Genomic prediction when some animals are not genotyped

Background

The use of genomic selection in breeding programs may increase the rate of genetic improvement, reduce the generation time, and provide higher accuracy of estimated breeding values (EBVs). A number of different methods have been developed for genomic prediction of breeding values, but many of them assume that all animals have been genotyped. In practice, not all animals are genotyped, and the methods have to be adapted to this situation.

Results

In this paper we provide an extension of a linear mixed model method for genomic prediction to the situation with non-genotyped animals. The model specifies that a breeding value is the sum of a genomic and a polygenic genetic random effect, where genomic genetic random effects are correlated with a genomic relationship matrix constructed from markers and the polygenic genetic random effects are correlated with the usual relationship matrix. The extension of the model to non-genotyped animals is made by using the pedigree to derive an extension of the genomic relationship matrix to non-genotyped animals. As a result, in the extended model the estimated breeding values are obtained by blending the information used to compute traditional EBVs and the information used to compute purely genomic EBVs. Parameters in the model are estimated using average information REML and estimated breeding values are best linear unbiased predictions (BLUPs). The method is illustrated using a simulated data set.

Conclusions

The extension of the method to non-genotyped animals presented in this paper makes it possible to integrate all the genomic, pedigree and phenotype information into a one-step procedure for genomic prediction. Such a one-step procedure results in more accurate estimated breeding values and has the potential to become the standard tool for genomic prediction of breeding values in future practical evaluations in pig and cattle breeding.     

Accuracy of direct genomic breeding values for nationally evaluated traits in US Limousin and Simmental beef cattle

Background

In national evaluations, direct genomic breeding values can be considered as correlated traits to those for which phenotypes are available for traditional estimation of breeding values. For this purpose, estimates of the accuracy of direct genomic breeding values expressed as genetic correlations between traits and their respective direct genomic breeding values are required.

Methods

We derived direct genomic breeding values for 2239 registered Limousin and 2703 registered Simmental beef cattle genotyped with either the Illumina BovineSNP50 BeadChip or the Illumina BovineHD BeadChip. For the 264 Simmental animals that were genotyped with the BovineHD BeadChip, genotypes for markers present on the BovineSNP50 BeadChip were extracted. Deregressed estimated breeding values were used as observations in weighted analyses that estimated marker effects to derive direct genomic breeding values for each breed. For each breed, genotyped individuals were clustered into five groups using K-means clustering, with the aim of increasing within-group and decreasing between-group pedigree relationships. Cross-validation was performed five times for each breed, using four groups for training and the fifth group for validation. For each trait, we then applied a weighted bivariate analysis of the direct genomic breeding values of genotyped animals from all five validation sets and their corresponding deregressed estimated breeding values to estimate variance and covariance components.

Results

After minimizing relationships between training and validation groups, estimated genetic correlations between each trait and its direct genomic breeding values ranged from 0.39 to 0.76 in Limousin and from 0.29 to 0.65 in Simmental. The efficiency of selection based on direct genomic breeding values relative to selection based on parent average information ranged from 0.68 to 1.28 in genotyped Limousin and from 0.51 to 1.44 in genotyped Simmental animals. The efficiencies were higher for 323 non-genotyped young Simmental animals, born after January 2012, and ranged from 0.60 to 2.04.

Conclusions

Direct genomic breeding values show promise for routine use by Limousin and Simmental breeders to improve the accuracy of predicted genetic merit of their animals at a young age and increase response to selection. Benefits from selecting on direct genomic breeding values are greater for breeders who use natural mating sires in their herds than for those who use artificial insemination sires. Producers with unregistered commercial Limousin and Simmental cattle could also benefit from being able to identify genetically superior animals in their herds, an opportunity that has in the past been limited to seed stock animals.     

