Iterative kriging for removing spatial autocorrelation in analysis of forest genetic trials

Conventional analysis of spatially correlated data in inadequately blocked field genetic trials may give erroneous results that would seriously affect breeding decisions. Forest genetic trials are commonly very large and strongly heterogeneous, so adjustments for micro-environmental heterogeneity become indispensable. This study explores the use of geostatistics to account for the spatial autocorrelation in four Pinus pinaster Ait. progeny trials established on hilly and irregular terrains with a randomized complete block design and large blocks. Data of five different traits assessed at age 8 were adjusted using an iterative method based on semivariograms and kriging, and the effects on estimates of variance components, heritability, and family effects were evaluated in relation to conventional analysis. Almost all studied traits showed nonrandom spatial structures. Therefore, after the adjustments for spatial autocorrelation, the block and family × block variance components, which were extremely high in the conventional analysis, almost disappeared. The reduction of the interaction variance was recovered by the family variance component, resulting in higher heritability estimates. The removal of the spatial autocorrelation also affected the estimation of family effects, resulting in important changes in family ranks after the spatial adjustments. Comparison among families was also greatly improved due to higher accuracy of the family effect estimations. The analysis improvement was larger for growth traits, which showed the strongest spatial heterogeneity, but was also evident for other traits such as straightness or number of whorls. The present paper demonstrates how spatial autocorrelation can drastically affect the analysis of forest genetic trials with large blocks. The iterative kriging procedure presented in this paper is a promising tool to account for this spatial heterogeneity.     

Genetics of microenvironmental sensitivity of body weight in rainbow trout (Oncorhynchus mykiss) selected for improved growth

Microenvironmental sensitivity of a genotype refers to the ability to buffer against non-specific environmental factors, and it can be quantified by the amount of residual variation in a trait expressed by the genotype's offspring within a (macro)environment. Due to the high degree of polymorphism in behavioral, growth and life-history traits, both farmed and wild salmonids are highly susceptible to microenvironmental variation, yet the heritable basis of this characteristic remains unknown. We estimated the genetic (co)variance of body weight and its residual variation in 2-year-old rainbow trout (Oncorhynchus mykiss) using a multigenerational data of 45,900 individuals from the Finnish national breeding programme. We also tested whether or not microenvironmental sensitivity has been changed as a correlated genetic response when genetic improvement for growth has been practiced over five generations. The animal model analysis revealed the presence of genetic heterogeneity both in body weight and its residual variation. Heritability of residual variation was remarkably lower (0.02) than that for body weight (0.35). However, genetic coefficient of variation was notable in both body weight (14%) and its residual variation (37%), suggesting a substantial potential for selection responses in both traits. Furthermore, a significant negative genetic correlation (-0.16) was found between body weight and its residual variation, i.e., rapidly growing genotypes are also more tolerant to perturbations in microenvironment. The genetic trends showed that fish growth was successfully increased by selective breeding (an average of 6% per generation), whereas no genetic change occurred in residual variation during the same period. The results imply that genetic improvement for body weight does not cause a concomitant increase in microenvironmental sensitivity. For commercial production, however, there may be high potential to simultaneously improve weight gain and increase its uniformity if both criteria are included in a selection index.     

Breeding bird diversity in relation to environmental gradients in China

Geographic variation in species richness has been explained by different theories such as energy, productivity, energy–water balance, habitat heterogeneity, and freezing tolerance. This study determines which of these theories best account for gradients of breeding bird richness in China. In addition, we develop a best-fit model to account for the relationship between breeding bird richness and environment in China. Breeding bird species richness in 207 localities (3271 km² per locality on average) from across China was related to thirteen environmental variables after accounting for sampling area. The Akaike's information criterion (AIC) was used to evaluate model performance. We used Moran's I to determine the magnitude of spatial autocorrelation in model residuals, and used simultaneous autoregressive model to determine coefficients of determination and AIC of explanatory variables after accounting for residual spatial autocorrelation. Of all environmental variables examined, normalized difference vegetation index, a measure of plant productivity, is the best variable to explain the variance in breeding bird richness. We found that species richness of breeding birds at the scale examined is best predicted by a combination of plant productivity, elevation range, seasonal variation in potential evapotranspiration, and mean annual temperature. These variables explained 47.3% of the variance in breeding bird richness after accounting for sampling area; most of the explained variance in richness is attributable to the first two of the four variables.     

