Abstract
Competitive exclusion is proved for a discrete-time, size-structured,nonlinear matrix model of m-species competition in the chemostat. The winner isthe population able to grow at the lowest nutrient concentration. This extends theresults of earlier work of the first author [11] where the case $m = 2$ was treated.
Highlights
The classical chemostat model of microbial growth and competition for a limiting substrate has played a central role in population biology
A conceptually simpler approach to modeling size structure was taken by Gage, Williams and Horton in [5] who formulated what is referred to as a nonlinear matrix model for the evolution, in discrete time steps, of a finite set of biomass classes
There, it was shown that, like the classical chemostat model, competitive exclusion holds for two competing microbial populations
Summary
The classical chemostat model of microbial growth and competition for a limiting substrate has played a central role in population biology. There, it was shown that, like the classical chemostat model, competitive exclusion holds for two competing microbial populations. The analysis in [11] made use of the fact that an associated reduced discrete dynamical system, which captures the time evolution of the total biomass of each strain, is order-preserving in the case of two competitors so that monotonicity arguments could be applied. This feature does not hold for more than two competitors. The discrete-time, size-structured model of m-species competition in the chemostat is given by xin+1 Sn+1.
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