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

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)

	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

\(\sigma_{{BV_{dir} }}^{2}\), \(\sigma_{{BV_{mat} }}^{2}\) 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

ISSN: 1297-9686