Tore Ericsson

Hierarchical Spatial Process Models for Multiple Traits in Large Genetic Trials

This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets of multiple traits of interest. Direct application of such multivariate models to large spatial datasets is often computationally infeasible because of cubic order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several thousand iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negates the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects we discuss a multivariate predictive process that reduces the computational burden by projecting the original process onto a subspace generated by realizations of the original process at a specified set of locations (or knots). We illustrate the proposed methods using a synthetic dataset with multivariate additive and dominant genetic effects and anisotropic spatial residuals, and a large dataset from a scots pine (Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability.

Comparison of REML and Gibbs sampling estimates of multi-trait genetic parameters in Scots pine

Multi-trait (co)variance estimation is an important topic in plant and animal breeding. In this study we compare estimates obtained with restricted maximum likelihood (REML) and Bayesian Gibbs sampling of simulated data and of three traits (diameter, height and branch angle) from a 26-year-old partial diallel progeny test of Scots pine (Pinus sylvestris L.). Based on the results from the simulated data we can conclude that the REML estimates are accurate but the mode of posterior distributions from the Gibbs sampling can be overestimated depending on the level of the heritability. The mean and median of the posteriors were considerably higher than the expected values of the heritabilities. The confidence intervals calculated with the delta method were biased downwardly. The highest probablity density (HPD) interval provides a better interval estimate, but could be slightly biased at the lower level. Similar differences between REML and Gibbs sampling estimates were found for the Scots pine data. We conclude that further simulation studies are needed in order to evaluate the effect of different priors on (co)variance components in the genetic individual model.

High heritability for heartwood in north Swedish Scots pine

Abstract In 44-year-old full-sibs of north Swedish Scots pine (Pinus sylvestris L.), the estimated heritability of heartwood diameter was 0.5 despite the influence of environmental changes (caused by an earlier thinning) which apparently had reduced the heritabilities of height and diameter to around zero. The heritability of bole straightness was estimated to be 0.6. The coefficient of additive genetic variation of heartwood diameter was estimated at 0.2. If a reliable ‘heartwood-meter’ becomes available that allows nondestructive measurements to be rapidly made in the field it should be possible to breed for or against heartwood formation with less effort compared with that required in breeding aimed at improving regular production traits.

Genetic parameters for earlywood and latewood densities and development with increasing age in Scots pine

Abstract• Each annual ring in pines consists of earlywood and latewood with considerable difference in density and width. To get a better determination of the genetic regulation of total wood density in Scots pine (Pinus sylvestris L.), density and width of those ring sections were measured in annual ring numbers 12 to 21 of Scots pines in a full-sib progeny test. Tree height and stem diameter were also measured.• Heritabilities for the annual ring sections increased with age for earlywood density from 0.08 to approximately 0.25; latewood density showed similar reductions. Heritability over all 10 annual rings was 0.25 for earlywood density, 0.22 for latewood density, 0.29 for height and 0.10 for stem diameter. Genetic correlations between earlywood and latewood density and growth traits were negative, while they were strongly positive between densities of adjacent annual rings (0.70–1.0).• Despite the higher heritability of earlywood density, the strong positive genetic correlation between those traits indicates little benefit from focusing solely on earlywood density when selecting for wood density. Analysing earlywood and latewood separately does not benefit from including the width of the corresponding ring section as a covariate. Juvenile wood may possibly turn into mature wood 15–20 y from the pith.Résumé• Chaque cerne annuel chez les pins est composé de bois initial et de bois final avec une différence de densité et de largeur. Pour obtenir une meilleure détermination de la régulation génétique de la densité totale de bois chez le pin sylvestre (Pinus sylvestris L.), la densité et la largeur de ces sections de cernes annuels ont été mesurées chez 12 à 21 pins sylvestres dans un essai de descendance de plein frères. La hauteur des arbres et le diamètre des troncs ont également été mesurés.• Les héritabilités pour les sections de cernes annuels augmentent avec l’âge pour la densité du bois initial de 0,08 à environ 0,25 ; la densité du bois final a montré des réductions similaires. L’héritabilité sur l’ensemble de 10 cernes a été de 0,25 pour la densité du bois initial, de 0,22 pour la densité du bois final, de 0,29 pour la hauteur et de 0,10 pour diamètre du tronc. Les corrélations génétiques entre densité du bois initial et du bois final et caractéristiques de la croissance ont été négatives, alors qu’elles ont été fortement positives entre la densité des cernes adjacents (0,70–1,0).• Malgré la plus forte héritabilité de la densité du bois initial, la forte corrélation génétique entre ces caractéristiques montre qu’il y a peu d’intérêt à se concentrer uniquement sur la densité du bois initial lors de la sélection pour la densité du bois. Analyser bois initial et bois final séparément ne bénéficie pas de l’inclusion comme covariable de la largeur de la section du cerne correspondant. Le bois juvénile peut devenir à son tour du bois adulte, 15–20 ans à partir de la moelle.

Genetic analysis of fibre size in a full-sib Pinus sylvestris L. progeny test

Fibre length, fibre width, tree height and stem diameter in 25-yr-old Scots pine (Pinus sylvestris L.) were investigated by genetic analysis. The analysis was carried out on nearly 400 trees for all traits simultaneously using multiple-trait, individual tree equations with simultaneous variance estimation. Narrow-sense heritabilities were estimated at about 0.3 for all traits except for stem diameter, which was lower (0.17). Low genetic coefficients of variation for fibre length may be partially explained by the sampling method, which was 5 mm increment boring resulting in fibre fragmentation, but the method served well for heritability and correlation analysis. The additive genetic correlation was strongly negative between fibre length and stem diameter, and strongly positive between fibre width and growth traits. The pair of fibre traits showed mutually strong negative additive-genetic but weak positive environmental correlation. The pair of growth traits showed no genetic but strong positive environmental correlation. Other correlation estimates were minor and uncertain, with the exception of a weak negative environmental correlation between fibre length and stem diameter. An additional approach, where stem diameter was regarded as a covariate, revealed positive environmental correlation between fibre length and tree height and negative environmental correlation between fibre width and tree height.

