title: Methods to estimate breeding values in honey bees.
abstract: BACKGROUND
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  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.
authors.forename: Evert W
authors.initials: EW
authors.lastname: Brascamp
authors.forename: Piter
authors.initials: P
authors.lastname: Bijma
mesh_terms: D000818:Animals; D001516:Bees / Q000235:genetics*; D001947:Breeding / Q000379:methods*; D005260:Female; D006238:Haploidy; D008297:Male; D008957:Models, Genetic; D012098:Reproduction