Genetic mapping reveals new loci and alleles for flowering time and plant height using the double round-robin population of barley

Flowering time and plant height are two critical determinants of yield potential in barley (Hordeum vulgare). Despite their role in plant physiological regulation, a complete overview of the genetic complexity of flowering time and plant height regulation in barley is still lacking. Using a double round-robin population originated from the crossings of 23 diverse parental inbred lines, we aimed to determine the variance components in the regulation of flowering time and plant height in barley as well as to identify new genetic variants by single and multi-population QTL analyses and allele mining. Despite similar genotypic variance, we observed higher environmental variance components for plant height than flowering time. Furthermore, we detected new QTLs for flowering time and plant height. Finally, we identified a new functional allelic variant of the main regulatory gene Ppd-H1. Our results show that the genetic architecture of flowering time and plant height might be more complex than reported earlier and that a number of undetected, small effect, or low-frequency genetic variants underlie the control of these two traits.

Genetic parameters for calf feeding traits derived from automated milk feeding machines and number of bovine respiratory disease treatments in North American Holstein calves

Precision livestock farming technologies, such as automatic milk feeding machines, have increased the availability of on-farm data collected from dairy operations. We analyzed feeding records from automatic milk feeding machines to evaluate the genetic background of milk feeding traits and bovine respiratory disease (BRD) in North American Holstein calves. Data from 10,076 preweaning female Holstein calves were collected daily over a period of 6 yr (3 yr included per-visit data), and daily milk consumption (DMC), per-visit milk consumption (PVMC), daily sum of drinking duration (DSDD), drinking duration per-visit, daily number of rewarded visits (DNRV), and total number of visits per day were recorded over a 60-d preweaning period. Additional traits were derived from these variables, including total consumption and duration variance (TCV and TDV), feeding interval, drinking speed (DS), and preweaning stayability. A single BRD-related trait was evaluated, which was the number of times a calf was treated for BRD (NTT). The NTT was determined by counting the number of BRD incidences before 60 d of age. All traits were analyzed using single-step genomic BLUP mixed-model equations and fitting either repeatability or random regression models in the BLUPF90+ suite of programs. A total of 10,076 calves with phenotypic records and genotypic information for 57,019 SNP after the quality control were included in the analyses. Feeding traits had low heritability estimates based on repeatability models (0.006 ± 0.0009 to 0.08 ± 0.004). However, total variance traits using an animal model had greater heritabilities of 0.21 ± 0.023 and 0.23 ± 0.024, for TCV and TDV, respectively. The heritability estimates increased with the repeatability model when using only the first 32 d preweaning (e.g., PVMC = 0.040 ± 0.003, DMC = 0.090 ± 0.009, DSDD = 0.100 ± 0.005, DS = 0.150 ± 0.007, DNRV = 0.020 ± 0.002). When fitting random regression models (RRM) using the full dataset (60-d period), greater heritability estimates were obtained (e.g., PVMC = 0.070 [range: 0.020, 0.110], DMC = 0.460 [range: 0.050, 0.680], DSDD = 0.180 [range: 0.010, 0.340], DS = 0.19 [range: 0.070, 0.430], DNRV = 0.120 [range: 0.030, 0.450]) for the majority of the traits, suggesting that RRM capture more genetic variability than the repeatability model with better fit being found for RRM. Moderate negative genetic correlations of -0.59 between DMC and NTT were observed, suggesting that automatic milk feeding machines records have the potential to be used for genetically improving disease resilience in Holstein calves. The results from this study provide key insights of the genetic background of early in-life traits in dairy cattle, which can be used for selecting animals with improved health outcomes and performance.

