
Blackburn, N., Fenchel, T. and Mitchel, J., “Microscale nutrient patches in planktonic habitats shown by chemotactic bacteria”, Science 282 (1998) 2254–2256; doi:10.1126/science.282.5397.2254.Google Scholar
Boras, J. A., Sala, M. M., Baltar, F., Aristegui, J., Duarte, C. M. and Vaqué, D., “Effect of viruses and protists on bacteria in eddies of the Canary Current region (subtropical northeast Atlantic)”, Limnol. Oceanogr. 55 (2010) 885–898; doi:10.4319/lo.2009.55.2.0885.Google Scholar
Boras, J. A., Sala, M. M., Vázquez-Dominguez, E., Weinbauer, M. G. and Vaqué, D., “Annual changes of bacterial mortality due to viruses and protists in an oligotrophic coastal environment (NW Mediterranean)”, Environ. Microbiol. 11 (2009) 1181–1193; doi:10.1111/j.1462-2920.2008.01849.x.Google Scholar
Bratbak, G., Heldal, M., Thingstad, T. F., Riemann, B. and Haslund, O. H., “Incorporation of viruses into the budget of microbial C-transfer. A first approach”, Mar. Ecol. Prog. Ser. 83 (1992) 273–280; doi:10.3354/meps083273.Google Scholar
Breitbart, M., Miyake, J. H. and Rohwer, F., “Global distribution of nearly identical phage-encoded DNA sequences”, FEMS Microbiol. Lett. 236 (2004) 249–256; doi:10.1016/j.femsle.2004.05.042.Google Scholar
Casas, V., Miyake, J., Balsley, H., Roark, J., Telles, S., Leeds, S., Zurita, I., Breitbart, M., Bartlett, D., Azam, F. and Rohwer, F., “Widespread occurrence of phage-encoded exotoxin genes in terrestrial and aquatic environments in Southern California”, FEMS Microbiol. Lett. 261 (2006) 141–149; doi:10.1111/j.1574-6968.2006.00345.x.Google Scholar
Chin, W. C., Orellana, M. V. and Verdugo, P., “Spontaneous assembly of marine dissolved organic matter into polymer gels”, Nature 391 (1998) 568–572; doi:10.1038/35345.Google Scholar
Courchamp, F., Berec, J. and Gascoigne, J., Allee effects in ecology and conservation (Oxford University Press, New York, 2008).Google Scholar
Cullen, R. M., Korobeinikov, A. and Walker, W. J., “Seasonality and critical community size for infectious diseases”, ANZIAM J. 44 (2003) 501–512; doi:10.1017/S144618110001289X.Google Scholar
d’Herelle, M. F., “Sur un microbe invisible antagoniste des bacilles dysentériques”, C. R. Acad. Sci. Paris 165 (1917) 373–375; doi:10.4161/bact.1.1.14941.Google Scholar
Faruque, S. M., Rahman, M. M., Asadulghani, Nasirul Islam, K. M. N. and Mekalanos, J. J., “Lysogenic conversion of environmental Vibrio mimicus strains by CTX$\unicode[STIX]{x1D719}$”, Infect. Immun. 67 (1999) 5723–5729; doi:10.1128/IAI.67.11.5723-5729.1999.Google Scholar
Fuhrman, J. A., “Marine viruses and their biogeochemical and ecological effects”, Nature 399 (1999) 541–548; doi:10.1038/21119.Google Scholar
Gantmacher, F. R., The theory of matrices, Volume 2 (Chelsea, New York, 1959).Google Scholar
Gavin, C., Pokrovskii, A., Prentice, M. and Sobolev, V., “Dynamics of a Lotka–Volterra type model with applications to marine phage population dynamics”, J. Phys.: Conf. Ser. 55 (2006) 80–93; doi:10.1088/1742-6596/55/1/008.Google Scholar
Gol’dshtein, V., Zinoviev, A., Sobolev, V. and Shchepakina, E., “Criterion for thermal explosion with reactant consumption industry gas”, Proc. R. Soc. Lond. Ser. A 452 (1996) 2103–2119; doi:10.1098/rspa.1996.0111.Google Scholar
Hoffmann, K. H., Rodriguez-Brito, B., Breitbart, M., Bangor, D., Angly, F., Felts, B., Nulton, J., Rohwer, F. and Salamon, P., “Power law rank-abundance models for marine phage communities”, FEMS Microbiol. Lett. 273 (2007) 224–228; doi:10.1111/j.1574-6968.2007.00790.x.Google Scholar
