Figure 8.

Simulations reveal the behaviors shown in Figure 7. If queens seize a small amount of control over male production (a), then a subsequent mutation, acting in workers, does not cause them to become sterile (b). If queens seize a large amount of control over male production (c), then a subsequent mutation, acting in workers, causes them to become sterile (d). Thus, queen control can facilitate the formation of a sterile worker caste. (In (b) and (d), r _1/2 denotes the colony efficiency when 1/2 of workers in the colony have the phenotype for worker sterility. We follow the assumption for r _z in Equation (16) for determining the value of r _1/2 = 1.1 for these simulations. The initial conditions are (a) X _{AA, 0} = 1 − 10⁻³ and X _{AA, 1} = 10⁻³, (b) X _{CC, 0} = 1 − 10⁻¹ and X _{CC, 1} = 10⁻¹, (c) X _{AA, 0} = 1 − 10⁻³ and X _{AA, 1} = 10⁻³, and (d) X _{CC, 0} = 1 − 10⁻³ and X _{CC, 1} = 10⁻³. For (b) and (d), we introduce the c allele for worker sterility at time t = 2,000. For panels (a) and (c), ${\overline{p}}_a$ is given by Equation (12), while for panels (b) and (d), ${\overline{p}}_c$ is given by Equation (23). For calculating ${\overline{p}}_c$, p _1/2 is given by the assumption for p _z in Equation (16).)