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Table 1 Variable definitions

From: A theoretical derivation of response to selection with and without controlled mating in honeybees

Variable

Definition

t

Subscript referring to the year. If variables are used without this subscript it is assumed that they are constant for all years

\(B_t\) / \(P_t\)

Average true breeding value of breeding/passive colonies of year t \(=B_t-B_{t-1}\) (resp. \(=P_t-P_{t-1}\)) Annual genetic gain among the breeding/passive colonies \(=B_t-P_t\).

\(\Delta B_t\) / \(\Delta P_t\)

\(D_t\)

Genetic lag between the breeding population and the passive population

T

Time lag, time it takes for the passive population to reach the genetic level of the breeding population

\(p_t\), p

Probability that a sire drone in an uncontrolled mating comes from a breeding colony

\(q_t\), q

Proportion of passive queens with a dam queen from the breeding population

\(S_{1,t}\), \(S_1\)

Genetic selection differential of colonies selected for breeding queen production

\(S_{2,t}\), \(S_2\)

Genetic selection differential of colonies selected for DPQ production

\(N_b\) / \(N_p\)

Number of breeding/passive colonies per year

\(h^2_m\) / \(h^2_d\)

Maternal/direct heritability

\(r_{md}\)

Correlation between maternal and direct effects