Performance of Improved Pinus sylvestris in Northern Sweden

Genetic gain from utilization of improved planting stock of Scots pine (Pinus sylvestris L.) in northern Sweden is presented. A total of 36 genetic field tests, comprising more than 177 000 individual trees, was analysed with respect to tree height and survival at the age of 9–13 yrs. The field tests included control pollinated progenies from 434 phenotypically selected parent trees constituting the clones of 11 commercial seed orchards, and 16 natural stand control lots. The field test covered a wide geographical and climatic gradient (latitude 62.3–67.8° N, temperature sum 496–1056 day-degrees). covering the area used for commercial forestry in northern Sweden. Progenies of selected trees had 10% superior height growth, whereas differences in survival were small and non-significant. Thus, selection of individual trees within a stand did not result in the strong negative relationship between growth and survival normally observed among provenances of different latitudinal origin. The height superiority did not show any significant dependency on the growth conditions of the site (temperature climate), the transfer distance of the seedlings or the age of trees. The effect of improved regeneration stock on volume production during an entire rotation period was discussed using growth and yield functions, and indicated substantial volume gain at the time of both first thinning and final harvest.

Economic weight of tree survival relative to volume production in tree breeding: A case study with Pinus sylvestris in northern Sweden

Abstract The primary aim of the study was to estimate economic weights of survival relative to volume production per unit area, and to analyse the observable impact of changing survival, for five different breeding populations of Scots pine in northern Sweden. The economic weights were calculated from the model previously presented by the authors. Data from genetic field trials associated with the breeding populations were used both to estimate economic weights and to analyse the validity of the model. The breeding populations used were chosen to encompass a range of climatic conditions. The effects on the estimates of economic weights of increasing harshness (expressed as decreasing temperature sum), actual levels of both survival and patchiness of survival, and different initial stand densities were also analysed. The results showed that an appropriately parameterized model can be used to estimate economic weights for Scots pine in northern Sweden. Both the economic weight of survival and the observable impact of changing survival varied markedly between the studied breeding populations. Decreasing temperature sum had no trend with increasing economic weight of survival whereas decreasing survival and increasing patchiness of survival increased the estimated economic weight of survival more than three-fold.

Genetic parameter estimates of growth and survival of Pinus sylvestris with mixed model multiple-trait restricted maximum likelihood analysis

To improve adaptation and production of forest trees in areas with a harsh climate, it is important to consider survival ability in addition to growth traits. For breeding decisions, parameters such as heritabilities and genetic correlations between such traits need to be estimated. Multitrait, restricted maximum likelihood (REML) estimation was used in a full-sib Scots pine ( Pinus sylvestris L. ) progeny trial in northern Sweden to utilize all available information regarding survival and growth on the individual tree level and to avoid bias due to selection caused by mortality. The trial was evaluated at the ages of 6, 11 15 and 27 yrs, including estimation of age-age genetic correlations, which were high. During the period, the mortality reached 36%, the heritability of survival increased from 0.02 to 0.05, and heritability of tree height varied between 0.06 and 0.13. The genetic correlation estimates between survival and height were all positive and varied between 0.03 and 0.65.Univariate estimation, considering only growth and ignoring survival, resulted in much higher heritabilities of tree height. This should be an effect due to the mortality and thus a bias caused by selection.

A model to estimate economic weight of tree survival relative to volume production taking patchiness into account

Abstract Economic weights are needed for genetic selection to weigh different traits in multitrait breeding. The aim of this study was to develop, for commercial forest species, a model for estimating economic weights of survival relative to volume production per unit area. The model takes the patchiness across a stand and the polygenic nature of the factors influencing survival into account and consists of three submodels. The first submodel calculates volume production and a patchiness coefficient, using a production area that is divided into smaller units or production cells. The patchiness coefficient is defined in the model as the variance of survival between the production cells. The second submodel calculates volume production as a function of survival and the patchiness coefficient. The third submodel is a threshold model, which transforms the genetic change in survival from the observable scale to the underlying (liability) scale, thus providing a measure of economic weight. The model behaviour was studied using growth functions for Pinus sylvestris L. in northern Sweden. Both the absolute value of survival and its patchiness coefficient affected the projected production per unit area. When survival was higher than 50%, the relative economic weight of survival increased with decreasing survival and an increasing patchiness coefficient. The relative economic weight of survival was found to be insensitive to changes in site index and harvesting age, but was clearly affected by different initial stand densities.

Genetic evaluation, multiple‐trait selection criteria and genetic thinning of pinus contorta var. latifolia seed orchards in sweden

Seedling seed orchards were established in Sweden with 1112 open pollinated progenies of Pinus contorta Douglas ex Loudon plus‐trees, selected from 88 wild stands in western Canada. The progenies were also grown in Swedish test plantations. Breeding values (best linear unbiased predictors) were calculated for tree condition, height, and ramicorn whorl frequency, assessed at ages ranging between 8 and 12 yrs. On the harshest sites, damage caused by weather and fungi, e.g. Gremmeniella abietina, were also evaluated. Categorical data were transformed into values on a normal score scale to improve the efficiency of the evaluation. Breeding values for all assessed traits were combined to form total‐value indices. These indices were then used to guide the genetic thinning of the seed orchards, where single trees were selected from groups of four. The genetic gains resulting from the thinning operations on 1010 of the progenies were estimated to range from 2% for the milder utilization areas to 6% for the harshe...