  A trademark of eusocial insect species is reproductive division of labor, in
which workers forego their own reproduction while the queen produces almost all
offspring. The presence of the queen is key for maintaining social harmony, but
the specific role of the queen in the evolution of eusociality remains unclear.
A long-discussed scenario is that a queen either behaviorally or chemically
sterilizes her workers. However, the demographic and ecological conditions that
enable such manipulation are unknown. Accordingly, we propose a simple model of
evolutionary dynamics that is based on haplodiploid genetics. We consider a
mutation that acts in a queen, causing her to control the reproductive behavior
of her workers. Our mathematical analysis yields precise conditions for the
evolutionary emergence and stability of queen-induced worker sterility. These
conditions do not depend on the queen's mating frequency. Moreover, we find
that queen control is always established if it increases colony reproductive
efficiency and can evolve even if it decreases colony efficiency. We further
outline the conditions under which queen control is evolutionarily stable
against invasion by mutant, reproductive workers.
