Fielding, A.; Plotkin, J. B.; Akcay, E.

Individuals in many species perform several costly tasks whose benefits are shared with neighbors: bacteria secrete distinct public metabolites, plants emit distinct defensive volatiles, and human foragers acquire distinct shared foods. Performing one of these tasks often changes the benefits and costs of the other: a forager who brings in one kind of food provides different nutritional benefits to neighbors than one who brings in several kinds, and the difference depends on what the neighbors bring. Here we ask which divisions of labor evolve when two tasks interact. We model the interaction at both the group and the individual level, and we derive the long-run outcomes of the replicator dynamics as functions of the task payoffs and the interaction parameters. Interactions between tasks produce long-run outcomes that cannot occur when the tasks are independent. In particular, specialists, who perform one task but not the other, can coexist in a stable division of labor only if the tasks interact, and in most cases only if the interaction is more favorable when different individuals perform the two tasks than when one individual performs both. We also show that a specialized division of labor can be bistable with a non-specialized one, and we prove that, when both tasks are identical anti-coordination games, individuals in the specialized population have higher fitness. This bistability produces hysteresis in both the division of labor and fitness as interaction parameters vary. Populations with identical payoffs can therefore evolve to divisions of labor with different mean fitness.