Selection for uniformity in livestock by exploiting genetic heterogeneity of residual variance

In some situations, it is worthwhile to change not only the mean, but also the variability of traits by selection. Genetic variation in residual variance may be utilised to improve uniformity in livestock populations by selection. The objective was to investigate the effects of genetic parameters, breeding goal, number of progeny per sire and breeding scheme on selection responses in mean and variance when applying index selection. Genetic parameters were obtained from the literature. Economic values for the mean and variance were derived for some standard non-linear profit equations, e.g. for traits with an intermediate optimum. The economic value of variance was in most situations negative, indicating that selection for reduced variance increases profit. Predicted responses in residual variance after one generation of selection were large, in some cases when the number of progeny per sire was at least 50, by more than 10% of the current residual variance. Progeny testing schemes were more efficient than sib-testing schemes in decreasing residual variance. With optimum traits, selection pressure shifts gradually from the mean to the variance when approaching the optimum. Genetic improvement of uniformity is particularly interesting for traits where the current population mean is near an intermediate optimum.     

Genetic and environmental heterogeneity of residual variance of weight traits in Nellore beef cattle

Background

Many studies have provided evidence of the existence of genetic heterogeneity of environmental variance, suggesting that it could be exploited to improve robustness and uniformity of livestock by selection. However, little is known about the perspectives of such a selection strategy in beef cattle.

Methods

A two-step approach was applied to study the genetic heterogeneity of residual variance of weight gain from birth to weaning and long-yearling weight in a Nellore beef cattle population. First, an animal model was fitted to the data and second, the influence of additive and environmental effects on the residual variance of these traits was investigated with different models, in which the log squared estimated residuals for each phenotypic record were analyzed using the restricted maximum likelihood method. Monte Carlo simulation was performed to assess the reliability of variance component estimates from the second step and the accuracy of estimated breeding values for residual variation.

Results

The results suggest that both genetic and environmental factors have an effect on the residual variance of weight gain from birth to weaning and long-yearling in Nellore beef cattle and that uniformity of these traits could be improved by selecting for lower residual variance, when considering a large amount of information to predict genetic merit for this criterion. Simulations suggested that using the two-step approach would lead to biased estimates of variance components, such that more adequate methods are needed to study the genetic heterogeneity of residual variance in beef cattle.     

Genomic analysis of dominance effects on milk production and conformation traits in Fleckvieh cattle

Background

Estimates of dominance variance in dairy cattle based on pedigree data vary considerably across traits and amount to up to 50% of the total genetic variance for conformation traits and up to 43% for milk production traits. Using bovine SNP (single nucleotide polymorphism) genotypes, dominance variance can be estimated both at the marker level and at the animal level using genomic dominance effect relationship matrices. Yield deviations of high-density genotyped Fleckvieh cows were used to assess cross-validation accuracy of genomic predictions with additive and dominance models. The potential use of dominance variance in planned matings was also investigated.

Results

Variance components of nine milk production and conformation traits were estimated with additive and dominance models using yield deviations of 1996 Fleckvieh cows and ranged from 3.3% to 50.5% of the total genetic variance. REML and Gibbs sampling estimates showed good concordance. Although standard errors of estimates of dominance variance were rather large, estimates of dominance variance for milk, fat and protein yields, somatic cell score and milkability were significantly different from 0. Cross-validation accuracy of predicted breeding values was higher with genomic models than with the pedigree model. Inclusion of dominance effects did not increase the accuracy of the predicted breeding and total genetic values. Additive and dominance SNP effects for milk yield and protein yield were estimated with a BLUP (best linear unbiased prediction) model and used to calculate expectations of breeding values and total genetic values for putative offspring. Selection on total genetic value instead of breeding value would result in a larger expected total genetic superiority in progeny, i.e. 14.8% for milk yield and 27.8% for protein yield and reduce the expected additive genetic gain only by 4.5% for milk yield and 2.6% for protein yield.

Conclusions

Estimated dominance variance was substantial for most of the analyzed traits. Due to small dominance effect relationships between cows, predictions of individual dominance deviations were very inaccurate and including dominance in the model did not improve prediction accuracy in the cross-validation study. Exploitation of dominance variance in assortative matings was promising and did not appear to severely compromise additive genetic gain.     

