Estimation in a multiplicative mixed model involving a genetic relationship matrix.

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.

Quantitative and molecular genetics of juvenile wood traits in radiata and slash/Caribbean pines.

The Juvenile Wood Initiative (JWI) project has been running successfully since July 2003 under a Research Agreement with FWPA and Letters of Association with the consortium partners STBA (Southern Tree Breeding Association), ArborGen and FPQ (Forestry Plantations Queensland). Over the last five and half years, JWI scientists in CSIRO, FPQ, and STBA have completed all 12 major milestones and 28 component milestones according to the project schedule. We have made benchmark progress in understanding the genetic control of wood formation and interrelationships among wood traits. The project has made 15 primary scientific findings and several results have been adopted by industry as summarized below. This progress was detailed in 10 technical reports to funding organizations and industry clients. Team scientists produced 16 scientific manuscripts (8 published, 1 in press, 2 submitted, and several others in the process of submission) and 15 conference papers or presentations. Primary Scientific Findings. The 15 major scientific findings related to wood science, inheritance and the genetic basis of juvenile wood traits are: 1. An optimal method to predict stiffness of standing trees in slash/Caribbean pine is to combine gravimetric basic density from 12 mm increment cores with a standing tree prediction of MoE using a time of flight acoustic tool. This was the most accurate and cheapest way to rank trees for breeding selection for slash/Caribbean hybrid pine. This method was also recommended for radiata pine. 2. Wood density breeding values were predicted for the first time in the STBA breeding population using a large sample of 7,078 trees (increment cores) and it was estimated that selection of the best 250 trees for deployment will produce wood density gains of 12.4%. 3. Large genetic variation for a suite of wood quality traits including density, MFA, spiral grain, shrinkage, acoustic and non-acoustic stiffness (MoE) for clear wood and standing trees were observed. Genetic gains of between 8 and 49% were predicted for these wood quality traits with selection intensity between 1 to 10% for radiata pine. 4. Site had a major effect on juvenile-mature wood transition age and the effect of selective breeding for a shorter juvenile wood formation phase was only moderate (about 10% genetic gain with 10% selection intensity, equivalent to about 2 years reduction of juvenile wood). 5. The study found no usable site by genotype interactions for the wood quality traits of density, MFA and MoE for both radiata and slash/Caribbean pines, suggesting that assessment of wood properties on one or two sites will provide reliable estimates of the genetic worth of individuals for use in future breeding. 6. There were significant and sizable genotype by environment interactions between the mainland and Tasmanian regions and within Tasmania for DBH and branch size. 7. Strong genetic correlations between rings for density, MFA and MoE for both radiata and slash/Caribbean pines were observed. This suggests that selection for improved wood properties in the innermost rings would also result in improvement of wood properties in the subsequent rings, as well as improved average performance of the entire core. 8. Strong genetic correlations between pure species and hybrid performance for each of the wood quality traits were observed in the hybrid pines. Parental performance can be used to identify the hybrid families which are most likely to have superior juvenile wood properties of the slash/Caribbean F1 hybrid in southeast Queensland. 9. Large unfavourable genetic correlations between growth and wood quality traits were a prominent feature in radiata pine, indicating that overcoming this unfavourable genetic correlation will be a major technical issue in progressing radiata pine breeding. 10. The project created the first radiata pine 18 k cDNA microarray and generated 5,952 radiata pine xylogenesis expressed sequence tags (ESTs) which assembled into 3,304 unigenes. 11. A total of 348 genes were identified as preferentially expressed genes in earlywood or latewood while a total of 168 genes were identified as preferentially expressed genes in either juvenile or mature wood. 12. Juvenile earlywood has a distinct transcriptome relative to other stages of wood development. 13. Discovered rapid decay of linkage disequilibrium (LD) in radiata pine with LD decaying to approximately 50% within 1,700 base pairs (within a typical gene). A total of 913 SNPS from sequencing 177,380 base pairs were identified for association genetic studies. 14. 149 SNPs from 44 genes and 255 SNPs from a further 51 genes (total 95 genes) were selected for association analysis with 62 wood traits, and 30 SNPs were shortlisted for their significant association with variation of wood quality traits (density, MFA and MoE) with individual significant SNPs accounting for between 1.9 and 9.7% of the total genetic variation in traits. 15. Index selection using breeding objectives was the most profitable selection method for radiata pine, but in the long term it may not be the most effective in dealing with negative genetic correlations between wood volume and quality traits. A combination of economic and biological approaches may be needed to deal with the strong adverse correlation.

Prediction of breeding values for average fruit weight in mango using a multivariate individual mixed model

Mango is an important horticultural fruit crop and breeding is a key strategy to improve ongoing sustainability. Knowledge of breeding values of potential parents is important for maximising progress from breeding. This study successfully employed a mixed linear model methods incorporating a pedigree to predict breeding values for average fruit weight from highly unbalanced data for genotypes planted over three field trials and assessed over several harvest seasons. Average fruit weight was found to be under strong additive genetic control. There was high correlation between hybrids propagated as seedlings and hybrids propagated as scions grafted onto rootstocks. Estimates of additive genetic correlation among trials ranged from 0.69 to 0.88 with correlations among harvest seasons within trials greater than 0.96. These results suggest that progress from selection for broad adaptation can be achieved, particularly as no repeatable environmental factor that could be used to predict G x E could be identified. Predicted breeding values for 35 known cultivars are presented for use in ongoing breeding programs.