Hi Alex - we checked this with our staff from the Museum's Live Exhibits team, and they've supplied the following:
The type of adult ant produced depends on the level of nourishment provided to the larvae; normally larvae that are provided with the highest level of care and nourishment will become sexually mature winged females, or queens. Winged males and queens emerge in spring, normally after rain, mating occurs during Nuptial flight; after which the queen will found a new colony. Collecting a queen can be very difficult as meat ant nests can extend deep underground, up to 3m, this is where the queen and her brood live.
Hope that helps.