Single-step genomic evaluation improves accuracy of breeding value predictions for resistance to infectious pancreatic necrosis virus in rainbow trout

The aim of this study was to compare the accuracy of breeding values (EBVs) predicted using the traditional pedigree based Best Linear Unbiased Prediction (PBLUP) and the single-step genomic Best Linear Unbiased Prediction (ssGBLUP) for resistance against infectious pancreatic necrosis virus (IPNV) in rainbow trout. A total of 2278 animals were challenged against IPNV and 768 individuals were genotyped using a 57?K single nucleotide polymorphism array for rainbow trout. Accuracies for both methods were assessed using five-fold cross-validation. The heritabilities were higher for PBLUP compared to ssGBLUP. The ssGBLUP accuracies outperformed PBLUP in 7 and 11% for days to death and binary survival, respectively. The ssGBLUP could be an alternative approach to improve the accuracy of breeding values for resistance against infectious pancreatic necrosis virus in rainbow trout, using information from genotyped and non-genotyped animals.     

Genomic selection for growth and wood quality in Eucalyptus: capturing the missing heritability and accelerating breeding for complex traits in forest trees

? Genomic selection (GS) is expected to cause a paradigm shift in tree breeding by improving its speed and efficiency. By fitting all the genome-wide markers concurrently, GS can capture most of the 'missing heritability' of complex traits that quantitative trait locus (QTL) and association mapping classically fail to explain. Experimental support of GS is now required. ? The effectiveness of GS was assessed in two unrelated Eucalyptus breeding populations with contrasting effective population sizes (N(e) = 11 and 51) genotyped with > 3000 DArT markers. Prediction models were developed for tree circumference and height growth, wood specific gravity and pulp yield using random regression best linear unbiased predictor (BLUP). ? Accuracies of GS varied between 0.55 and 0.88, matching the accuracies achieved by conventional phenotypic selection. Substantial proportions (74-97%) of trait heritability were captured by fitting all genome-wide markers simultaneously. Genomic regions explaining trait variation largely coincided between populations, although GS models predicted poorly across populations, likely as a result of variable patterns of linkage disequilibrium, inconsistent allelic effects and genotype × environment interaction. ? GS brings a new perspective to the understanding of quantitative trait variation in forest trees and provides a revolutionary tool for applied tree improvement. Nevertheless population-specific predictive models will likely drive the initial applications of GS in forest tree breeding.     

QTL mapping for resistance to Ceratocystis wilt in <Emphasis Type="Italic">Eucalyptus</Emphasis>

Ceratocystis wilt caused by the fungus Ceratocystis fimbriata, is currently one of the major diseases in commercial plantations of Eucalyptus trees in Brazil. Deployment of resistant genotypes has been the main strategy for effective disease management. The present study aimed at identifying genomic regions underlying the genetic control of resistance to Ceratocystis wilt in Eucalyptus by quantitative trait loci (QTL) mapping in an outbred hybrid progeny derived from a cross between (Eucalyptus dunnii × Eucalyptus grandis) × (Eucalyptus urophylla × Eucalyptus globulus). A segregating population of 127 individuals was phenotyped for resistance to Ceratocystis wilt using controlled inoculation under a completely randomized design with five clonal replicates per individual plant. The phenotypic resistance response followed a continuous variation, enabling us to analyze the trait in a quantitative manner. The population was genotyped with 114 microsatellite markers and 110 were mapped with an average interval of 12.3 cM. Using a sib-pair interval-mapping approach five QTLs were identified for disease resistance, located on linkage groups 1, 3, 5, 8, and 10, and their estimated individual heritability ranged from 0.096 to 0.342. The QTL on linkage group 3 overlaps with other fungal disease-resistance QTLs mapped earlier and is consistent with the annotation of several disease-resistance genes on this chromosome in the E. grandis genome. This is the first study to identify and attempt to quantify the effects of QTLs associated with resistance to Ceratocystis wilt in Eucalyptus.     

