Following previous notation, the following recursive equation for gametic effects holds: (15) Each gametic effect is modelled as (i) a weighted average of the gametic effects of its ancestors (for non-founder individuals) or of haplotypic effects (for founder individuals), plus (ii) independent random variables due to mendelian sampling [ 15], ϕ.
The two building blocks in the previous section (modelling of expectations of gametic effects in founders by LD, and of non founders by conditioning on founders and LA) allow us to construct several linear models considering LD, LA, or both.
In addition, the increase in the estimate of the covariance between paternal and maternal gametic effects was also of this magnitude.
As expected, Model SD absorbed close to half of the additive genetic variance of the paternal gametic effects and another half of the maternal effects.
Finally, with Model AMS, the presence of a significant amount of variation in the paternal gametic effects reduced the magnitude of the direct and maternal additive genetic variance components compared to the results obtained with Model AM.
The estimation of gametic effects via marker-assisted BLUP requires the inverse of the conditional gametic relationship matrix G.
Model SD assigned most of the genetic variance to paternal gametic effects, although negligible amounts of variability were also assigned to the gametic maternal variance component.
Model SD assigned a significant proportion of the variance to both paternal and maternal gametic effects, but the covariance between them was almost null.
For the Bayesian approach, albeit the "data augmentation" of gametic effects in (23) or (24) partly simplifies computations, the full posterior conditionals of θ do not have closed forms; Metropolis-Hastings might be used.
Then,, where Q and G (the covariance matrix of gametic effects) are computed as above in equations (19, 20).
