A quantitative genetic model for mixed diploid and triploid hybrid progenies in tree breeding and evolution

Interspecific hybridization has played a critical role in tree evolution and breeding. The findings of triploidy in forest trees stimulate the development of a quantitative genetic model to estimate the nature of gene action. The model is based on clonally replicated triploid progenies derived from a two-level population and individual-within-population mating design in which offspring have a double dose of alleles from the parent and a single dose of alleles from the other parent. With the same genetic assumptions of a diploid model, except non-Mendelian behavior at meiosis, and the experimental variances estimated from a linear statistical model, total genetic variances in the triploid progenies are separated into additive, dominance, and epistatic components. In addition, by combining the new model with the already existing model based on disomic expression, the partitioning of additive, dominant, and epistatic variances can be obtained for a mixed diploid/triploid F1 progeny population. This paper provides an alternative technique to study the modes of quantitative inheritance for outcrossing, long-lived forest trees in which inbred lines cannot be easily generated. The accuracy for estimating gene action using this technique is discussed.