不同林分起源的相容性生物量模型构建

目前为止已有不同方法构建生物量相容性模型,但不同林分起源的生物量相容性模型很少报道。针对此问题,以150株南方马尾松(Pinus masson iana)地上生物量数据为例,利用比例平差法和非线性联立方程组法建立不同起源地上生物量以及干材、干皮、树枝和树叶各分项生物量相容的通用性模型。根据分配层次不同,两种方法又各自考虑总量直接控制和分级联合控制两种方案。从直径、树高、地径、枝下高和冠幅5个林分变量中选取不同的变量构建一元、二元和三元生物量模型,并利用加权最小二乘回归法消除生物量模型中存在的异方差性。结果为:比例平差法和非线性联立方程组法都能有效保证各分项生物量总和等于总生物量,模型预测精度满足要求。总体而言,非线性联立方程组方法比比例平差方法精度高,同时两种方法中总量直接控制法比分级联合控制法预测效果好;各分项生物量模型本身作为权函数能有效消除异方差;各分项对应的三元生物量模型预测精度最高,其次是二元生物量模型,最低是一元生物量模型,但这些差异不是很大。总之,为权衡考虑模型预测精度和调查成本,建议把直径和树高作为协变量利用总量直接控制非线性联立方程组法对不同起源生物量建模。     

Persistence of accuracy of genomic estimated breeding values over generations in layer chickens

Background

The predictive ability of genomic estimated breeding values (GEBV) originates both from associations between high-density markers and QTL (Quantitative Trait Loci) and from pedigree information. Thus, GEBV are expected to provide more persistent accuracy over successive generations than breeding values estimated using pedigree-based methods. The objective of this study was to evaluate the accuracy of GEBV in a closed population of layer chickens and to quantify their persistence over five successive generations using marker or pedigree information.

Methods

The training data consisted of 16 traits and 777 genotyped animals from two generations of a brown-egg layer breeding line, 295 of which had individual phenotype records, while others had phenotypes on 2,738 non-genotyped relatives, or similar data accumulated over up to five generations. Validation data included phenotyped and genotyped birds from five subsequent generations (on average 306 birds/generation). Birds were genotyped for 23,356 segregating SNP. Animal models using genomic or pedigree relationship matrices and Bayesian model averaging methods were used for training analyses. Accuracy was evaluated as the correlation between EBV and phenotype in validation divided by the square root of trait heritability.

Results

Pedigree relationships in outbred populations are reduced by 50% at each meiosis, therefore accuracy is expected to decrease by the square root of 0.5 every generation, as observed for pedigree-based EBV (Estimated Breeding Values). In contrast the GEBV accuracy was more persistent, although the drop in accuracy was substantial in the first generation. Traits that were considered to be influenced by fewer QTL and to have a higher heritability maintained a higher GEBV accuracy over generations. In conclusion, GEBV capture information beyond pedigree relationships, but retraining every generation is recommended for genomic selection in closed breeding populations.     

Genomic selection in forest tree breeding

Genomic selection (GS) involves selection decisions based on genomic breeding values estimated as the sum of the effects of genome-wide markers capturing most quantitative trait loci (QTL) for the target trait(s). GS is revolutionizing breeding practice in domestic animals. The same approach and concepts can be readily applied to forest tree breeding where long generation times and late expressing complex traits are also a challenge. GS in forest trees would have additional advantages: large training populations can be easily assembled and accurately phenotyped for several traits, and the extent of linkage disequilibrium (LD) can be high in elite populations with small effective population size (N _e) frequently used in advanced forest tree breeding programs. Deterministic equations were used to assess the impact of LD (modeled by N _e and intermarker distance), the size of the training set, trait heritability, and the number of QTL on the predicted accuracy of GS. Results indicate that GS has the potential to radically improve the efficiency of tree breeding. The benchmark accuracy of conventional BLUP selection is reached by GS even at a marker density ~2 markers/cM when N _e ≤ 30, while up to 20 markers/cM are necessary for larger N _e. Shortening the breeding cycle by 50% with GS provides an increase ≥100% in selection efficiency. With the rapid technological advances and declining costs of genotyping, our cautiously optimistic outlook is that GS has great potential to accelerate tree breeding. However, further simulation studies and proof-of-concept experiments of GS are needed before recommending it for operational implementation.     

