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Table 3 Phenotypic and genetic evolution of the population over 20 years for the parameter setups with an initial negative 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 3 1 26.11 (3.18) 2.42 (0.39) 4.41 (0.79) 0.75 (0.74) 37.35 (6.15) 5.67 (3.06) 6.16 (3.20) − 0.491 (0.240)
8 18.83 (2.38) 2.69 (0.35) 2.11 (0.66) 3.26 (0.64) 37.01 (5.64) 6.99 (2.43) 6.97 (2.51) − 0.525 (0.148)
4 1 26.47 (2.89) 3.79 (0.44) 6.31 (0.81) − 0.35 (0.79) 40.93 (6.09) 11.11 (4.63) 5.57 (2.44) − 0.461 (0.219)
8 20.45 (2.56) 3.85 (0.42) 3.92 (0.68) 2.18 (0.68) 38.69 (5.22) 13.38 (3.93) 6.87 (2.11) − 0.526 (0.155)
M 3 1 35.42 (4.93) 3.07 (0.41) 4.02 (0.98) 2.43 (0.98) 36.08 (5.00) 5.03 (2.59) 5.15 (2.67) − 0.528 (0.217)
8 24.41 (3.63) 3.29 (0.37) 2.02 (0.75) 4.51 (0.75) 35.89 (4.68) 6.10 (1.99) 6.37 (1.86) − 0.518 (0.131)
4 1 36.90 (4.17) 4.44 (0.48) 6.45 (0.83) 0.95 (0.88) 39.43 (5.90) 9.22 (4.10) 4.88 (2.37) − 0.503 (0.232)
8 25.41 (3.47) 4.44 (0.46) 4.05 (0.71) 3.14 (0.70) 37.68 (5.15) 12.52 (4.04) 6.13 (2.05) − 0.522 (0.141)
  1. Values in brackets represent sampling standard deviations over 160 replicates
  2. Parameter setups 3 and 4 are fully described in Table 1. In setup 3, direct (\(dir\)) and maternal (\(mat\)) genetic variances in the base population are equal, while in parameter setup 4, \(\sigma_{{BV_{dir} }}^{2} = 2 \cdot \sigma_{{BV_{mat} }}^{2}\). In both setups, the direct-maternal genetic correlation in the base population equals − 0.5.
  3. L is within-maternal-line selection; M is mass selection; \(n_{D}\) is the number of drones mating each queen; F is the inbreeding coefficient; \(\frac{{P_{{\left[ {24} \right]}} }}{{\sigma_{P} }}\) is the standardized performance of colonies in year 24; \(\frac{{BV_{dir}^{{Q_{{\left[ {23} \right]}} }} }}{{\sigma_{{BV_{dir} }} }}\) and \(\frac{{BV_{mat}^{{Q_{{\left[ {23} \right]}} }} }}{{\sigma_{{BV_{mat} }} }}\) are the direct and maternal standardized breeding values of queens born in year 23, respectively; \(V\left( {P_{{\left[ {24} \right]}} } \right)\) 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; \(r_{{BV_{dir} , BV_{{mat_{{\left[ {23} \right]}} }} }}\) is the genetic correlation between direct and maternal effects from queens born in year 23.