NDLI: Competition between phytoplankton and bacteria: exclusion and coexistence

Content Provider	Springer Nature Link
Author	Masci, Pierre Beît, Eric Grognard, Frédéric Bernard, Olivier
Copyright Year	2014
Abstract	Resource-based competition between microorganisms species in continuous culture has been studied extensively both experimentally and theoretically, mostly for bacteria through Monod and Contois “constant yield” models, or for phytoplankton through the Droop “variable yield” models. For homogeneous populations of N bacterial species (Monod) or N phytoplanktonic species (Droop), with one limiting substrate and under constant controls, the theoretical studies indicated that competitive exclusion occurs: only one species wins the competition and displaces all the others (Armstrong and McGehee in Am Nat 115:151, 1980; Hsu and Hsu in SIAM J Appl Math 68:1600–1617, 2008). The winning species expected from theory is the one with the lowest “substrate subsistence concentration” $$s^{\star }$$ , such that its corresponding equilibrium growth rate is equal to the dilution rate $$D$$ . This theoretical result was validated experimentally with phytoplankton (Tilman and Sterner in Oecologia 61(2):197–200, 1984) and bacteria (Hansen and Hubell in Science 207(4438):1491–1493, 1980), and observed in a lake with microalgae (Tilman in Ecology 58(22):338–348, 1977). On the contrary for aggregating bacterial species described by a Contois model, theory predicts coexistence between several species (Grognard et al. in Discrete Contin Dyn Syst Ser B 8(1):73–93, 2007). In this paper we present a generalization of these results by studying a competition between three different types of microorganisms: planktonic (or free) bacteria (represented by a generalized Monod model), aggregating bacteria (represented by a Contois model) and free phytoplankton (represented by a Droop model). We prove that the outcome of the competition is a coexistence between several aggregating bacterial species with a free species of bacteria or phytoplankton, all the other free species being washed out. This demonstration is based mainly on the study of the substrate concentration’s evolution caused by competition; it converges towards the lowest subsistence concentration $$s^{\star }$$ , leading to three different types of competition outcomes: (1) the best free bacteria or phytoplankton competitor excludes all other species; (2) only some aggregating bacterial species coexist in the chemostat; (3) A coexistence between the single best free species, with one or several aggregating species.
Ending Page	1006
Page Count	48
Starting Page	959
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	5
Volume Number	70
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-04-20
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Dynamical systems in biology Population dynamics (general) Biology, chemistry, medicine Global stability Mathematical and Computational Biology Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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