title: Estimation of genetic variance for macro- and micro-environmental sensitivity using double hierarchical generalized linear models.
abstract: BACKGROUND
  Genetic variation for environmental sensitivity indicates that animals are genetically different in their response to environmental factors. Environmental factors are either identifiable (e.g. temperature) and called macro-environmental or unknown and called micro-environmental. The objectives of this study were to develop a statistical method to estimate genetic parameters for macro- and micro-environmental sensitivities simultaneously, to investigate bias and precision of resulting estimates of genetic parameters and to develop and evaluate use of Akaike's information criterion using h-likelihood to select the best fitting model.
  
  
  METHODS
  We assumed that genetic variation in macro- and micro-environmental sensitivities is expressed as genetic variance in the slope of a linear reaction norm and environmental variance, respectively. A reaction norm model to estimate genetic variance for macro-environmental sensitivity was combined with a structural model for residual variance to estimate genetic variance for micro-environmental sensitivity using a double hierarchical generalized linear model in ASReml. Akaike's information criterion was constructed as model selection criterion using approximated h-likelihood. Populations of sires with large half-sib offspring groups were simulated to investigate bias and precision of estimated genetic parameters.
  
  
  RESULTS
  Designs with 100 sires, each with at least 100 offspring, are required to have standard deviations of estimated variances lower than 50% of the true value. When the number of offspring increased, standard deviations of estimates across replicates decreased substantially, especially for genetic variances of macro- and micro-environmental sensitivities. Standard deviations of estimated genetic correlations across replicates were quite large (between 0.1 and 0.4), especially when sires had few offspring. Practically, no bias was observed for estimates of any of the parameters. Using Akaike's information criterion the true genetic model was selected as the best statistical model in at least 90% of 100 replicates when the number of offspring per sire was 100. Application of the model to lactation milk yield in dairy cattle showed that genetic variance for micro- and macro-environmental sensitivities existed.
  
  
  CONCLUSIONS
  The algorithm and model selection criterion presented here can contribute to better understand genetic control of macro- and micro-environmental sensitivities. Designs or datasets should have at least 100 sires each with 100 offspring.
authors.affiliation: Wageningen UR Livestock Research, Animal Breeding and Genomics Centre, PO Box 65, 8200 AB, Lelystad, The Netherlands. han.mulder@wur.nl
authors.forename: Han A
authors.initials: HA
authors.lastname: Mulder
authors.forename: Lars
authors.initials: L
authors.lastname: Rönnegård
authors.forename: W Freddy
authors.initials: WF
authors.lastname: Fikse
authors.forename: Roel F
authors.initials: RF
authors.lastname: Veerkamp
authors.forename: Erling
authors.initials: E
authors.lastname: Strandberg
mesh_terms: D000465:Algorithms; D000818:Animals; D002417:Cattle; D003198:Computer Simulation; D004777:Environment; D059647:Gene-Environment Interaction; D014644:Genetic Variation; D016014:Linear Models; D008957:Models, Genetic; D009010:Monte Carlo Method; D019655:Quantitative Trait, Heritable