  Microbes produce metabolic resources that are important for cell growth yet
leak across membranes into the extracellular environment. Other microbes in the
same environment can use these resources and adjust their own metabolic
production accordingly---causing other resources to leak into the environment.
The combined effect of these processes is an economy in which organismal growth
and metabolic production are coupled to others in the community. We propose a
model for the co-evolving dynamics of metabolite concentrations, production
regulation, and population frequencies for the case of two cell types, each
requiring and capable of producing two metabolites. In this model, beneficial
trade relations emerge without any coordination, via individual-level
production decisions that maximize each cell's growth rate given its perceived
environment. As we vary production parameters of the model, we encounter three
paradoxical behaviors, where a change that should intuitively benefit some cell
type, actually harms it. (1) If a cell type is more efficient than its
counterpart at producing a metabolite and becomes even more efficient, its
frequency in the population can decrease. (2) If a cell type is less efficient
than its counterpart at producing a metabolite but becomes less inefficient,
the growth rate of the population can decrease. (3) Finally, if a cell type
controls its counterpart's production decisions so as to maximize its own
growth rate, the ultimate growth rate it achieves can be lower than if the two
cell types each maximized their own growth. These three paradoxes highlight the
complex and counter-intuitive dynamics that emerge in simple microbial
economies.