Cross-validation analysis for genetic evaluation models for ranking in endurance horses

Ranking trait was used as a selection criterion for competition horses to estimate racing performance. In the literature the most common approaches to estimate breeding values are the linear or threshold statistical models. However, recent studies have shown that a Thurstonian approach was able to fix the race effect (competitive level of the horses that participate in the same race), thus suggesting a better prediction accuracy of breeding values for ranking trait. The aim of this study was to compare the predictability of linear, threshold and Thurstonian approaches for genetic evaluation of ranking in endurance horses. For this purpose, eight genetic models were used for each approach with different combinations of random effects: rider, rider–horse interaction and environmental permanent effect. All genetic models included gender, age and race as systematic effects. The database that was used contained 4065 ranking records from 966 horses and that for the pedigree contained 8733 animals (47% Arabian horses), with an estimated heritability around 0.10 for the ranking trait. The prediction ability of the models for racing performance was evaluated using a cross-validation approach. The average correlation between real and predicted performances across genetic models was around 0.25 for threshold, 0.58 for linear and 0.60 for Thurstonian approaches. Although no significant differences were found between models within approaches, the best genetic model included: the rider and rider–horse random effects for threshold, only rider and environmental permanent effects for linear approach and all random effects for Thurstonian approach. The absolute correlations of predicted breeding values among models were higher between threshold and Thurstonian: 0.90, 0.91 and 0.88 for all animals, top 20% and top 5% best animals. For rank correlations these figures were 0.85, 0.84 and 0.86. The lower values were those between linear and threshold approaches (0.65, 0.62 and 0.51). In conclusion, the Thurstonian approach is recommended for the routine genetic evaluations for ranking in endurance horses.     

Prediction of haplotypes for ungenotyped animals and its effect on marker-assisted breeding value estimation

Background

In livestock populations, missing genotypes on a large proportion of animals are a major problem to implement the estimation of marker-assisted breeding values using haplotypes. The objective of this article is to develop a method to predict haplotypes of animals that are not genotyped using mixed model equations and to investigate the effect of using these predicted haplotypes on the accuracy of marker-assisted breeding value estimation.

Methods

For genotyped animals, haplotypes were determined and for each animal the number of haplotype copies (nhc) was counted, i.e. 0, 1 or 2 copies. In a mixed model framework, nhc for each haplotype were predicted for ungenotyped animals as well as for genotyped animals using the additive genetic relationship matrix. The heritability of nhc was assumed to be 0.99, allowing for minor genotyping and haplotyping errors. The predicted nhc were subsequently used in marker-assisted breeding value estimation by applying random regression on these covariables. To evaluate the method, a population was simulated with one additive QTL and an additive polygenic genetic effect. The QTL was located in the middle of a haplotype based on SNP-markers.

Results

The accuracy of predicted haplotype copies for ungenotyped animals ranged between 0.59 and 0.64 depending on haplotype length. Because powerful BLUP-software was used, the method was computationally very efficient. The accuracy of total EBV increased for genotyped animals when marker-assisted breeding value estimation was compared with conventional breeding value estimation, but for ungenotyped animals the increase was marginal unless the heritability was smaller than 0.1. Haplotypes based on four markers yielded the highest accuracies and when only the nearest left marker was used, it yielded the lowest accuracy. The accuracy increased with increasing marker density. Accuracy of the total EBV approached that of gene-assisted BLUP when 4-marker haplotypes were used with a distance of 0.1 cM between the markers.

Conclusions

The proposed method is computationally very efficient and suitable for marker-assisted breeding value estimation in large livestock populations including effects of a number of known QTL. Marker-assisted breeding value estimation using predicted haplotypes increases accuracy especially for traits with low heritability.     

