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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
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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
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Copyright
© Australian Mathematical Society 2020

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