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  • 1980-1984  (3)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 46 (1984), S. 155-174 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract If two microbial populations compete for a single resource in a homogeneous environment with time invariant inputs they cannot coexist indefinitely if the resource competed for is not renewed by biological activity within the system. Mathematical studies have shown that in a predator-prey system, where the resource (prey) is self-renewing, the two competitors (predators) can coexist in a limit cycle. This suggests that if the resource competed for is renewed by biological activity within the system coexistence can occur in any microbial system provided that it exhibits the same features as, but without being, a predator-prey one. A food chain involving commensalism, competition and amensalism is presented here. Two subcases are considered. It is only when maintenance effects are taken into account that coexistence, in limit cycles, can occur for this system. Limit cycle solutions for the system are demonstrated with the help of computer simulations. Some necessary conditions for coexistence are presented, as are some speculations regarding the possible physical explanations of the results.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-184X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Mathematical studies for ecosystems involving 2 predators competing for a growing prey population have shown that the 2 competitors can coexist in a state of sustained oscillations for a range of values of the system parameters. For the case of 1 suspension-feeding protozoan population, recent experimental observations suggest that the predator-prey interaction is complicated by the ability of the bacteria to grow on products produced by the lysis of protozoan cells. This situation is studied here for the case where 2 suspension-feeding protozoan populations compete for a growing bacterial population in a chemostat. Computer simulations show that the 2 protozoan populations can coexist over a range of the operating parameters. Some necessary conditions for coexistence are presented as are some speculations regarding the possible physical explanations of results.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 25 (1983), S. 2419-2439 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: It is known that two microbial populations competing for a single resource in a homogeneous environment with time-invariant inputs cannot coexist in a steady state. The case where two microbial populations compete for a single resource in a chemostat but one of them exhibits attachment to the chemostat walls is studied theoretically. Because of the cells' attachment to the walls, the environment is no longer homogeneous. The present article considers the case where the attached cells form no more than a monolayer. Other situations occur, often frequently, but we do not consider them here. Two models are used to represent the attachment to the walls: the Topiwala-Hamer model and a model which assumes that the attachment of microbial cells to the solid surfaces is a reversible process. The first model does not allow the population that exhibits wall attachment to wash out from the chemostat, in contrast to the second model (which nevertheless reduces to the first one in the limit). It has been found that in most of the possible cases for both models, the two competitors can coexist in a stable steady state for a wide range of the operating parameters space. The results of the stability analysis are discussed and analytical expressions for the conditions and the boundaries of the domains of stable coexistence are given for all the possible situations that may arise.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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