Biases of incomplete linear models in forest genetic data analysis and optimal methods for estimating type B genetic correlations

Potential biases of incomplete mixed models in the estimation of variance component, heritability, and the prediction of breeding gains are theoretically formulated based on balanced data. For a given incomplete mixed model, the magnitudes of biases are functions of population genetic architecture, mating design, and field experimental designs, which can be precisely assessed using the derived formulae. It was found that most incomplete mixed models over-estimate additive genetic variance, resulting in upward-biased heritability and inflated genetic gains. The relative consequence of bias is severe for traits under weak additive genetic control with the strong influence of non-additive genetic effects. For incomplete mixed models ignoring additive genetic effects (GCA) x environment (E) interactions, the potential biases are linearly related to the number of environments included in the data. For incomplete mixed models ignoring dominance effects, biases are linearly proportional to the number of crosses that each parent is mated. For pure additive genetic models ignoring both dominance effects and GCA x E interaction, the biases are cumulative and can be as high as 60% of the true parameter. For unbalanced data, the formulae can be used to approximate the minimum biases for a given incomplete mixed model by substituting for the average number of design parameters of an experiment.;The search for optimal statistical methods in estimating type B genetic correlations is begun by developing a new univariate approach. The new method estimates type B genetic correlations using predicted parental GCA effects with the technique of best linear unbiased prediction (BLUP) in each individual environment. Numerical comparisons using simulated forest genetic data with various genetic architecture and data imbalance have demonstrated its unbiasedness, better match to underlying true population parameters, and suitability to various experimental designs and data imbalance.;The unbiasedness and precision of multivariate methods in estimating type B genetic correlations are also investigated with a simulation study. It was concluded that constrained multivariate methods produce empirically unbiased estimates of type B genetic correlations which have higher estimation precision, especially when heritabilities of traits are low in the concerned environments. The practical importance of keeping estimates within parameter space and other additional advantages makes the constrained multivariate method a desirable choice.