The continuous culture of micro-organisms using the chemostat is an important research technique in microbiology and population biology. It offers advantages in the form of economical production of micro-organisms for the industrial microbiologist and is a laboratory idealization of nature for population studies. The paper studies a mathematical model, based on Michaelis-Menten kinetics, for one substrate and n competing species. Given the parameters of the system, we answer the basic question as to which species survive and which do not, and determine the limiting behaviors. The primary conclusion is that the species will survive whose Michaelis-Menten constant is smallest in comparison with its intrinsic rate of natural increase.

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A Mathematical Theory for Single-Nutrient Competition in Continuous Cultures of Micro-Organisms

Multiplicities and instabilities in chemically reacting systems — a review

The atmospheric concentration of methane, a greenhouse gas, has more than doubled during the past 200 years. Consequently, identifying the factors influencing the flux of methane into the atmosphere is becoming increasingly important. Methanotrophs, microaerophilic organisms widespread in aerobic soils and sediments, oxidize methane to derive energy and carbon for biomass. In so doing, they play an important role in mitigating the flux of methane into the atmosphere. Several physico-chemical factors influence rates of methane oxidation in soil, including soil diffusivity; water potential; and levels of oxygen, methane, ammonium, nitrate, nitrite, and copper. Most of these factors exert their influence through interactions with methane monooxygenase (MMO), the enzyme that catalyzes the reaction converting methane to methanol, the first step in methane oxidation. Although biological factors such as competition and predation undoubtedly play a role in regulating the methanotroph population in soils, and thereby limit the amount of methane consumed by methanotrophs, the significance of these factors is unknown. Obtaining a better understanding of the ecology of methanotrophs will help elucidate the mechanisms that regulate soil methane oxidation.

The Regulation of Methane Oxidation in Soil

Complex dynamics in a model microbial system

Consumer-resource interactions are fundamental components of ecological communities. Classic features of consumer-resource models are that temporal dynamics are often cyclic, with a ¼-period lag between resource and consumer population peaks. However, there are few published empirical examples of this pattern. Here, we show that many published examples of consumer-resource cycling show instead patterns indicating eco-evolutionary dynamics. When prey evolve along a trade-off between defence and competitive ability, two-species consumer-resource cycles become longer and antiphase (half-period lag, so consumer maxima coincide with minima of the resource species). Using stringent criteria, we identified 21 two-species consumer-resource time series, published between 1934 and 1997, suitable to investigate for eco-evolutionary dynamics. We developed a statistical method to probe for a transition from classic to eco-evolutionary cycles, and find evidence for eco-evolutionary type cycles in about half of the studies. We show that rapid prey evolution is the most likely explanation for the observed patterns.

A newly discovered role of evolution in previously published consumer-resource dynamics.

The predation of bacteria by protozoan in both continuous and batch cultures was studied using experimental and modeling techniques The predator organism was the ciliate, Tetrahymena pyriformis The bacterium, Aerobacter aerogenes, served as the prey Several batch growth responses were observed each initiated at a different nutrient level Continuous cultures were conducted over a range of dilution rates The models studied were partially successful in simulating the empirical data Deviations between the model and the actual population behavior are discussed and possible explanations for the differences proposed

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T. D. Lustig

Papers

Experimental and mathematical modeling studies of protozoan predation on bacteria