# 4.1.2. Pedigree data

A unique queen identification number is a central requirement for genetic evaluation. The international unique queen identification number (QID) (see www.beebreed.eu for coding) consists of:

- Country code: 2 digits
- Breeder ID (within country) 3 digits
- Queen no. within the studbook of the breeder 5 digits
- Year of birth of the queen 4 digits

The international QID is automatically linked with an
alphabetic race code (**C** for *A. m. carnica*, **L** for *A. m. ligustica* and
**M** for *A. m. mellifera) *if the authorized breeder enters the
corresponding database with his password.

The Statistical model used in the modified BLUP Animal Model is the following:

where: **y** = a vector
of records/traits of the colonies (e.g., honey production, defence behaviour);
**b** = a vector of fixed year/beekeeper/location effects; **u _{1}**
= a vector of random worker (direct) effects;

**u**= a vector of random queen (maternal) effects;

_{2}**e**= a vector of random residual effects;

**X**= incidence matrix relating the observations to the corresponding environment (apiary within tester and year effect);

** **=incidence matrix relating the observations to
corresponding worker effects; = incidence matrix relating the observations
to the corresponding queen effects.

Solutions are obtained from the following mixed model equations:

where

with: _{ }= additive genetic
variance for worker effects; _{ }= additive genetic
variance for queen effects; _{ }= additive genetic covariance between worker and queen
effects; = residual error variance; = inverse
of the additive genetic relationship matrix.

Many production and behavioural traits are correlated genetically (are influenced by some of the same genes). The more traits that are targeted with the breeding programme, the less progress can be made for any single trait. A multi-trait approach, which considers the genetic correlation between traits, is applied so that predicted breeding values for individual traits in the breeding goal are combined according to the demands of the breeders (Ehrhardt and Bienefeld, unpublished).

Phenotypic and genetic parameters (Bienefeld and Pirchner, 1990; Bienefeld and Pirchner, 1991) are re-estimated from time to time. All aspects of estimation procedures for the estimation of variance components (data structure, method and model of estimation, effects included in the model, and so on) should be as similar as possible to the estimation procedures for breeding values.

The accuracy of genetic evaluation depends on the quality of the relationship information and the possibility of the statistical procedures to distinguish the genetic component from the total phenotypic variance. The estimations may even lead to misinterpretation if they are not statistically adequate. Breeding values, inbreeding coefficients, and tools for breeding plans should be published. Breeding values are estimated once a year and are published mid-February of each year.