Computation of the inverse additive relationship matrix for autopolyploid and multiple-ploidy populations.

Rules to generate the inverse additive relationship matrix (A ) are defined to enable the adoption restricted maximum likelihood (REML) and best linear unbiased prediction (BLUP) in autopolyploid populations with multiple ploidy levels. Many important agronomic, horticultural, ornamental, forestry, and aquaculture species are autopolyploids. However, the adoption of restricted maximum likelihood (REML), for estimating co/variance components, and best linear unbiased prediction (BLUP), for predicting breeding values, has been hampered in autopolyploid breeding by the absence of an appropriate means of generating the inverse additive relationship matrix (A ).

Genetic control of interactions among individuals: contrasting outcomes of indirect genetic effects arising from neighbour disease infection and competition in a forest tree.

Indirect genetic effects (IGEs) are heritable effects of individuals on trait values of their conspecifics. IGEs may substantially affect response to selection, but empirical studies on IGEs are sparse and their magnitude and correlation with direct genetic effects are largely unknown in plants. Here we used linear mixed models to estimate genetic (co)variances attributable to direct and indirect effects for growth and foliar disease damage in a large pedigreed population of Eucalyptus globulus.

Use of the numerator relationship matrix in genetic analysis of autopolyploid species.

Mixed models incorporating the inverse of a numerator relationship matrix (NRM) are widely used to estimate genetic parameters and to predict breeding values in animal breeding. A simple and quick method to directly calculate the inverse of the NRM has been historically developed for diploid animal species. Mixed models are less used in plant breeding partly because the existing method for diploids is not applicable to autopolyploid species.