Accounting for genomic pre-selection in national BLUP evaluations in dairy cattle

Background

In future Best Linear Unbiased Prediction (BLUP) evaluations of dairy cattle, genomic selection of young sires will cause evaluation biases and loss of accuracy once the selected ones get progeny.

Methods

To avoid such bias in the estimation of breeding values, we propose to include information on all genotyped bulls, including the culled ones, in BLUP evaluations. Estimated breeding values based on genomic information were converted into genomic pseudo-performances and then analyzed simultaneously with actual performances. Using simulations based on actual data from the French Holstein population, bias and accuracy of BLUP evaluations were computed for young sires undergoing progeny testing or genomic pre-selection. For bulls pre-selected based on their genomic profile, three different types of information can be included in the BLUP evaluations: (1) data from pre-selected genotyped candidate bulls with actual performances on their daughters, (2) data from bulls with both actual and genomic pseudo-performances, or (3) data from all the genotyped candidates with genomic pseudo-performances. The effects of different levels of heritability, genomic pre-selection intensity and accuracy of genomic evaluation were considered.

Results

Including information from all the genotyped candidates, i.e. genomic pseudo-performances for both selected and culled candidates, removed bias from genetic evaluation and increased accuracy. This approach was effective regardless of the magnitude of the initial bias and as long as the accuracy of the genomic evaluations was sufficiently high.

Conclusions

The proposed method can be easily and quickly implemented in BLUP evaluations at the national level, although some improvement is necessary to more accurately propagate genomic information from genotyped to non-genotyped animals. In addition, it is a convenient method to combine direct genomic, phenotypic and pedigree-based information in a multiple-step procedure.     

Accuracy of genomic selection models in a large population of open-pollinated families in white spruce

Genomic selection (GS) is of interest in breeding because of its potential for predicting the genetic value of individuals and increasing genetic gains per unit of time. To date, very few studies have reported empirical results of GS potential in the context of large population sizes and long breeding cycles such as for boreal trees. In this study, we assessed the effectiveness of marker-aided selection in an undomesticated white spruce (Picea glauca (Moench) Voss) population of large effective size using a GS approach. A discovery population of 1694 trees representative of 214 open-pollinated families from 43 natural populations was phenotyped for 12 wood and growth traits and genotyped for 6385 single-nucleotide polymorphisms (SNPs) mined in 2660 gene sequences. GS models were built to predict estimated breeding values using all the available SNPs or SNP subsets of the largest absolute effects, and they were validated using various cross-validation schemes. The accuracy of genomic estimated breeding values (GEBVs) varied from 0.327 to 0.435 when the training and the validation data sets shared half-sibs that were on average 90% of the accuracies achieved through traditionally estimated breeding values. The trend was also the same for validation across sites. As expected, the accuracy of GEBVs obtained after cross-validation with individuals of unknown relatedness was lower with about half of the accuracy achieved when half-sibs were present. We showed that with the marker densities used in the current study, predictions with low to moderate accuracy could be obtained within a large undomesticated population of related individuals, potentially resulting in larger gains per unit of time with GS than with the traditional approach.     

Effects of propagule type on genetic parameters of wood density and growth in a loblolly pine progeny test at ages 10 and 11?years

Nine full-sib families of loblolly pine (Pinus taeda L.) were produced by a 3 × 3 factorial mating design. Rooted cuttings and seedlings of full-sib families were tested together in two field locations. Twelve-millimeter wood increment cores were collected from 10- and 11-year-old test trees. On each of the two sites, there were six blocks and a split-plot design, with propagule type as the whole plot and family as the sub-plot. In addition to the collection of wood samples, height and diameter of 1,600 trees were measured. No significant differences were found between cuttings and seedlings for wood density and growth traits. Significant family variation was found for growth and wood density. Genetic parameters estimated for wood density and growth traits using seedlings and rooted cuttings showed that individual-tree and family heritability estimates from rooted cuttings were similar to or higher than those from seedlings for all traits. Half-sib breeding values for parents were highly correlated based on seedling and rooted cutting estimates for height (0.95) and wood density (0.99) but not for diameter (0.56), which suggests that wood density and height breeding value estimates from rooted cuttings in clonal progeny tests can be estimated by traditional seedling tests, but not for tree diameter.     

