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. Author summary Many organisms produce "public goods", substances that may directly benefit their competitors as well as themselves. Because goods production is costly, understanding the evolutionary stability of public goods production has been a subject of considerable interest: what keeps cheaters from taking over a population and driving producers to extinction? Here, we ask when partial privatization of public goods (that is, when producers retain some portion of the good for their own exclusive use) is sufficient to stabilize production even in the absence of spatial structure, and how this depends on environmental conditions. We derive lower bounds for the amount of privatization needed to stabilize production and find that these bounds depend critically on environmental conditions. We further investigate the case of two public goods, each needed for the acquisition of the other, and each a resource whose availability limits growth. We find that the ecological dynamics of such colimiting resources can interact, with privatization of one resource subsidizing more-public, or even fully public, production of the other. Finally, we offer the perspective that producers are not "losers" in a race of loss-of-function mutations, but rather can do no better than to produce the resource in a given set of conditions.
