Modeling microbial metabolic trade-offs in a chemostat
Fig 3
Multistability, chain of invasion, and non-invasible strategy.
A. Example of a metabolic model with a trade-off in allocation of resources for import of two essential nutrients, with the lower of the two import rates determining growth rate. Species Red and species Blue allocate resources differently (indicated by parameter αa, see S1 Appendix). B. Bistability of the system in (A) shown in chemical space. Black curves with arrows show the trajectories of simulations with different initial conditions. Inset: the fitness landscape created by species Red or Blue alone, with colors corresponding to the steady-state environments shown by colored dots in the main panel. C. The evolving fitness landscape. Fitness landscape created by species with different internal resource allocation strategies (marked by diamond shapes). Starting from species Blue, the species having the highest growth rate in the steady-state fitness landscape created by the “former” species is selected. This creates a chain of invasion from Blue to Light Green, Yellow, Deep Green, Deep Purple, all the way (intermediate processes omitted) to the species Black, which places itself on the peak of its own fitness landscape. The same procedure is also performed starting with species Red. D. Depiction of non-invasible strategies under different supply conditions. Black-white background indicates the maximal growth rate of the model in (A) under each environment, and the contour of maximal growth rates contains different strategies (represented by red-to-blue color). Growth contours of three species adopting one of the “maximizing strategies” are colored by their strategies. The supply conditions allowing these strategies to be “non-invasible” (supply lines) are marked by dashed black lines. E. Chain of invasion. Addition of the strategy with the fastest growth rate under the steady-state environment created by the existing consortium, as indicated in (C), is repeated 22 times. The sequentially added strategies are marked by colored circles, with the value of αa give for some representative strategies. An arrow from node j to node i indicates that strategy j can invade the environment created by strategy i.