SNP markers trace familial linkages in a cloned population of Pinus taeda—prospects for genomic selection

Advances in DNA sequencing technology have made possible the genotyping of thousands of single-nucleotide polymorphism (SNP) markers, and new methods of statistical analysis are emerging to apply these advances in plant breeding programs. We report the utility of markers for prediction of breeding values in a forest tree species using empirical genotype data (3,406 polymorphic SNP loci). A total of 526 Pinus taeda L. clones tested widely in field trials were phenotyped at age 5?years. Only 149 clones from 13 full-sib crosses were genotyped. Markers were fit simultaneously to predict marker additive and dominance effects. Subsets of the 149 genotyped clones were used to train a model using all markers. Cross-validation strategies were followed for the remaining subset of genotyped individuals. The accuracy of genomic estimated breeding values ranged from 0.61 to 0.83 for wood lignin and cellulose content, and from 0.30 to 0.68 for height and volume traits. The accuracies of predictions based on markers were comparable with the accuracies based on pedigree. Because of the small number of SNP markers used and the relatively small population size, we suggest that observed accuracies in this study trace familial linkage rather than historical linkage disequilibrium with trait loci. Prediction accuracies of models that use only a subset of markers were generally comparable with the accuracies of the models using all markers, regardless of whether markers are associated with the phenotype. The results suggest that using SNP loci for selection instead of phenotype is efficient under different relative lengths of the breeding cycle, which would allow cost-effective applications in tree breeding programs. Prospects for applications of genomic selection to P. taeda breeding are discussed.     

Inclusion of cow records in genomic evaluations and impact on bias due to preferential treatment

Background

Today, genomic evaluations are an essential feature of dairy cattle breeding. Initially, genomic evaluation targeted young bulls but recently, a rapidly increasing number of females (both heifers and cows) are being genotyped. A rising issue is whether and how own performance of genotyped cows should be included in genomic evaluations. The purpose of this study was to assess the impact of including yield deviations, i.e. own performance of cows, in genomic evaluations.

Methods

Two different genomic evaluations were performed: one including only reliable daughter yield deviations of proven bulls based on their non-genotyped daughters, and one including both daughter yield deviations for males and own yield deviations for genotyped females. Milk yield, the trait most prone to preferential treatment, and somatic cell count, for which such a bias is very unlikely, were studied. Data consisted of two groups of animals from the three main dairy breeds in France: 11 884 elite females genotyped by breeding companies and 7032 cows genotyped for a research project (and considered as randomly selected from the commercial population).

Results

For several measures that could be related to preferential treatment bias, the elite group presented a different pattern of estimated breeding values for milk yield compared to the other combinations of trait and group: for instance, for milk yield, the average difference between estimated breeding values with or without own yield deviations was significantly different from 0 for this group. Correlations between estimated breeding values with or without yield deviations were lower for elite females than for randomly selected cows for milk yield but were very similar for somatic cell count.

Conclusions

This study demonstrated that including own milk performance of elite females leads to biased (over-estimated) genomic evaluations. Thus, milk production records of elite cows require specific treatment in genomic evaluation.     

