Competitive exclusion in a discrete-time, size-structured chemostat model

Discrete and Continuous Dynamical Systems-series B - DISCRETE CONTIN DYN SYS-SER B 05/2000; 1(2). DOI: 10.3934/dcdsb.2001.1.183

ABSTRACT Competitive exclusion is proved for a discrete-time, size-structured, nonlinear matrix model of m-species competition in the chemostat. The winner is the population able to grow at the lowest nutrient concentration. This extends the results of earlier work of the rst author 11] where the case m = 2 was treated.

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    ABSTRACT: In biology, the principle of competitive exclusion, largely attributed to the Russian biologist G. F. Gause, states that two species competing for common resources (food, territory etc.) cannot coexist, and that one of the species drives the other to extinction. We make a survey of discrete-time mathematical models that address this issue and point out the main mathematical methods used to prove the occurrence of competitive exclusion in these models. We also offer examples of models in which competitive exclusion fails to take place, or at least it is not the only outcome. Finally, we present an extension of the competitive exclusion results in [1, 5] to a more general model.
    THEORY AND APPLICATIONS OF DIFFERENCE EQUATIONS AND DISCRETE DYNAMICAL SYSTEMS; Springer Proceedings in Mathematics & Statistics 102, Edited by Z. Alsharawi, J.M. Cushing, S. Elaydi, 01/2014: chapter Competitive Exclusion Through Discrete Time Models: pages 1-19; Springer-Verlag Berlin Heidelberg.
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    ABSTRACT: A system of difference equations derived from a general matrix population model with a dynamically varying resource is used to study two extreme forms of intra-specific competition. Both the per capita survival probability and birth rate are dependent on an individual's hierarchical ranking in the population. It is shown that contest competition yields a larger equilibrium size than the scramble competition. Moreover, contest competition may also be more stable in the sense that the interior steady state is always locally asymptotically stable if the inherent net reproductive number is larger than 1.
    Nonlinear Analysis 11/2005; 63(5). · 1.64 Impact Factor


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