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Table 1 Genetic and phenotypic variances, correlations between direct and maternal effects, and heritabilities for direct and maternal effects for the four parameter setups (1, 2, 3, and 4)

From: A simulation study of a honeybee breeding scheme accounting for polyandry, direct and maternal effects on colony performance

  Parameter setup
1 2 3 4
\(\sigma_{{BV_{dir} }}^{2}\) 10 20 10 20
\(\sigma_{{BV_{mat} }}^{2}\) 10 10 10 10
\(r_{{BV_{dir} , BV_{mat} }}\) 0 0 − 0.50 − 0.50
Monoandrous mating (queen mated with a single drone)
 \(\sigma_{P}^{2}\) 47.50 55.00 42.5 47.93
 \(h_{dir}^{2}\) 0.21 0.36 0.24 0.42
 \(h_{mat}^{2}\) 0.21 0.18 0.24 0.21
Polyandrous mating (queen mated with 8 drones)
 \(\sigma_{P}^{2}\) 43.13 46.25 38.13 39.18
 \(h_{dir}^{2}\) 0.23 0.43 0.26 0.51
 \(h_{mat}^{2}\) 0.23 0.22 0.26 0.26
  1. \(\sigma_{{BV_{dir} }}^{2}\), \(\sigma_{{BV_{mat} }}^{2}\) and \(\sigma_{P}^{2}\) represent, respectively, the variances (\(\sigma^{2}\)) of the queens’ direct (\(dir\)) and maternal (\(mat\)) breeding values (\(BV\)) and of the colony’s performance (\(P\)) in the base population; \(r_{{BV_{dir} , BV_{mat} }}\) is the direct-maternal genetic correlation; \(\sigma_{P}^{2}\) is the phenotypic variance in the initial population. \(h_{dir}^{2}\) and \(h_{mat}^{2}\) are the heritabilities for direct (\(dir\)) and maternal (\(mat\)) effects, respectively