Genetic-based interactions among tree neighbors: identification of the most influential neighbors, and estimation of correlations among direct and indirect genetic effects for leaf disease and growth in Eucalyptus globulus.

An individual's genes may influence the phenotype of neighboring conspecifics. Such indirect genetic effects (IGEs) are important as they can affect the apparent total heritable variance in a population, and thus the response to selection. We studied these effects in a large, pedigreed population of Eucalyptus globulus using variance component analyses of Mycosphearella leaf disease, diameter growth at age 2 years, and post-infection diameter growth at ages 4 and 8 years. In a novel approach, we initially modeled IGEs using a factor analytic (FA) structure to identify the most influential neighbor positions, with the FA loadings being position-specific regressions on the IGEs. This involved sequentially comparing FA models for the variance-covariance matrices of the direct and indirect effects of each neighbor. We then modeled IGEs as a distance-based, combined effect of the most influential neighbors. This often increased the magnitude and significance of indirect genetic variance estimates relative to using all neighbors. The extension of a univariate IGEs model to bivariate analyses also provided insights into the genetic architecture of this population, revealing that: (1) IGEs arising from increased probability of neighbor infection were not associated with reduced growth of neighbors, despite adverse fitness effects being evident at the direct genetic level; and (2) the strong, genetic-based competitive interactions for growth, established early in stand development, were highly positively correlated over time. Our results highlight the complexities of genetic-based interactions at the multi-trait level due to (co)variances associated with IGEs, and the marked discrepancy occurring between direct and total heritable variances.

Managing the rate of increase in average co-ancestry in a rolling front tree breeding strategy.

In breeding forest trees, as for livestock, the goal is to capture as much genetic gain as possible for the breeding objective, while limiting long- and short-term inbreeding. The Southern Tree Breeding Association (STBA) is responsible for breeding Australia's two main commercial forest tree species and has adopted algorithms and methods commonly used in animal breeding to achieve this balance. Discrete generation breeding is the norm for most tree breeding programmes. However, the STBA uses an overlapping generation strategy, with a new stream of breeding initiated each year. A feature of the species bred by the STBA (Pinus radiata and Eucalyptus globulus) is the long interval (up to 7 years) between when an individual is mated and when its progeny is first assessed in field trials and performance data included in the national performance database. Mate selection methods must therefore recognize the large pool of unmeasured progeny generated over recent years of crossing. In addition, the substantial delay between when an individual is selected in a field trial and when it is clonally copied into a mating facility (breeding arboretum) means that selection and mating must occur as a two-step process. In this article, we describe modifications to preselection and mate selection algorithms that allow unmeasured progeny (juveniles) to be recognized. We also demonstrate that the addition of hypothetical new progeny to the juvenile pool is important for computing the increase in average co-ancestry in the population. Methods outlined in this article may have relevance to animal breeding programmes where between mating and progeny measurement, new rounds of mating are initiated.

Use of the EM algorithm to detect QTL affecting multiple-traits in an across half-sib family analysis.

QTL detection experiments in livestock species commonly use the half-sib design. Each male is mated to a number of females, each female producing a limited number of progeny. Analysis consists of attempting to detect associations between phenotype and genotype measured on the progeny. When family sizes are limiting experimenters may wish to incorporate as much information as possible into a single analysis. However, combining information across sires is problematic because of incomplete linkage disequilibrium between the markers and the QTL in the population. This study describes formulae for obtaining MLEs via the expectation maximization (EM) algorithm for use in a multiple-trait, multiple-family analysis. A model specifying a QTL with only two alleles, and a common within sire error variance is assumed. Compared to single-family analyses, power can be improved up to fourfold with multi-family analyses. The accuracy and precision of QTL location estimates are also substantially improved. With small family sizes, the multi-family, multi-trait analyses reduce substantially, but not totally remove, biases in QTL effect estimates. In situations where multiple QTL alleles are segregating the multi-family analysis will average out the effects of the different QTL alleles.

Estimating genotypes with independently sampled descent graphs.

A method for estimating genotypic and identity-by-descent probabilities in complex pedigrees is described. The method consists of an algorithm for drawing independent genotype samples which are consistent with the pedigree and observed genotype. The probability distribution function for samples obtained using the algorithm can be evaluated up to a normalizing constant, and combined with the likelihood to produce a weight for each sample. Importance sampling is then used to estimate genotypic and identity-by-descent probabilities. On small but complex pedigrees, the genotypic probability estimates are demonstrated to be empirically unbiased. On large complex pedigrees, while the algorithm for obtaining genotype samples is feasible, importance sampling may require an infeasible number of samples to estimate genotypic probabilities with accuracy.

Asymptotic rates of response from forest tree breeding strategies using best linear unbiased prediction.

