If one takes time to do a literature review on Genetic Parameters? in forestry there are at least two things that are very obvious:
- Normally, Genetic Parameters? are estimated using designed experiments, and
- The calculation of heritability (h2) will involve different Variance Components?, depending who is writing the paper.
Whatever the approach people are using to estimate Variance Components? (ANOVA expectations, REML, MCMC), they will end up with additive variance — or family variance that will estimate part of the additive variance — and a series of other components, one for each random effect, which are then used to calculate phenotypic variance.
Traditionally, heritability is the ratio of additive variance to phenotypic variance. Everybody seems to agree on the numerator; however, for a given experimental design people will choose to different components for the denominator. I will contend that for modern BLUP applications, only the additive and residual variances should be included in the denominator.
The process of predicting breeding values implies a reduction of dimensionality for the data set. For example, when using a regression approach, there is a translation from a bidimensional space (defined by progeny and parents coordinates) to a unidimensional space (defined by the regression line).
Work out this explanation for:
- Complete random trial — just to move to an ANOVA framework.
- A single-tree plots experiment with random blocks. Thus, the model comprises an overall mean, random blocks effects and additive genetic effects and residuals.
Heritability is often interpreted as the proportion of phenotypic variation explained by additive genetic variation. This is perfectly fine, but its main use is as an indicator of the accuracy of selection.
Initially, heritability was estimated as the regression of progeny phenotypic assessments on parental phenotypic assessments. This would consider either the phenotypes of only one parent or the average of both parents. Thus, heritability was a regression coefficient. When moving to agricultural and forestry designed experiments, it was necessary to introduce other sources of variation.
The introduction of selection indices by Hazel (in 1943) lent itself to account for different sources of variation.
Cotterill and Dean (I think in their book on selection indices) explain that the the selection index uses phenotypes that have been adjusted by their corresponding fixed effects, and that heritabilities used to construct the index coefficients should include the variances for all random effects.
This reasoning is appropriate for a two stage prediction process, whereby in a first instance there is estimation of variance components, often using linear mixed models. Later, in a second stage, the breeding values are predicted using a selection index common to all individuals, or specific to each family (BLP).
The question is ‘What happens when researchers start using BLUP tools?’ When using BLUP’s mixed model equations produce a simultaneous estimation of fixed effects and prediction of breeding values that takes into account both fixed and random effects.