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Table 2 Phenotypic and genetic evolution of the population over 20 years for the parameter setups without an initial direct–maternal correlation

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

Selection strategy Setup \(n_{D}\) F (%) \(\frac{{P_{{[{24}]}} }}{{\sigma_{P} }}\) \(\frac{{BV_{dir}^{{Q_{{[ {23} ]}} }} }}{{\sigma_{{BV_{dir} }} }}\) \(\frac{{BV_{mat}^{{Q_{{[ {23} ]}} }} }}{{\sigma_{{BV_{mat} }} }}\) \(V\left( {P_{{[ {24} ]}} } \right)\) \(V\left( {BV_{dir}^{{Q_{{[ {23} ]}} }} } \right)\) \(V\left( {BV_{mat}^{{Q_{{[ {23} ]}} }} } \right)\) \(r_{{BV_{dir} , BV_{{mat_{{[ {23} ]}} }} }}\)
L 1 1 25.68 (2.56) 4.24 (0.49) 5.92 (0.81) 3.45 (0.72) 40.09 (6.29) 5.47 (2.23) 5.88 (2.67) − 0.089 (0.275)
8 19.49 (2.19) 4.63 (0.39) 4.62 (0.63) 5.10 (0.64) 40.88 (5.93) 6.68 (2.20) 6.66 (2.15) − 0.030 (0.197)
16 18.57 (2.14) 4.82 (0.42) 4.60 (0.60) 5.43 (0.63) 39.31 (6.19) 6.89 (1.91) 6.38 (2.02) − 0.074 (0.203)
2 1 27.15 (3.36) 5.81 (0.54) 7.74 (0.80) 3.11 (0.79) 43.72 (7.50) 10.04 (4.41) 5.73 (2.58) − 0.022 (0.265)
8 20.23 (2.18) 6.11 (0.48) 6.07 (0.65) 4.79 (0.67) 42.64 (6.54) 12.50 (3.64) 6.48 (2.14) − 0.036 (0.206)
M 1 1 38.72 (4.97) 5.27 (0.50) 6.20 (0.90) 5.27 (0.87) 38.00 (5.57) 4.40 (1.87) 4.55 (2.22) − 0.062 (0.283)
8 26.58 (3.63) 5.53 (0.49) 5.11 (0.70) 6.47 (0.75) 37.72 (5.27) 5.92 (1.89) 5.76 (1.83) − 0.060 (0.185)
16 25.51 (3.23) 5.56 (0.44) 4.93 (0.77) 6.61 (0.67) 38.51 (5.00) 5.95 (7.89) 5.98 (1.60) − 0.054 (0.182)
2 1 38.94 (5.01) 6.76 (0.55) 7.96 (0.86) 4.88 (0.79) 40.82 (6.24) 7.98 (3.58) 4.47 (1.83) − 0.085 (0.289)
8 27.30 (4.05) 7.11 (0.53) 6.68 (0.73) 6.12 (0.68) 41.08 (6.06) 11.01 (3.17) 5.84 (1.98) − 0.064 (0.205)
  1. Values in brackets represent sampling standard deviations over 160 replicates
  2. Parameter setups 1 and 2 are fully described in Table 1. In setup 1, direct (\(dir\)) and maternal (\(mat\)) genetic variances in the base population are equal (\(\sigma_{{BV_{dir} }}^{2} = \sigma_{{BV_{mat} }}^{2}\)), while in parameter setup 2, \(\sigma_{{BV_{dir} }}^{2} = 2 \cdot \sigma_{{BV_{mat} }}^{2}\). In both setups, the direct-maternal genetic correlation in the base population is null.
  3. L is within-maternal-line selection; M is mass selection; \(n_{D}\) is number of drones mating each queen; F is the inbreeding coefficient; \(\frac{{P_{{[ {24} ]}} }}{{\sigma_{P} }}\) is the standardized performance of colonies in year 24; \(\frac{{BV_{dir}^{{Q_{{[ {23} ]}} }} }}{{\sigma_{{BV_{dir} }} }}\) and \(\frac{{BV_{mat}^{{Q_{{[ {23}]}} }} }}{{\sigma_{{BV_{mat} }} }}\) are the direct and maternal standardized breeding values of queens born in year 23, respectively; \(V\left( {P_{{[ {24} ]}} } \right)\) is the phenotypic variance of colonies performing in year 24; \(V\left( {BV_{dir}^{{Q_{23} }} } \right)\) and \(V\left( {BV_{mat}^{{Q_{23} }} } \right)\) are the direct and maternal genetic variances of queens born in year 23; \(r_{{BV_{dir} , BV_{{mat_{{[ {23}]}} }} }}\) is the genetic correlation between direct and maternal effects from queens born in year 23.