Allelopathy

Allelopathy involves negative interactions mediated by substances released by the competing populations. There are many possible configurations of such interactions. A population can excrete a substance inhibitory only to a single competitor species, or one that is inhibitory to many species, including perhaps itself. In addition, the populations involved might compete for one or more nutrient substances. To illustrate the stoichiometric approach to allelopathic interactions, consider two populations competing for a nutrient that both require, while each population also excretes a substance that inhibits both populations. For example, some of the bacterial strains inhabiting mammalian guts might compete for one of the dietary nutrients present, while excreting a common and inhibitory metabolic by-product, such as hydrogen sulfide or a volatile fatty acid.

On the plane of inhibitor concentration versus resource concentration, the ZNGI graphs of each population are now positively sloping curves (Figure 6). Increasing concentration of the inhibitor reduces the growth potential of a population, so to maintain a steady state the population must consume the nutrient resource more rapidly to restore its growth rate. When the ZNGI graphs of the populations intersect (as in Figure 6), steady-state coexistence is possible. Biologically, such an intersection arises from a tradeoff between the ability to compete for the nutrient in the absence of the inhibitor, and susceptibility to the inhibitory effects on growth rate.

As drawn in Figure 6, species 1 is a superior nutrient competitor but also more sensitive to the inhibitor. Feasibility of its coexistence with a more resistant, inferior competitor for the nutrient depends on mass-conservation constraints that express the stoichiometry of inhibitor production in relation to nutrient consumption for each population. These constraints are negatively sloping lines that pass through a supply point on the R-axis when the populations themselves are the only source of the inhibitor (Figure 6). As in other examples, feasibility of steady-state coexistence requires that these bounds enclose the intersection of the ZNGI graphs. Finally, the populations again have impact vectors displaying stability properties, and also expressing the stoichiometry of inhibitor production relative to nutrient consumption. When the more sensitive species produces relatively more of the inhibitor, its coexistence with the resistant species is stable because each species then has a stronger negative impact on its own growth rate than that of the other species.

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Figure 5 Competition and commensalism between a yeast, Saccharomyces cerevisiae (species 1) and a bacteriaum, Lactobacillus casei (species 2). Both species compete for glucose (resource 1), and the yeast produce riboflavin, which bacteria require as an essential nutrient (resource 2). (a) The ZNGI graphs (Zi) and impact vectors (I) predict that stable coexistence is possible. (b) The supply point (S1 ,S2) and mass-conservation constraints (Mi) for the nutrient supply tested, for which stable coexistence was predicted and observed. Drawn from the data of Megee RD, Drake JF, Frederickson AG, and Tsuchiya HM (1971) Studies in intermicrobial symbiosis: Saccharomyces cerevisiae and Lactobacillus casei. Canadian Journal of Microbiology 18: 1733-1742.

Nutrient concentration

Figure 6 Allelopathy involving two populations that compete for one nutrient. ZNGI graphs (indicated by Z) intersect at the circled point, making steady-state coexistence possible. The shaded feasible region for steady states is superimposed, bounded by mass-conservation constraints for populations 1 and 2 (indicated by M), as are impact vectors implying stable coexistence (indicated by I).

Nutrient concentration

Figure 6 Allelopathy involving two populations that compete for one nutrient. ZNGI graphs (indicated by Z) intersect at the circled point, making steady-state coexistence possible. The shaded feasible region for steady states is superimposed, bounded by mass-conservation constraints for populations 1 and 2 (indicated by M), as are impact vectors implying stable coexistence (indicated by I).

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