Prediction of breeding values and selection responses with genetic heterogeneity of environmental variance

There is empirical evidence that genotypes differ not only in mean, but also in environmental variance of the traits they affect. Genetic heterogeneity of environmental variance may indicate genetic differences in environmental sensitivity. The aim of this study was to develop a general framework for prediction of breeding values and selection responses in mean and environmental variance with genetic heterogeneity of environmental variance. Both means and environmental variances were treated as heritable traits. Breeding values and selection responses were predicted with little bias using linear, quadratic, and cubic regression on individual phenotype or using linear regression on the mean and within-family variance of a group of relatives. A measure of heritability was proposed for environmental variance to standardize results in the literature and to facilitate comparisons to "conventional" traits. Genetic heterogeneity of environmental variance can be considered as a trait with a low heritability. Although a large amount of information is necessary to accurately estimate breeding values for environmental variance, response in environmental variance can be substantial, even with mass selection. The methods developed allow use of the well-known selection index framework to evaluate breeding strategies and effects of natural selection that simultaneously change the mean and the variance.     

Including dominance effects in the prediction model through locus-specific weights on heterozygous genotypes can greatly improve genomic predictive abilities

The dominance effect is considered to be a key factor affecting complex traits. However, previous studies have shown that the improvement of the model, including the dominance effect, is usually less than 1%. This study proposes a novel genomic prediction method called CADM, which combines additive and dominance genetic effects through locus-specific weights on heterozygous genotypes. To the best of our knowledge, this is the first study of weighting dominance effects for genomic prediction. This method was applied to the analysis of chicken (511 birds) and pig (3534 animals) datasets. A 5-fold cross-validation method was used to evaluate the genomic predictive ability. The CADM model was compared with typical models considering additive and dominance genetic effects (ADM) and the model considering only additive genetic effects (AM). Based on the chicken data, using the CADM model, the genomic predictive abilities were improved for all three traits (body weight at 12th week, eviscerating percentage, and breast muscle percentage), and the average improvement in prediction accuracy was 27.1% compared with the AM model, while the ADM model was not better than the AM model. Based on the pig data, the CADM model increased the genomic predictive ability for all the three pig traits (trait names are masked, here designated as T1, T2, and T3), with an average increase of 26.3%, and the ADM model did not improve, or even slightly decreased, compared with the AM model. The results indicate that dominant genetic variation is one of the important sources of phenotypic variation, and the novel prediction model significantly improves the accuracy of genomic prediction.Subject terms: Animal breeding, Quantitative trait     

The impact of population structure on genomic prediction in stratified populations

Key message

Impacts of population structure on the evaluation of genomic heritability and prediction were investigated and quantified using high-density markers in diverse panels in rice and maize.

Abstract

Population structure is an important factor affecting estimation of genomic heritability and assessment of genomic prediction in stratified populations. In this study, our first objective was to assess effects of population structure on estimations of genomic heritability using the diversity panels in rice and maize. Results indicate population structure explained 33 and 7.5 % of genomic heritability for rice and maize, respectively, depending on traits, with the remaining heritability explained by within-subpopulation variation. Estimates of within-subpopulation heritability were higher than that derived from quantitative trait loci identified in genome-wide association studies, suggesting 65 % improvement in genetic gains. The second objective was to evaluate effects of population structure on genomic prediction using cross-validation experiments. When population structure exists in both training and validation sets, correcting for population structure led to a significant decrease in accuracy with genomic prediction. In contrast, when prediction was limited to a specific subpopulation, population structure showed little effect on accuracy and within-subpopulation genetic variance dominated predictions. Finally, effects of genomic heritability on genomic prediction were investigated. Accuracies with genomic prediction increased with genomic heritability in both training and validation sets, with the former showing a slightly greater impact. In summary, our results suggest that the population structure contribution to genomic prediction varies based on prediction strategies, and is also affected by the genetic architectures of traits and populations. In practical breeding, these conclusions may be helpful to better understand and utilize the different genetic resources in genomic prediction.     

Simple consensus procedures are effective and sufficient in secondary structure prediction

We have analyzed the performance of majority voting on minimal combination sets of three state-of-the-art secondary structure prediction methods in order to obtain a consensus prediction. Using three large benchmark sets from the EVA server, our results show a significant improvement in the average Q3 prediction accuracy of up to 1.5 percentage points by consensus formation. The application of an additional trivial filtering procedure for predicted secondary structure elements that are too short, does not significantly affect the prediction accuracy. Our analysis also provides valuable insight into the similarity of the results of the prediction methods that we combine as well as the higher confidence in consistently predicted secondary structure.     

