Paradoxes in Leaky Microbial Trade

Abstract

Microbes produce metabolic resources that are important for cell growth yet leak into the environment. Other microbes can use these resources, adjust their own metabolic production accordingly, and alter the resources available for others. We analyze a model in which metabolite concentrations, production regulation, and population frequencies coevolve in the simple case of two cell types producing two metabolites. We identify three paradoxes where changes that should intuitively benefit a cell type actually harm it. For example, a cell type can become more efficient at producing a metabolite and its relative frequency can decrease-or alternatively the total population growth rate can decrease. Another paradox occurs when a cell type manipulates its counterpart's production so as to maximize its own instantaneous growth rate, only to achieve a lower final growth rate than had it not manipulated. These paradoxes highlight the complex and counterintuitive dynamics that emerge in simple microbial economies.

Cooperation and stability for complex systems in resource-limited environments

“…This isn't so much inconsistent with those evolutionary results, but adds a new criterion for stable coexistence at a positive equilibrium, explicitly depending on environmental context. Finally, we note that studies of the evolution of mutualistic exchange have invoked "biological markets" (29,47), in analogy with economic markets. We therefore propose that the criteria for ecological stability derived here may also be important, or at least will provoke interesting exploration, in other complex systems where markets structure the form of exchange networks (14,23,25,40).…”

Fundamental challenges in packing problems: from spherical to non-spherical particles

“…This has elucidated in particular the validity of Ulam's conjecture that the sphere is the worst packing object in 3d [69]. Analytical progress to prove this conjecture locally, that is, for shapes deformed from the sphere, has recently been made [89].…”

Individual‐ versus group‐optimality in the production of secreted bacterial compounds

“…One issue with genetic forms of division of labor is that the frequency of the two interacting partners required for group optimality might not be stable. This means that in the absence of any mechanism stabilizing strain frequency, one cell type could become dominant and thereby lower group performance (Tasoff et al 2015; Kallus et al 2017; Taillefumier et al 2017). The above scenarios are different from the one considered in our study, where division of labor can occur in clonal populations through phenotypic specialization, and where phenotypic switching between compound production and non-production could guarantee a stable proportion of the two phenotypes.…”