Fig. 1From: A theoretical derivation of response to selection with and without controlled mating in honeybeesIllustration of the genetic contributions of the breeding and passive colonies with uncontrolled mating. This figure motivates the recursion formulas Eq. 1 and 3. Worker groups in year t receive their breeding values in equal parts from their queens and the drones that are mating partners of the queens. Passive queens in year t receive their breeding values either from unselected breeding colonies of year \(t-2\) (probability \(q_t\)) or from passive colonies of year \(t-2\) (probability \(1-q_t\)). In the former case, the average inherited breeding value is \(B_{t-2}\); in the latter case, it is \(P_{t-2}\). Breeding queens inherit their breeding values from selected breeding colonies of year \(t-2\), with average breeding values equal to \(B_{t-2}+S_{1,t-2}\). Drones which mate with breeding or passive queens in year t may be offspring (and thus carry the breeding values) of either unselected breeding queens (probability \(p_t\)) or passive queens (probability \(1-p_t\)) of year \(t-2\). For the breeding values of unselected breeding and passive queens of year \(t-2\), the same considerations apply as for those of year tBack to article page