title: Identifying environmental variables explaining genotype-by-environment interaction for body weight of rainbow trout (Onchorynchus mykiss): reaction norm and factor analytic models.
abstract: BACKGROUND
  Identifying the relevant environmental variables that cause GxE interaction is often difficult when they cannot be experimentally manipulated. Two statistical approaches can be applied to address this question. When data on candidate environmental variables are available, GxE interaction can be quantified as a function of specific environmental variables using a reaction norm model. Alternatively, a factor analytic model can be used to identify the latent common factor that explains GxE interaction. This factor can be correlated with known environmental variables to identify those that are relevant. Previously, we reported a significant GxE interaction for body weight at harvest in rainbow trout reared on three continents. Here we explore their possible causes.
  
  
  METHODS
  Reaction norm and factor analytic models were used to identify which environmental variables (age at harvest, water temperature, oxygen, and photoperiod) may have caused the observed GxE interaction. Data on body weight at harvest was recorded on 8976 offspring reared in various locations: (1) a breeding environment in the USA (nucleus), (2) a recirculating aquaculture system in the Freshwater Institute in West Virginia, USA, (3) a high-altitude farm in Peru, and (4) a low-water temperature farm in Germany. Akaike and Bayesian information criteria were used to compare models.
  
  
  RESULTS
  The combination of days to harvest multiplied with daily temperature (Day*Degree) and photoperiod were identified by the reaction norm model as the environmental variables responsible for the GxE interaction. The latent common factor that was identified by the factor analytic model showed the highest correlation with Day*Degree. Day*Degree and photoperiod were the environmental variables that differed most between Peru and other environments. Akaike and Bayesian information criteria indicated that the factor analytical model was more parsimonious than the reaction norm model.
  
  
  CONCLUSIONS
  Day*Degree and photoperiod were identified as environmental variables responsible for the strong GxE interaction for body weight at harvest in rainbow trout across four environments. Both the reaction norm and the factor analytic models can help identify the environmental variables responsible for GxE interaction. A factor analytic model is preferred over a reaction norm model when limited information on differences in environmental variables between farms is available.
authors.affiliation: Animal Breeding and Genomics Centre, Wageningen University, P,O, Box 338, 6700, AH, Wageningen, The Netherlands. panya.sae-lim@nofima.no.
authors.forename: Panya
authors.initials: P
authors.lastname: Sae-Lim
authors.forename: Hans
authors.initials: H
authors.lastname: Komen
authors.forename: Antti
authors.initials: A
authors.lastname: Kause
authors.forename: Han A
authors.initials: HA
authors.lastname: Mulder
mesh_terms: D000818:Animals; D017756:Aquaculture; D001499:Bayes Theorem; D001835:Body Weight; D001947:Breeding; D004777:Environment; D005260:Female; D005838:Genotype; D017686:Oncorhynchus mykiss / Q000235:genetics* / Q000254:growth & development*; D017440:Photoperiod