Abstract
The production of costly public goods (as distinct from metabolic byproducts) has largely been understood through the realization that spatial structure can minimize losses to non-producing "cheaters" by allowing for the positive assortment of producers. In well-mixed systems, where positive assortment is not possible, the stable production of public goods has been proposed to depend on lineages that become indispensable as the sole producers of those goods while their neighbors lose production capacity through genome streamlining (the Black Queen Hypothesis). Here, we develop consumer-resource models motivated by nitrogen-fixing, siderophore-producing bacteria that consider the role of colimitation in shaping eco-evolutionary dynamics. Our models demonstrate that in well-mixed environments, single "public goods" can only be ecologically and evolutionarily stable if they are partially privatized (i.e., if producers reserve a portion of the product pool for private use). Colimitation introduces the possibility of subsidy: strains producing a fully public good can exclude non-producing strains so long as the producing strain derives sufficient benefit from the production of a second partially private good. We derive a lower bound for the degree of privatization necessary for production to be advantageous, which depends on external resource concentrations. Highly privatized, low-investment goods, in environments where the good is limiting, are especially likely to be stably produced. Coexistence emerges more rarely in our mechanistic model of the external environment than in past phenomenological approaches. Broadly, we show that the viability of production depends critically on the environmental context (i.e., external resource concentrations), with production of shared resources favored in environments where a partially-privatized resource is scarce.