# 4.2. Selection indexes and scores

Due to various reasons, there are cases where an organized data collection as described in section 4.1. is not possible or there is an incomplete data structure. In such cases, a direct comparison of the queens based on their performance can be used. However, one should be aware that this ranking is based on phenotypic value only and does not reflect the genetic potential of the queens. In addition, a lack of pedigree information can lead to inbreeding and it is not reliable in producing the next generation of queens. However, the following approaches can be useful if a breeding programme is not yet established or is in its infancy:

- Regression
analyses: In most breeding programmes, several traits are of interest
(morphological, behavioural and production level). Evaluation of the colonies
is only based on their own performance and additional information gained from
ancestors and progeny cannot be linked to them. In most cases, regression
analyses can be applied, e.g. linear, logistic or even ordinal, depending of
the quantity of information complementing the performance data. The adequate
choice is subject to understanding the data structure and statistical methods.
Nevertheless, in traits that are described quantitatively, linear regression
can be sufficient, with or without previous data transformation for obtaining
normality. If the traits are described in categorical values, logistic
regression can be used. The estimations will be a compromise between the
potential for corrections in environmental factors and the observed individual
performance leading to lower accuracy. In some cases, survival analyses are
appropriate (Rhodes
*et al*., 2004), particularly in disease tolerance. - Z-score: a simple way for comparing colonies across apiaries. It assumes that differences between apiary average scores are entirely due to location differences (this is not completely true due to interactions between the genetic origin and the location). Each testing apiary is described in terms of its own mean and standard deviation, then the individual colony performances are transformed into standard deviation units and compared (Rinderer, 1986). The resulting individual score is called z-score: z = X – M / s where: X = colony score; M = apiary average score; s = apiary standard deviation.
- Selection index
according to Rinderer (1986): the aim of a selection index is to express the
breeding value from the point of view of several traits in a single number. The
selection index proposed by Rinderer (1986) considers the colony’s individual
phenotypic scores, the heritability (
*h*^{2}) of the traits and the genetic correlations between them, as well as the economic value of the characteristics (based on breeding programme and beekeeper preference). A simple version of the index considers only the z-scores and the relative economic value of the chosen traits: I = z_{a}V + z_{b }where: z_{a}= z-score for trait A; z_{b}= z-score for trait B; V = relative importance of trait A compared to trait B (e.g. if trait A half as important as trait B then V = 0.5). - The above equation
can further incorporate the heritabilities and genetic correlations between
traits: I = z
_{a}V (*h*^{2}_{a}/*h*^{2}_{b}) + z_{b }(1 – r_{g}) Where:*h*^{2}_{a }*=*heritability of trait A;*h*^{2}_{b }*=*heritability of trait B; r_{g}= genetic correlation between traits (correlation between breeding values). - Selection index
according to Cornuet and Moritz (1987): when groups of sister queens are
considered in the testing programme, a selection index J which considers the
relationships inside the family (mother-daughter covariance, between sisters
covariance and aunt-niece covariance) can be used. Plausible values for
covariances result in the following formula, which considers a single trait: J
_{ij}= 0.163 (m_{ij}– m_{i}) + 0.348 m_{i }Where: m_{ij}= colony value; m_{i }= average family value.