Mathematical model allowing the coexistence of closely related competitors at the initial stage of evolution

The mathematical model presented here aims to elucidate the essential mechanisms of coexistence of species, especially those of closely related forms, as a result of competition in the same environment. It describes a system where the fate of the competitors or mutants is observed at the initial stage of evolution. The model encompasses both the external variables and the internal state of the competitors, which differ only in one of the metabolic rate constants. Results of simulations, even with the simplified form of the model, show that stable coexistence of closely related forms in a uniform environment is possible. In addition, the model allows the analysis of the limitations on the level of differences and similarities among the competitors for achieving a state of coexistence. The essential mechanisms for the coexistence of closely related competitors are proposed to be the involvement of the metabolic network in allowing the same growth rate of competitors which have different internal states, and the interplay between the internal states of the competitors and the external variables of their environment.     

Fate of a mutant emerging at the initial stage of evolution

A simple system was constructed and used in the experimental elucidation of the fate of a mutant emerging in a population. ThreeEscherichia coli strains having the same genetic background except for their glutamine synthetase gene were used as model competitors. The difference in the enzyme gene were introduced by random mutation. Competition between these bacterial strains was carried out and observed in a continuous liquid culture. In most cases, the competitors stably coexist either in a steady state or in an oscillating state. In addition, the competition between the strains was found to be a deterministic process and not a stochastic one. These results showed that an emerging mutant in a population, be it a closely related one to the original members, can attain a state of stable coexistence even in a homogeneous environment. The ability of each of the emerging mutants to maintain its stable coexistence with the original population gives rise to the accumulation of various mutants in a population. Therefore, evolution starts from gradual accumulation of various mutants in the population, which in turn leads to the diversification of the population. As our experimental system is a minimum model for the various competitions in the natural ecosystem, the observed competitive coexistence is proposed to be a general phenomenon in nature.     

How small can the difference among competitors be for coexistence to occur

Closely related competitors comprising ofEscherichia coli strains having the same metabolic system and differing only with a few bases on the glutamine synthetase gene in the plasmid pKGN were previously shown to coexist in a chemostat. The differences among these closely related competitors can be considered large enough to allow coexistence as the level of enzyme activity is different. To bring the difference among competitors to the slightest possible, the mutation was introduced on the noncoding region of the plasmid pKGN harbored in the wild-type strain (strain W). The new strain, strain W’, carries the plasmid pKGN’ with a 4-base insertion at theHind III site in the polycloning site of pKGN. As the noncoding region is a nucleotide segment that is not translated into amino acids, the relatedness between strains W and W’ is the closest possible from the genetic point of view. Interestingly, though both strains are almost identical, they can coexist stably in a chemostat irrespective of the initial population size. These experimental results suggest that in the natural ecosystem, no matter how akin competitors are, coexistence is not impossible.     

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