Figure 2.

ESS proportions of the males that are workers' sons (ψ) predicted by collective worker interests in colonies headed by a single monandrous queen (r = 3/4) as a function of the proportion of the queen's eggs that are female (f) according to (i) Model 1a (blue curves), where colonies are founded by lone queens and worker-laid eggs randomly compete with male- and gyne-destined queen-laid eggs and (ii) Model 1b (red curves), where colonies reproduce by swarming and worker-laid eggs randomly compete with male-, gyne- as well as worker-destined queen-laid eggs, thereby impacting colony productivity. The curve for Model 1b is drawn for parameter values appropriate for Melipona stingless bees (b = 0.044, q = 0.0847, μ = 0.024, see electronic supplementary material, tables S2–S4), and the dots are observed values in eight species of Melipona (see the electronic supplementary material, table S4). Curves are drawn for the case where n = 1 (dotted lines), 2 (dashed lines) or 10 (full lines) workers would reproduce in a colony.