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Table 2 Annual genetic gain in the breeding population (\(\Delta B_t\)) and passive population (\(\Delta P_t\)) as well as genetic lag (\(D_t\)) and time lag (T) between sub-populations in honeybees

From: A theoretical derivation of response to selection with and without controlled mating in honeybees

  Uncontrolled mating Controlled mating
\(\Delta B_t\) \(\frac{p+q}{3+3q}\cdot S_1\) \(\frac{S_1+S_2}{5}\)
\(\Delta P_t\) \(\frac{p+q}{3+3q}\cdot S_1\) \(\frac{S_1+S_2}{5}\)
\(D_t\) \(\frac{S_1}{1+q}\) \(\frac{6}{p+2q-pq}\cdot \frac{S_1+S_2}{5}-\frac{p}{p+2q-pq}\cdot S_1\)
T \(\frac{3}{p+q}\) \(\frac{6}{p+2q-pq}-\frac{5p}{p+2q-pq}\cdot \frac{S_1}{S_1+S_2}\)
  1. Results are given depending on the probability p of a sire drone in an uncontrolled mating to come from the breeding population, the probability q of a queen from the passive population to have a dam from the breeding population, and maternal and paternal genetic selection differentials for reproducing colonies, \(S_1\) and \(S_2\)