Understanding the unexplained: The magnitude and correlates of individual differences in residual variance

Behavioral and physiological ecologists have long been interested in explaining the causes and consequences of trait variation, with a focus on individual differences in mean values. However, the majority of phenotypic variation typically occurs within individuals, rather than among individuals (as indicated by average repeatability being less than 0.5). Recent studies have further shown that individuals can also differ in the magnitude of variation that is unexplained by individual variation or environmental factors (i.e., residual variation). The significance of residual variation, or why individuals differ, is largely unexplained, but is important from evolutionary, methodological, and statistical perspectives. Here, we broadly reviewed literature on individual variation in behavior and physiology, and located 39 datasets with sufficient repeated measures to evaluate individual differences in residual variance. We then analyzed these datasets using methods that permit direct comparisons of parameters across studies. This revealed substantial and widespread individual differences in residual variance. The magnitude of individual variation appeared larger in behavioral traits than in physiological traits, and heterogeneity was greater in more controlled situations. We discuss potential ecological and evolutionary implications of individual differences in residual variance and suggest productive future research directions.     

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.     

香椿种质生长及叶部表型性状的遗传变异分析

以84个香椿(Toona sinensis(A.Juss.)Roem.)种质为材料,对其2个生长性状和18个叶部性状(包含6个质量性状和12个数量性状)进行测定。结果显示,香椿6个叶部质量性状变异类型丰富,呈现出多态化特点,单一性状的主要表型多为1~2个。苗高、地径及叶部表型等14个数量性状在种质间的差异均达到极显著水平,且除地径外,其他性状的遗传方差分量均大于环境方差分量,表明此类性状主要受遗传控制。参试的14个数量性状的平均表型变异系数为20.35%,平均遗传变异系数为16.36%;综合表型和遗传变异系数,叶柄长度较其他性状变异大,而叶片夹角稳定性最高,各数量性状(除地径外)遗传变异系数与表型变异系数之差小于7%。香椿种质各性状间Shannon-Weaver遗传多样性指数相差不大(1.892~2.069),遗传多样性水平高,具有良好的遗传改良基础。聚类分析可将84个香椿种质分为5类,类群Ⅰ表现为生长旺盛、小比叶重型;类群Ⅱ生长较快、叶片较大;类群Ⅲ种质数量最多,属生长缓慢、大比叶重型;类群Ⅳ特征为大叶片、多叶型;类群Ⅴ为小叶片、稀叶型。研究结果表明参试香椿种质变异丰富,遗传多样性水平高,能为良种选育、遗传改良等研究提供丰富的遗传材料。     

Improving accuracy of breeding values by incorporating genomic information in spatial-competition mixed models

Climate change and the increasing demand for sustainable energy resources require urgent strategies to increase the accuracy of selection in tree breeding (associated with higher gain). We investigated the combined pedigree and genomic-based relationship approach and its impact on the accuracy of predicted breeding values using data from 5-year-old Eucalyptus grandis progeny trial. The number of trees that can be genotyped in a tree breeding population is limited; therefore, the combined approach can be a feasible and efficient strategy to increase the genetic gain and provide more accurate predicted breeding values. We calculated the accuracy of predicted breeding values for two growth traits, diameter at breast height and total height, using two evaluation approaches: the combined approach and the classical pedigree-based approach. We also investigated the influence of two different trait heritabilities as well as the inclusion of competition genetic effects or environmental heterogeneity in an individual-tree mixed model on the estimated variance components and accuracy of breeding values. The genomic information of genotyped trees is automatically propagated to all trees with the combined approach, including the non-genotyped mothers. This increased the accuracy of overall breeding values, except for the non-genotyped trees from the competition model. The increase in the accuracy was higher for the total height, the trait with low heritability. The combined approach is a simple, fast, and accurate genomic selection method for genetic evaluation of growth traits in E. grandis and tree species in general. It is simple to implement in a traditional individual-tree mixed model and provides an easy extension to individual-tree mixed models with competition effects and/or environmental heterogeneity.     

