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

Table 3 Phenotypic and genetic evolution of the population over 20 years for the parameter setups with an initial negative direct-maternal correlation

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)
	3	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)
	4	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)
	3	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)
	4	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)

Values in brackets represent sampling standard deviations over 160 replicates
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.
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.

ISSN: 1297-9686