Linkage and Association Mapping for Two Major Traits Used in the Maritime Pine Breeding Program: Height Growth and Stem Straightness

BackgroundIncreasing our understanding of the genetic architecture of complex traits, through analyses of genotype-phenotype associations and of the genes/polymorphisms accounting for trait variation, is crucial, to improve the integration of molecular markers into forest tree breeding. In this study, two full-sib families and one breeding population of maritime pine were used to identify quantitative trait loci (QTLs) for height growth and stem straightness, through linkage analysis (LA) and linkage disequilibrium (LD) mapping approaches.ResultsThe populations used for LA consisted of two unrelated three-generation full-sib families (n = 197 and n = 477). These populations were assessed for height growth or stem straightness and genotyped for 248 and 217 markers, respectively. The population used for LD mapping consisted of 661 founders of the first and second generations of the breeding program. This population was phenotyped for the same traits and genotyped for 2,498 single-nucleotide polymorphism (SNP) markers corresponding to 1,652 gene loci. The gene-based reference genetic map of maritime pine was used to localize and compare the QTLs detected by the two approaches, for both traits. LA identified three QTLs for stem straightness and two QTLs for height growth. The LD study yielded seven significant associations (P ≤ 0.001): four for stem straightness and three for height growth. No colocalisation was found between QTLs identified by LA and SNPs detected by LD mapping for the same trait.ConclusionsThis study provides the first comparison of LA and LD mapping approaches in maritime pine, highlighting the complementary nature of these two approaches for deciphering the genetic architecture of two mandatory traits of the breeding program.     

Single-step methods for genomic evaluation in pigs

Genetic evaluation based on information from phenotypes, pedigree and markers can be implemented using a recently developed single-step method. In this paper we compare accuracies of predicted breeding values for daily gain and feed conversion ratio (FCR) in Danish Duroc pigs obtained from different versions of single-step methods, the traditional pedigree-based method and the genomic BLUP (GBLUP) method. In particular, we present a single-step method with an adjustment of the genomic relationship matrix so that it is compatible to the pedigree-based relationship matrix. Comparisons are made for both genotyped and non-genotyped animals and univariate and bivariate models. The results show that the three methods with marker information (two single-step methods and GBLUP) produce more accurate predictions of genotyped animals than the pedigree-based method. In addition, single-step methods provide more accurate predictions for non-genotyped animals. The results also show that the single-step method with adjusted genomic relationship matrix produce more accurate predictions than the original single-step method. Finally, the results for the bivariate analyses show a somewhat improved accuracy and reduced inflation of predictions for FCR for the two single-step methods compared with the univariate analyses. The conclusions are: first, the methods with marker information improve prediction compared with the pedigree-based method; second, a single-step method, contrary to GBLUP, provides improved predictions for all animals compared to the pedigree-based method; and third, a single-step method should be used with an adjustment of the genomic relationship matrix.     

基于树冠重叠面积的天然混交林林木竞争指数

构建基于树冠重叠面积和林木混交关系的竞争指数,探究天然混交林林分及主要树种竞争的表达方法,并以甘肃省小陇山林区锐齿槲栎天然混交林为研究对象,采用胸径、树高、冠幅、距离等信息的2期调查数据,对新构建的基于树冠重叠面积的天然混交林林木竞争(CIM)指数进行验证,并选取Spearman系数,对CIM竞争指数和传统竞争指数进行相关性分析。结果表明,采用树冠投影重叠和考虑树高关系确定竞争木的方法能有效避免竞争木多选或漏选; CIM1、CIM2、CIM3能够表达出混交林竞争压力变化,表现出竞争压力越大林木蓄积生长量越小的趋势,将树种混交因子引入竞争指数能够提高蓄积生长量与竞争指数的相关性,更加客观的描述林分中竞争状况。竞争指数与蓄积生长量相关性由大到小排序为CIM2>CIM3>CIM1>Bella竞争指数(CIO)>简单竞争指数(CI)>CIO2>CIO1,表明竞争指数 CIM2对混交林竞争表达更具参考意义。林分中主要树种锐齿槲栎由于相邻木中同树种相邻木增加,导致竞争压力增大。天然混交林中树种组成复杂多样,林木分布不均匀,在竞争指数中引入树种混交因子能够较为真实的反映林木竞争状况。     