Holmfeldt, K., Middelboe, M., Nybroe, O. and Riemann, L., “Large variabilities in host strain susceptibility and phage host range govern interactions between lytic marine phages and their Flavobacterium hosts”, Appl. Environ. Microbiol. 73 (2007) 6730–6739; doi:10.1128/AEM.01399-07.Google Scholar
Korobeinikov, A., “Global asymptotic properties of virus dynamics models with dose dependent parasite reproduction and virulence, and nonlinear incidence rate”, Math. Med. Biol. 26 (2009) 225–239; doi:10.1093/imammb/dqp006.Google Scholar
Korobeinikov, A., “Stability of ecosystems: global properties of a general prey–predator model”, Math. Med. Biol. 26 (2009) 309–321; doi:10.1093/imammb/dqp009.Google Scholar
Korobeinikov, A., Shchepakina, E. and Sobolev, V., “Paradox of enrichment and system order reduction: bacteriophages dynamics as case study”, Math. Med. Biol. 33 (2016) 359–369; doi:10.1093/imammb/dqv025.Google Scholar
Lekunberri, I., Lefort, T., Romero, E., Vázquez-Domínguez, E., Romera-Castillo, C., Marrasé, C., Peters, F., Weinbauer, M. and Gasol, J. M., “Effects of a dust deposition event on coastal marine microbial abundance and activity, bacterial community structure, and ecosystem function”, J. Plankton Res. 32 (2010) 381–396; doi:10.1093/plankt/fbp137.Google Scholar
McGrath, S. and van Sinderen, D. (eds), Bacteriophage: genetics and molecular biology, 1st edn (Caister Academic Press, Norfolk, UK, 2007).Google Scholar
Mehrotra, M., Wang, G. and Johnson, W., “Multiplex PCR for detection of genes for Staphylococcus aureus exterotoxins, exfoliative toxins, toxic shock syndrome toxin 1, and methicillin resistance”, J. Clin. Microbiol. 38 (2000) 1032–1035; https://www.ncbi.nlm.nih.gov/pmc/articles/PMC86330/.Google Scholar
Mortell, M., O’Malley, R., Pokrovskii, A. and Sobolev, V., Singular perturbations and hysteresis (SIAM, Philadephia, PA, 2005).Google Scholar
Prentice, M., Private communication, Department of Medical Microbiology, The University College Cork, Cork, Ireland, 2009.Google Scholar
Rosenzweig, M. L., “Paradox of enrichment: destabilization of exploitation ecosystems in ecological time”, Science 171 (1971) 385–387; doi:10.1126/science.171.3969.385.Google Scholar
Shchepakina, E., Sobolev, V. and Mortell, M., Singular perturbations: introduction to system order reduction methods with applications (Springer, Cham, Switzerland, 2014).Google Scholar
Thingstad, T. F. and Lignell, R., “Theoretical models for the control of bacterial growth rate, abundance, diversity and carbon demand”, Aquat. Microb. Ecol. 13 (1997) 19–27; doi:10.3354/ame013019.Google Scholar
Twort, F. W., “An investigation on the nature of ultra-microscopic viruses”, Lancet 186(4814) (1915) 1241–1243; doi:10.1016/S0140-6736(01)20383-3.Google Scholar
Weinbauer, M. G. and Höfle, M. G., “Significance of viral lysis and flagellate grazing as factors controlling bacterioplankton production in a eutrophic lake”, Appl. Environ. Microbiol. 64(2) (1998) 431–438; doi:10.1128/AEM.64.2.431-438.1998.Google Scholar
Wodarz, D., Nowak, M. A. and Bangham, C. R. M., “The dynamics of HTLV-1 and the CTL response”, Immunol. Today 20 (1999) 220–227; doi:10.1016/S0167-5699(99)01446-2.Google Scholar
Wommack, K. E. and Colwell, R. R., “Virioplankton: viruses in aquatic ecosystems”, Microbiol. Mol. Biol. Rev. 64(1) (2000) 69–114; doi:10.1128/MMBR.64.1.69-114.2000.Google Scholar
Wommack, K. E., Ravel, J., Hill, R. T. and Colwell, R. R., “Hybridization analysis of Chesapeake Bay virioplankton”, Appl. Environ. Microbiol. 65 (1999) 241–250; doi:10.1128/AEM.65.1.241-250.1999.Google Scholar