Fig. 4: Graphical representation of the second condition necessary for coexistence. | The ISME Journal

Fig. 4: Graphical representation of the second condition necessary for coexistence.

From: Constrained proteome allocation affects coexistence in models of competitive microbial communities

Fig. 4

Here we consider a system with NS = 10 species and NR = 3 resources (for ease of representation). In this case, the system can be represented on a bi-dimensional simplex (i.e., a triangle) where each vertex corresponds to one of the available resources. On this simplex, we can draw the rescaled nutrient supply rate vector \(\vec {\hat s}\) (black star) and the rescaled initial proteome fractions \(\vec {\hat \varphi } _\sigma \left( {t = 0} \right)\) allocated by the species to the uptake and metabolism of the resources (colored triangles); their convex hull is drawn in orange. We have also drawn the stationary values \(\vec {\hat \varphi } _\sigma ^ \ast\) of the proteome fractions (colored circles), and their convex hull is drawn in purple. In this representation, if \(\vec {\hat s}\) lies on one on the sides of the simplex, it means that only two of the available resources are being externally supplied to the system, and analogously if one of the \(\vec {\hat \varphi } _\sigma ^ \ast\) lies on one of the sides of the simplex, it means that its corresponding species is uptaking and metabolizing only two of the available resources. In general, the positions of \(\vec {\hat s}\) and \(\vec {\hat \varphi } _\sigma ^ \ast\) depend on the relative ratios with which the resources are supplied or uptaken by the species.

Back to article page