Population dynamics and competition in chemostat models with adaptive nutrient uptake

Tang, Boyu; Sitomer, Ann; Jackson, Trachette L.

doi:10.1007/s002850050061

Cited by 24 publications

(13 citation statements)

References 12 publications

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“…Recently, a new mechanism of coexistence has been analyzed, based on a relationship of consumption to the amount and biochemical composition of food-as opposed to ''rigorous'' metabolism, when the coefficient of food consumption is constant (Tang et al 1997;Andersen et al 2004). …”

Section: Discussion: Coexistence Of Microbial Populations and Regulatmentioning

confidence: 99%

Coexistence of microbial populations and autostabilization of regulating factors in continuous culture: theory and experiments

Дегерменджи

2010

Aquat Ecol

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The paper summarizes the author's theoretical and experimental researches aimed at studying the rule of stable coexistence of interacting microbial populations within same trophic level. Populations of yeast and algae interact in open continuous cultures through regulating factors (RFs), which come together by the ability to be released or taken up by a microbial population and affect the growth of this and other population. Theoretical and experimental studies show that in steady state, the number of coexisting species is not greater than the number of RFs. Two-dimensional regions with different resultant species compositions of experimental equilibrium communities are plotted in the coordinates of ''input levels of RFs''. This is perhaps the first study showing that the background steady-state levels of RFs in the system are not related to their input levels. This effect has been termed autostabilization of RFs, and its theoretical basis has been developed. A new criterion of intra-and inter-population microbial interactions has been introduced for RFs-growth acceleration response to a change in population density. Based on the proposed new criterion, experimental and theoretical estimates of the intensity and the sign of interactions between populations are given, allowing the quantification of their complex relationships, which was earlier unattainable. An integrated approach to detection of RFs has been proposed based on this criterion and the autostabilization effect.

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Section: Discussion: Coexistence Of Microbial Populations and Regulatmentioning

confidence: 99%

Coexistence of microbial populations and autostabilization of regulating factors in continuous culture: theory and experiments

Дегерменджи

2010

Aquat Ecol

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“…For instance, the model of adaptive nutrient uptake, where u denotes the low growing cells and v denotes the fast growing cells considered in [32] is obtained with attachment and detachment rates depending only on S α(·) = α(S), β(·) = β(S).…”

Section: Modeling Flocks or Aggregates In The Chemostatmentioning

confidence: 99%

Extensions of the chemostat model with flocculation

Fekih-Salem

Harmand

Lobry

et al. 2013

Journal of Mathematical Analysis and Applications

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a b s t r a c tIn this work, we study a model of the chemostat where the species are present in two forms, isolated and aggregated individuals, such as attached bacteria or bacteria in flocks. We show that our general model contains a lot of models that were previously considered in the literature. Assuming that flocculation and deflocculation dynamics is fast compared to the growth of the species, we construct a reduced chemostat-like model in which both the growth functions and the apparent dilution rate depend on the density of the species. We also show that such a model involving monotonic growth rates may exhibit bi-stability, while it may occur in the classical chemostat model, but when the growth rate is nonmonotonic.

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“…According to the aforementioned assumptions, we have the following model:

({, \begin{matrix} array \frac{d N}{d t} = D (N_{0} - N) - \frac{m N}{k_{1} + N} x, \\ array \frac{d x}{d t} = \frac{α m N}{k_{1} + N} x - n x y - D_{1} x, \\ array \frac{d y}{d t} = β n x y - D_{2} y + \bar{p} . \end{matrix})

If D 1 = D 2 = D and

\overset{p}{true} = 0

, then system is of the classical chemostat model and the mathematical results can be seen in many references (e.g., ).…”

Section: Model Formulationmentioning

confidence: 99%

A kind of non-traditional biomanipulation model with constant releasing fish

Guo

Chen

Song

2017

Math. Meth. Appl. Sci.

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On the basis of the ideas of non‐traditional biomanipulation control in fresh water body, a kind of nutrient–algae fish model is presented to investigate the effects of constant releasing fish on the nutrient and the algae. The threshold conditions for the extinction of the algae are obtained by discussing the stability of boundary equilibrium. The conditions for the coexistence of the algae and the fish are obtained by discussing the existence and stability of positive equilibrium. Besides, Hopf bifurcation is also analyzed by considering the parameter about the amount of the released fish. Furthermore, a kind of optimal problem is presented, and the necessary condition for the existence of the optimal solution is given by Pontryagin maximum principle. Finally, the mathematical results are verified by numerical simulations. The mathematical results show that there is a threshold amount of the released fish, above which the activity of releasing fish can control the growth of the algae and further reduce the probability of the algae bloom, but can not decrease the eutrophication level of the water body. Copyright © 2017 John Wiley & Sons, Ltd.

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Population dynamics and competition in chemostat models with adaptive nutrient uptake

Cited by 24 publications

References 12 publications

Coexistence of microbial populations and autostabilization of regulating factors in continuous culture: theory and experiments

Coexistence of microbial populations and autostabilization of regulating factors in continuous culture: theory and experiments

Extensions of the chemostat model with flocculation

A kind of non-traditional biomanipulation model with constant releasing fish

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