Stable variation in public-good production can generate biological division of labor. Two key drivers are the size of interacting groups and the degree of assortment (relatedness) among individuals with similar investment levels. Here we extend adaptive-dynamic models of continuous public-goods investment by allowing assortment in group formation. We show that increasing group size typically enlarges the range of benefit and cost curvatures that permit evolutionary branching, whereas assortment tends to shrink this range and prevents branching under complete relatedness. For a broad class of models, branching requires diminishing marginal public benefits and diminishing marginal private costs, with costs decreasing faster than benefits. Finally, we analyze post-branching dynamics for one and two public goods, and find that assortment can stabilize the resulting two-type division of labor. Together, these results show how group size, assortment, and payoff curvature jointly determine when heterogeneity in public-goods production can evolve.
Fielding, A., Akcay, E., Plotkin, J. B.
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