Efficient methodologies based on animal models are widely used to estimate breeding values in farm animals. These methods are not applicable in honey bees because of their mode of reproduction. Observations are recorded on colonies, which consist of a single queen and thousands of workers that descended from the queen mated to 10 to 20 drones. Drones are haploid and sperms are copies of a drone’s genotype. As a consequence, Mendelian sampling terms of full-sibs are correlated, such that the covariance matrix of Mendelian sampling terms is not diagonal. In this paper, we show how the numerator relationship matrix and its inverse can be obtained for honey bee populations. We present algorithms to derive the covariance matrix of Mendelian sampling terms that accounts for correlated terms. The resulting matrix is a block-diagonal matrix, with a small block for each full-sib family, and is easy to invert numerically. The method allows incorporating the within-colony distribution of progeny from drone-producing queens and drones, such that estimates of breeding values weigh information from relatives appropriately. Simulation shows that the resulting estimated breeding values are unbiased predictors of true breeding values. Benefits for response to selection, compared to an existing approximate method, appear to be limited (~5%). Benefits may however be greater when estimating genetic parameters. This work shows how the relationship matrix and its inverse can be developed for honey bee populations, and used to estimate breeding values and variance components.

Heritabilities and genetic correlations were estimated for honey yield and behavioural traits in Austrian honey bees using data on nearly 15,000 colonies of the bee breeders association Biene Österreich collected between 1995 and 2014. The statistical models used distinguished between the genetic effect of workers and that of the queen of the colony. Heritability estimates for worker effect were larger than those for queen effect. Genetic correlations between both effects were negative. Heritability estimates for the sum of both effects (i.e. selection criterion) were 0.27, 0.37, 0.38 and 0.06 for honey yield, gentleness, calmness and swarming behaviour, respectively, indicating that meaningful genetic improvement is possible. Genetic correlations between these traits were generally small to medium, with large standard errors, with the exception of the high genetic correlation between gentleness and calmness. The models we present here can be used to estimate breeding values in honey bees.

Infestation with Varroa destructor is a serious cause of bee colony (Apis mellifera) losses on a global level. However, the presence of untreated survivor populations in many different regions supports the idea that selection for resistance can be successful. As colony survival is difficult or impossible to measure, differences in mite infestation levels and tests for specific behavioral traits are used for selective breeding for Varroa resistance. In this paper we looked into different definitions of mite infestation and linked these with brood hygiene (pin test), brood recapping and suppressed mite reproduction. We based our analyses on datasets of Apis mellifera carnica from three countries: Austria (147 records), Croatia (135) and Germany (207). We concluded that bee infestation in summer, adjusted for the level of natural mite fall in spring, is a suitable trait in the breeding objective, and also suggested including brood infestation rate and the increase rate of bee infestation in summer. Repeatability for bee infestation rate was about 0.55, for cells opened in pin test about 0.33, for recapping 0.35 and for suppressed mite reproduction (SMR) virtually zero. Although in most cases we observed correlations with the expected sign between infestation parameters and behavioral traits, the values were generally low (<0.2) and often not significantly different from zero.

Background: In honey bees, observations are usually made on colonies. The phenotype of a colony is affected by the average breeding value for the worker effect of the thousands of workers in the colony (the worker group) and by the breeding value for the queen effect of the queen of the colony. Because the worker group consists of multiple individuals, interpretation of the variance components and heritabilities of phenotypes observed on the colony and of the accuracy of selection is not straightforward. The additive genetic variance among worker groups depends on the additive genetic relationship between the drone-producing queens (DPQ) that produce the drones that mate with the queen. Results: Here, we clarify how the relatedness between DPQ affects phenotypic variance, heritability and accuracy of the estimated breeding values of replacement queens. Second, we use simulation to investigate the effect of assumptions about the relatedness between DPQ in the base population on estimates of genetic parameters. Relatedness between DPQ in the base generation may differ considerably between populations because of their history. Conclusions: Our results show that estimates of (co)variance components and derived genetic parameters were seriously biased (25% too high or too low) when assumptions on the relationship between DPQ in the statistical analysis did not agree with reality.

As usual in science, where one answer raises new questions, following our attempt to demystify the basic concept of honey bee breeding with our article The Basic Concept of Honey Bee Breeding Progr...