Before its connections with other stoichiometric approaches were fully recognized, the theory of competition sketched above was well verified with experiments on microalgae and bacteria. Experimental studies also turned up some exceptions. Many studies of interacting microbial populations reveal an important role for excreted substances that act as either resources or toxins. Such interactions mediated by excreted substances are also amenable to stoichiometric approaches.

For example, one such interaction involves two populations that compete for one resource, while one of the populations excretes a substance used as a second resource by the other population. This complex interaction is common in aquatic ecosystems: autotrophic algae require inorganic nutrients, and are often limited by the supply of either nitrogen or phosphorus. Heterotrophic aquatic bacteria require the same inorganic nutrients, but also need organic carbon, which is excreted by nutrient-limited algae as a by-product of excess photosynthesis. So it is common to find algae and bacteria competing for an inorganic nutrient, while the bacteria rely on dissolved organic carbon produced by the algae, an interaction combining competition and commensalism.

To represent this interaction graphically on the resource plane, the ZNGI of the algae is a line perpendicular to the axis for the first resource, the inorganic nutrient, expressing the fact that they do not require the second resource, organic carbon (Figure 4). The ZNGI of the bacteria is rectilinear, because inorganic nutrient and organic carbon are essential resources for them. The heterotrophic bacteria in aquatic ecosystems are usually better competitors for inorganic nutrients than are the algae, implying that the vertical limb of their ZNGI falls



(Si, S2)


Nutrient 1 concentration, R1

Figure 4 Competition and commensalism involving two populations. 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 Mi), as are impact vectors implying stable coexistence (indicated by /,-).

to the left of the algal ZNGI, an arrangement that makes coexistence possible.

The bacteria consume both of these resources, so their mass-conservation constraint and impact vector have slopes representing the organismal stoichiometry of the bacteria, as did these graphical constructs for the competition example presented above. But these constructs differ for the algae. Their mass-conservation constraint again passes through the supply point (S\,S2), but has a negative slope expressing the stoichiometry of organic carbon excretion in relation to inorganic nutrient consumption. The impact vector shares this slope, representing consumption of one resource, and production of another. The arrangement shown in Figure 4 is stabilizing, because the underlying consumption and production dynamics amplify the negative effects that each population has on its own growth rate.

The supply point in Figure 4 is drawn with the S2 component positive to illustrate an abiotic supply of organic carbon in addition to algal excretion, because many inland and coastal aquatic ecosystems receive organic carbon washed off the nearby landscape. Offshore in the deep ocean, this supply point moves close to the axis for resource 1, the inorganic nutrient, because here production by resident algae is virtually the only source of organic carbon. Experiments to test this view of algal-bacterial interactions go the other direction by enriching aquatic microbial communities with organic carbon. This moves the supply point and the feasible region upon the resource plane, until the feasible region moves beyond the intersection of the ZNGI graphs and the bacteria are predicted to competitively exclude the algae, an outcome which has been observed.

Although many experiments with algae and bacteria appear consistent with the scenario sketched above, none permits a complete parametrization of the stoichiometric model of competition and commensalism. However, sufficient information is available for a similar interaction between yeast (Saccharomyces cerevisiae) and a bacterium (Lactobacillus casei) (Figure 5). The yeast consumed glucose while excreting the vitamin riboflavin, and the bacteria required both glucose and riboflavin as essential nutrients. Stable coexistence was observed experimentally, as predicted. Commensalism based on excreted substances is common in microorganisms, and theoretically tends to produce stable coexistence under broad conditions, suggesting that this interaction could be an important source of microbial diversity.

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