Bayesian prediction of breeding values for multivariate binary and continuous traits in simulated horse populations using threshold-linear models with Gibbs sampling

Simulated data were used to determine the properties of multivariate prediction of breeding values for categorical and continuous traits using phenotypic, molecular genetic and pedigree information by mixed linear-threshold animal models via Gibbs sampling. Simulation parameters were chosen such that the data resembled situations encountered in Warmblood horse populations. Genetic evaluation was performed in the context of the radiographic findings in the equine limbs. The simulated pedigree comprised seven generations and 40 000 animals per generation. The simulated data included additive genetic values, residuals and fixed effects for one continuous trait and liabilities of four binary traits. For one of the binary traits, quantitative trait locus (QTL) effects and genetic markers were simulated, with three different scenarios with respect to recombination rate (r) between genetic markers and QTL and polymorphism information content (PIC) of genetic markers being studied: r = 0.00 and PIC = 0.90 (r0p9), r = 0.01 and PIC = 0.90 (r1p9), and r = 0.00 and PIC = 0.70 (r0p7). For each scenario, 10 replicates were sampled from the simulated horse population, and six different data sets were generated per replicate. Data sets differed in number and distribution of animals with trait records and the availability of genetic marker information. Breeding values were predicted via Gibbs sampling using a Bayesian mixed linear-threshold animal model with residual covariances fixed to zero and a proper prior for the genetic covariance matrix. Relative breeding values were used to investigate expected response to multi- and single-trait selection. In the sires with 10 or more offspring with trait information, correlations between true and predicted breeding values ranged between 0.89 and 0.94 for the continuous traits and between 0.39 and 0.77 for the binary traits. Proportions of successful identification of sires of average, favourable and unfavourable genetic value were 81% to 86% for the continuous trait and 57% to 74% for the binary traits in these sires. Expected decrease of prevalence of the QTL trait was 3% to 12% after multi-trait selection for all binary traits and 9% to 17% after single-trait selection for the QTL trait. The combined use of phenotype and genotype data was superior to the use of phenotype data alone. It was concluded that information on phenotypes and highly informative genetic markers should be used for prediction of breeding values in mixed linear-threshold animal models via Gibbs sampling to achieve maximum reduction in prevalences of binary traits.     

Best Linear Unbiased Prediction of Genomic Breeding Values Using a Trait-Specific Marker-Derived Relationship Matrix

Background

With the availability of high density whole-genome single nucleotide polymorphism chips, genomic selection has become a promising method to estimate genetic merit with potentially high accuracy for animal, plant and aquaculture species of economic importance. With markers covering the entire genome, genetic merit of genotyped individuals can be predicted directly within the framework of mixed model equations, by using a matrix of relationships among individuals that is derived from the markers. Here we extend that approach by deriving a marker-based relationship matrix specifically for the trait of interest.

Methodology/Principal Findings

In the framework of mixed model equations, a new best linear unbiased prediction (BLUP) method including a trait-specific relationship matrix (TA) was presented and termed TABLUP. The TA matrix was constructed on the basis of marker genotypes and their weights in relation to the trait of interest. A simulation study with 1,000 individuals as the training population and five successive generations as candidate population was carried out to validate the proposed method. The proposed TABLUP method outperformed the ridge regression BLUP (RRBLUP) and BLUP with realized relationship matrix (GBLUP). It performed slightly worse than BayesB with an accuracy of 0.79 in the standard scenario.

Conclusions/Significance

The proposed TABLUP method is an improvement of the RRBLUP and GBLUP method. It might be equivalent to the BayesB method but it has additional benefits like the calculation of accuracies for individual breeding values. The results also showed that the TA-matrix performs better in predicting ability than the classical numerator relationship matrix and the realized relationship matrix which are derived solely from pedigree or markers without regard to the trait. This is because the TA-matrix not only accounts for the Mendelian sampling term, but also puts the greater emphasis on those markers that explain more of the genetic variance in the trait.