Lifetime Reproductive Success and Heritability in Nature

The observation that traits closely related to fitness ("fitness traits") have lower heritabilities than traits more distantly associated with fitness has traditionally been framed in terms of Fisher's fundamental theorem of natural selection-fitness traits are expected to have low levels of additive genetic variance due to rapid fixation of alleles conferring highest fitness. Subsequent treatments have challenged this view by pointing out that high environmental and nonadditive genetic contributions to phenotypic variation may also explain the low heritability of fitness traits. Analysis of a large data set from the collared flycatcher Ficedula albicollis confirmed a previous finding that traits closely associated with fitness tend to have lower heritability. However, analysis of coefficients of additive genetic variation (CVA) revealed that traits closely associated with fitness had higher levels of additive genetic variation (VA) than traits more distantly associated with fitness. Hence, the negative relationship between a trait's association with fitness and its heritability was not due to lower levels of VA in fitness traits but was due to their higher residual variance. However, whether the high residual variance was mainly due to higher levels of environmental variance or due to higher levels of nonadditive genetic variance remains a challenge to be addressed by further studies. Our results are consistent with earlier suggestions that fitness-related traits may have more complex genetic architecture than traits more distantly associated with fitness.     

Estimation of genetic variation in residual variance in female and male broiler chickens

In breeding programs, robustness of animals and uniformity of end product can be improved by exploiting genetic variation in residual variance. Residual variance can be defined as environmental variance after accounting for all identifiable effects. The aims of this study were to estimate genetic variance in residual variance of body weight, and to estimate genetic correlations between body weight itself and its residual variance and between female and male residual variance for broilers. The data sets comprised 26 972 female and 24 407 male body weight records. Variance components were estimated with ASREML. Estimates of the heritability of residual variance were in the range 0.029 (s.e. = 0.003) to 0.047 (s.e. = 0.004). The genetic coefficients of variation were high, between 0.35 and 0.57. Heritabilities were higher in females than in males. Accounting for heterogeneous residual variance increased the heritabilities for body weight as well. Genetic correlations between body weight and its residual variance were -0.41 (s.e. = 0.032) and -0.45 (s.e. = 0.040), respectively, in females and males. The genetic correlation between female and male residual variance was 0.11 (s.e. = 0.089), indicating that female and male residual variance are different traits. Results indicate good opportunities to simultaneously increase the mean and improve uniformity of body weight of broilers by selection.     

Accuracy of pedigree and genomic predictions of carcass and novel meat quality traits in multi-breed sheep data assessed by cross-validation

Background

Genomic predictions can be applied early in life without impacting selection candidates. This is especially useful for meat quality traits in sheep. Carcass and novel meat quality traits were predicted in a multi-breed sheep population that included Merino, Border Leicester, Polled Dorset and White Suffolk sheep and their crosses.

Methods

Prediction of breeding values by best linear unbiased prediction (BLUP) based on pedigree information was compared to prediction based on genomic BLUP (GBLUP) and a Bayesian prediction method (BayesR). Cross-validation of predictions across sire families was used to evaluate the accuracy of predictions based on the correlation of predicted and observed values and the regression of observed on predicted values was used to evaluate bias of methods. Accuracies and regression coefficients were calculated using either phenotypes or adjusted phenotypes as observed variables.

Results and conclusions

Genomic methods increased the accuracy of predicted breeding values to on average 0.2 across traits (range 0.07 to 0.31), compared to an average accuracy of 0.09 for pedigree-based BLUP. However, for some traits with smaller reference population size, there was no increase in accuracy or it was small. No clear differences in accuracy were observed between GBLUP and BayesR. The regression of phenotypes on breeding values was close to 1 for all methods, indicating little bias, except for GBLUP and adjusted phenotypes (regression = 0.78). Accuracies calculated with adjusted (for fixed effects) phenotypes were less variable than accuracies based on unadjusted phenotypes, indicating that fixed effects influence the latter. Increasing the reference population size increased accuracy, indicating that adding more records will be beneficial. For the Merino, Polled Dorset and White Suffolk breeds, accuracies were greater than for the Border Leicester breed due to the smaller sample size and limited across-breed prediction. BayesR detected only a few large marker effects but one region on chromosome 6 was associated with large effects for several traits. Cross-validation produced very similar variability of accuracy and regression coefficients for BLUP, GBLUP and BayesR, showing that this variability is not a property of genomic methods alone. Our results show that genomic selection for novel difficult-to-measure traits is a feasible strategy to achieve increased genetic gain.     

