Heritability values were also estimated from genotype data, using a linear mixed model implemented on polygenic function [ 29, 30, 32– 32].
In brief, analyses were performed using a mixed model implemented through the software ASReml [ 28] where the trait ~ mean + fixed effects + SNP genotype + animal + error.
To estimate phenotypic correlations between different fatty acid contents, we adjusted the content of each fatty acid in each population separately by treating sex and slaughter batch as fixed effects and polygenic effects as random effects in a single-trait linear mixed model implemented by the polygenic function in the R package GenABEL [ 15].
The repeatability of estimated allele frequency in our dataset was determined using a linear mixed model implemented in the R package MCMCglmm [ 44] with locus included as a random effect, where repeatability was calculated as the proportion of the total variance explained by all loci.
To determine whether sniffing duration before a choice is made differed as a function of response choice (true positive, true negative, false positive, and false negative), we used a general linear mixed model (implemented using the lmer function of the lme4 package; Pinheiro and Bates 2000) with dog identity as a random effect.
We used Bayesian mixed models implemented in R (package mcmcglmm ) with uninformative priors, 17 000 iterations and burn‐in at 7000, which was always sufficient to insure auto‐correlations in Markov chain samples of < 0.1.
Finally, generalized linear mixed models, implemented in the 'glmmPQL' R CRAN package, were used to test whether admixture proportions of 'close to wheat' and 'distant from wheat' individuals differed statistically.
We also included two-way interaction effects between treatments, and between treatment and the variables sex, back pattern and population, using linear mixed models implemented in the nlme package in the software R [ 35].
We have shown that a mixed linear model implementing a realized relationship matrix based on aggregate SNP information can efficiently disentangle genetic effects from environmental family and cage effects when the number of causal genes is large and their effects are additive, e.g. REP and WT in this study.
A linear mixed effects model implemented using Restricted Maximum Likelihood was used to analyze the normalized log2 transformed fluorescence intensities for each gene, accounting for the effects of dye, treatment, bee and microarray.