Genetic gain equations are developed for selection on multiple traits using either multi- or univariate best linear unbiased predictors (BLUP) and for selection under controlled and open pollination and polymix mating schemes. The equations assume an infinite population and account for the effects of selection. A comparison with simulated populations under the same mating schemes show that the gain equations predict selection response well, with the predictions having some upward bias. The gain equations are used to compare across mating schemes, to compare univariate to multivariate analyses, and to measure the reduction in the rate of genetic gain due to selection disequilibrium. Results show controlled pollination schemes can offer as much as a 56% advantage in genetic gain relative to open pollination. The reduction in the rate of genetic gain due to selection disequilibrium is approximately 27% under controlled pollination for the breeding goals studied. The results show a limited benefit in using multivariate analyses for predicting breeding values.

Implications of using an average relationship matrix in genetic evaluation for a population using multiple-sire matings.

SUMMARY: Ambiguous paternity can be incorporated into the mixed model equations (MME) by including the average numerator relatinship matrix (average A), which averages the true sire-offspring relationship over the putative sires. A previous study has shown that some overestimation of genetic trend results from this substitution. A population of 40 breeding females and 2 breeding males was simulated 1,000 times with either random mating or sequential selection continuing for 8 breeding cycles. In the selection case candidates were ranked on estimated breeding values (EBVs) calculated from the MME with an animal model and the average A. Variances of the EBVs and prediction errors were computed. The results showed the average A incorrectly perceives both the variance of family sizes among males and the variance loss due to selection to be smaller. This will lead to an overestimation of genetic trend. ZUSAMMENFASSUNG: Folgerungen aus der Anwendung einer durchschnittlichen Verwandtschaftsmatrix bei der Zuchtwertschätzung für eine Population mit mehreren Vätern in einer Paarungsgruppe In den Mischmodellgleichungen kann eine unklare väterliche Abstammung durch die Verwendung einer durchschnittlichen Verwandtschaftsmatrix, die die Abstammung zu gleichen Teilen über die möglichen Väter aufteilt, berücksichtigt werden. Eine frühere Arbeit hat gezeigt, daß diese Maßnahme zu einer gewissen Überschätzung des genetischen Fortschritts führt. Eine Population mit 40 weiblichen und 2 männlichen Tieren wurde 1000mal über 8 Paarungsperioden simuliert und zwar mit und ohne gerichteter Selektion. Im Falle der Selektion wurden die Tiere aufgrund der mit einem Tiermodell und der durchschnittlichen Verwandtschaftsmatrix geschätzten Zuchtwerte geordnet. Die Varianzen der Zuchtwerte und der Schätzfehler wurden berechnet. Die Ergebnisse zeigen, daß durch eine durch-schnittliche Verwandtschaftsmatrix die Varianz der Größe der Nachkommensgruppen der Väter und der Verlust an genetischer Varianz aufgrund der Selektion unterschätzt wird. Dies führt zu einer Überschätzung des genetischen Fortschritts.

Implications of using an average relationship matrix in genetic evaluation of a population using multiple-sire matings.

SUMMARY: Ambiguous paternity can be incorporated into the mixed model equations (MME) by including the average numerator relationship matrix (average A), which averages the true sire-offspring relationship over the putative sires. A previous study has shown that some overestimation of genetic trend results from this substitution. A population of 40 breeding females and 2 breeding males was simulated 1000 times with either random mating or sequential selection continuing for eight breeding cycles. In the selection case, candidates were ranked on estimated breeding values (EBVs) calculated from the MME with an animal model and the average A. Variances of the EBVs and prediction errors were computed. The results showed that the average A incorrectly perceives both the variance of family sizes among males and the variance loss due to selection to be smaller. This leads to an overestimation of genetic trend. ZUSAMMENFASSUNG: Auswirkung der durchschnittlichen genetischen Verwandtschaftsmatrix auf die Zuchtwertschätzung in einer Population mit Paarungen mehrerer Vatertiere Zweifelhafte väterliche Abstammung kann in die Mischmodellgleichung (MME) mittels durch- schnittlicher Numerator Verwandtschaftsmatrix (Durchschnitt A) eingebaut werden, die die durchschnittlichen wahren Verwandtschaften der in Frage kommenden Vatertiere beinhaltet. Eine frühere Untersuchung hat gezeigt, daß der genetische Trend dadurch eine gewisse Überschätzung erfährt. Eine Population aus 40 weiblichen und 2 männlichen Zuchttieren wurde 1000 mal simuliert, entweder unter Panmixie oder unter sequentieller Selektion durch acht Zuchtzyklen. Im Selektionsfall wurden die Kandidaten nach dem geschätzten Zuchtwert (EBV) rangiert der aus MME des Tiermodells mit durchschnittlicher A geschätzt worden ist. Varianzen der EBV und Schätzungsfehler wurden berechnet. Es zeigt sich, daß durchschnittliche A die Varianzen der Familiengrößen zwischen Vatertieren und den Varianzverlust durch Selektion als zu gering erfaßt, was zu einer Überschätzung des genetischen Trends führt.