Isolating the cow-specific part of residual energy intake in lactating dairy cows using random regressions

The ability to properly assess and accurately phenotype true differences in feed efficiency among dairy cows is key to the development of breeding programs for improving feed efficiency. The variability among individuals in feed efficiency is commonly characterised by the residual intake approach. Residual feed intake is represented by the residuals of a linear regression of intake on the corresponding quantities of the biological functions that consume (or release) energy. However, the residuals include both, model fitting and measurement errors as well as any variability in cow efficiency. The objective of this study was to isolate the individual animal variability in feed efficiency from the residual component. Two separate models were fitted, in one the standard residual energy intake (REI) was calculated as the residual of a multiple linear regression of lactation average net energy intake (NEI) on lactation average milk energy output, average metabolic BW, as well as lactation loss and gain of body condition score. In the other, a linear mixed model was used to simultaneously fit fixed linear regressions and random cow levels on the biological traits and intercept using fortnight repeated measures for the variables. This method split the predicted NEI in two parts: one quantifying the population mean intercept and coefficients, and one quantifying cow-specific deviations in the intercept and coefficients. The cow-specific part of predicted NEI was assumed to isolate true differences in feed efficiency among cows. NEI and associated energy expenditure phenotypes were available for the first 17 fortnights of lactation from 119 Holstein cows; all fed a constant energy-rich diet. Mixed models fitting cow-specific intercept and coefficients to different combinations of the aforementioned energy expenditure traits, calculated on a fortnightly basis, were compared. The variance of REI estimated with the lactation average model represented only 8% of the variance of measured NEI. Among all compared mixed models, the variance of the cow-specific part of predicted NEI represented between 53% and 59% of the variance of REI estimated from the lactation average model or between 4% and 5% of the variance of measured NEI. The remaining 41% to 47% of the variance of REI estimated with the lactation average model may therefore reflect model fitting errors or measurement errors. In conclusion, the use of a mixed model framework with cow-specific random regressions seems to be a promising method to isolate the cow-specific component of REI in dairy cows.     

Accuracy and bias of genomic prediction with different de-regression methods

Genomic selection has become increasingly important in the breeding of animals and plants. The response variable is an important factor, influencing the accuracy of genomic selection. The de-regressed proof (DRP) based on traditional estimated breeding value (EBV) is commonly used as response variable. In the current study, simulated data from 16th QTL-MAS Workshop and real data from Chinese Holstein cattle were used to compare accuracy and bias of genomic prediction with two methods of calculating DRP. Our results with simulated data showed that the correlation between genomic EBV and true breeding value achieved using the Jairath method (DRP_J) was superior to that achieved using the Garrick method (DRP_G) for simulated trait 1 but the reverse was true for simulated trait 3, and these two methods performed comparably for simulated trait 2. For all three simulated traits, DRP_J yielded larger bias of genomic prediction. However, DRP_J outperformed DRP_G in both accuracy and unbiasedness for four milk production traits in Chinese Holstein. In the estimation of genomic breeding value using genomic BLUP model, two methods for weighting diagonal elements of incidence matrix associated with residual error were also compared. With increasing the proportion of genetic variance unexplained by markers, the accuracy of genomic prediction was decreased and the bias was increased. Weighting by the reliability of DRP produced accuracy comparable to the evaluation where the proportion of genetic variance unexplained by markers was considered, but with smaller bias in general.     

皂荚南方天然群体种实表型多样性

以系统揭示表型变异程度和变异规律为目的, 对皂荚(Gleditsia sinensis)南方分布区的10个天然群体的11个种实性状进行了比较分析。采用方差分析、多重比较、相关分析等多种分析方法, 对群体间和群体内的表型多样性以及与地理、环境因子的相关性进行了讨论。方差分析结果表明; 皂荚果实、种子等性状在群体间和群体内存在丰富的变异, 11个性状在群体间、群体内均达显著差异; 荚果性状在群体间和群体内的变异均大于种子性状, 11个性状的平均表型分化系数为20.42%, 群体内的变异(32.28%)大于群体间的变异(7.19%), 群体内的变异是皂荚的主要变异来源; 皂荚各性状平均变异系数为11.20%, 变异幅度为4.55%-18.38%。群体间荚果的变异(14.75%)高于群体间种子变异(6.95%), 表明种子变异稳定性高。荚果和种子各性状之间多呈极显著或显著正相关, 表现为荚果越大, 则种子越大, 种子的千粒重也越大; 荚果表现为同地理经度的南北变异, 种子则表现为同地理纬度的东西变异。研究结果为进一步开展皂荚遗传育种、保护生物学研究和皂荚种质资源利用奠定了基础。