A dynamic mathematical model of the chemostat

Young, Thomas B.; Bruley, Duane F.; Bungay, Henry R.

doi:10.1002/bit.260120506

Cited by 76 publications

(22 citation statements)

References 21 publications

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“…where AN is an integer greater than zero. This age must be less than the upper bound derived above T(N, + AN) < a , + T (15) but subtracting T from both sides of this inequality gives…”

Section: Behavior For High Frequency Forcingmentioning

confidence: 86%

Periodic forcing of microbial cultures: A model for induction synchrony.

Hjortsø

1987

Biotech & Bioengineering

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Periodic environmental shifts have been used to induce synchrony in many different microbial populations. In this article, the induction synchrony phenomenon is analyzed using an age distribution model in which the age at which the cells divide is subjected to periodic forcing. It is found that synchrony will occur whenever the period of the forcing lies in the interval between the youngest and the oldest division age that occur in the population during the forcing. The analysis also predicts that under certain conditions it should be possible to obtain a multimodal synchrony in which cells in the population are distributed among a set of discrete, synchronized cell lines. The behavior of the age distribution when the conditions for synchrony are not satisfied is briefly explored. It is found that the age distribution model is able to exhibit a very rich spectrum of possible dynamic behavior. Many of the phenomena observed can be thought of in terms that are familiar from nonlinear analysis, such as stable and unstable limit cycles, period doubling, halving, and chaos. The richness of dynamic behavior opens the possibility that environmental shifts or periodic forcing could be used as a powerful tool in discriminating models of microbial kinetics and cell cycle control.

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“…where AN is an integer greater than zero. This age must be less than the upper bound derived above T(N, + AN) < a , + T (15) but subtracting T from both sides of this inequality gives…”

Section: Behavior For High Frequency Forcingmentioning

confidence: 86%

Periodic forcing of microbial cultures: A model for induction synchrony.

Hjortsø

1987

Biotech & Bioengineering

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“…For both species there are tradeoffs between V max and K m which are defined later. The change in concentrations of Resource 1 and Resource 2 and changes in population density of Species 1, N 1, and Species 2, N 2, at time t are modelled in the following way (adapted from Young et al 1970):…”

Section: Resource Consumption Recycling and Microbial Growthmentioning

confidence: 99%

Evolution of resource use along a gradient of stress leads to increased facilitation

Lawrence

Barraclough

2016

Oikos

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The stress‐gradient hypothesis (SGH) posits that the relative importance of facilitative interactions versus negative interactions increases as levels of abiotic stress increase. Originally formulated in empirical studies of plant populations, in recent years the SGH has been found to describe how interactions change in response to stress in a wide range of species including algae, mussels and moths. However, there has been little theory attempting to predict patterns from first principles in relation to different types of interactions. Here, we use mathematical models of microbial populations to investigate whether patterns consistent with the SGH arise when species interact through resource use and allelopathy. Evolution alters the degree to which competition for resource use versus facilitation (cross‐feeding) occurs. Our results are consistent with the SGH; species interactions evolve to be more facilitative as average stress intensifies. This occurs because at greater stress the species evolve to become specialists on either of the two resources thereby decreasing overlap in resource use and increasing facilitation through cross‐feeding. In addition, the production of toxic allelopathic compounds decreases as stress intensifies due to density‐dependent effects. Our results suggest that the SGH could arise through fundamental interactions that are common to many organisms and therefore that the SGH could be a more widespread phenomenon than previously recognised.

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“…There is some evidence to suggest that growth kinetics are time dependent and follow a first-order response (Young et al, 1970;Young and Bungay, 1973). The appropriate form which leads to the Monod equation at steady state is…”

Section: Reactor Modelmentioning

confidence: 99%