Estimation of heritability with genomic information by method R

Estimating heritabilities with large genomic models by established methods such as restricted maximum likelihood (REML) or Bayesian via Gibbs sampling is computationally expensive. Alternatively, heritability can be estimated indirectly by method R and by maximum predictivity, referred to as MaxPred here, at a much lower computing cost. By method R, the heritability used for predictions with whole and partial data is considered the best estimate when the predictions based on partial data are unbiased relative to those with the complete data. By MaxPred, the heritability estimate is the one that maximizes predictivity. This study compared heritability estimation with genomic information using average information REML (AI-REML), method R and MaxPred. A simulated population was generated with ten generations of 5000 animals each and an effective population size of 80. Each animal had one record for a trait with a heritability of 0.3, a phenotypic variance of 10.0 and was genotyped at 50 k SNP. In method R, the heritability estimate is found when the expectation of a regression coefficient is equal to one. The regression is the EBV of selection candidates calculated with the whole dataset regressed on the EBV of candidates calculated from a partial dataset. In this study, we used the GBLUP framework and therefore, GEBV was calculated. The partial dataset was created by removing the last generation of phenotypes. Predictivity was defined as the correlation between the adjusted phenotypes of the selection candidates and their GEBV calculated from the partial data. We estimated the heritability for populations that included between three and 10 generations. In every scenario, predictivity increased as more data was used and was the highest at the simulated heritability. However, the predictivity for all data subsets and all heritabilities compared did not differ more than 0.01, suggesting MaxPred is not the best indication for heritability estimation. For the whole dataset, the heritability was estimated as 0.30 ± 0.01, 0.26 ± 0.01 and 0.30 ± 0.04 for AI-REML without genomics, AI-REML with genomics and method R with genomics, respectively. Heritability estimation with genomics by method R reduced timing by 83%, implying a reduction in computing time from 9.5 to 1.6 h, on average, compared to AI-REML with genomics. Method R has the potential to estimate heritabilities with large genomic information at a low cost when many generations of animals are present; however, the standard error can be high when only a few iterations are used.

A boosting method to select the random effects in linear mixed models

This paper proposes a novel likelihood-based boosting method for the selection of the random effects in linear mixed models. The nonconvexity of the objective function to minimize, which is the negative profile log-likelihood, requires the adoption of new solutions. In this respect, our optimization approach also employs the directions of negative curvature besides the usual Newton directions. A simulation study and a real-data application show the good performance of the proposal.

Long-read sequencing-based transcriptomic landscape in longissimus dorsi and transcriptome-wide association studies for growth traits of meat rabbits

Rabbits are an attractive meat livestock species that can efficiently convert human-indigestible plant biomass, and have been commonly used in biological and medical researches. Yet, transcriptomic landscape in muscle tissue and association between gene expression level and growth traits have not been specially studied in meat rabbits. In this study Oxford Nanopore Technologies (ONT) long-read sequencing technology was used for comprehensively exploring transcriptomic landscape in Longissimus dorsi for 115 rabbits at 84 days of age, and transcriptome-wide association studies (TWAS) were performed for growth traits, including body weight at 84 days of age and average daily gain during three growth periods. The statistical analysis of TWAS was performed using a mixed linear model, in which polygenic effect was fitted as a random effect according to gene expression level-based relationships. A total of 18,842 genes and 42,010 transcripts were detected, among which 35% of genes and 47% of transcripts were novel in comparison with the reference genome annotation. Furthermore, 45% of genes were widely expressed among more than 90% of individuals. The proportions (±SE) of phenotype variance explained by genome-wide gene expression level ranged from 0.501 ± 0.216 to 0.956 ± 0.209, and the similar results were obtained when explained by transcript expression level. In contrast, neither gene nor transcript was detected by TWAS to be statistically significantly associated with these growth traits. In conclusion, these novel genes and transcripts that have been extensively profiled in a single muscle tissue using long-read sequencing technology will greatly improve our understanding on transcriptional diversity in rabbits. Our results with a relatively small sample size further revealed the important contribution of global gene expression to phenotypic variation on growth performance, but it seemed that no single gene has an outstanding effect; this knowledge is helpful to include intermediate omics data for implementing genetic evaluation of growth traits in meat rabbits.

Genetic parameters for yearling male reproduction traits in tropical composite cattle population

Fertility is economically important but is hard to quantify and measure in breeding programs which has led extensive breeding programs to ignore fertility in their selection criteria. While female fertility traits have been extensively researched, male fertility traits have been largely ignored. It is estimated that 20% to 40% of bulls have sub-fertility, reducing the number of calves born and profits, highlighting the importance of investigating bull fertility. The most practical measure of male fertility is a bull breeding soundness evaluation (BBSE) which assesses structure as well as semen quality and quantity. Generally, traits recorded in a BBSE are neither genetically evaluated nor used for selection in breeding programs. All traits recorded during a BBSE were analyzed through a series of univariate and bivariate linear mixed models using a genomic relationship matrix to estimate genetic parameters. All genotype and phenotype data were obtained from a tropical composite commercial cattle population and imputed to 27,638 single-nucleotide polymorphisms (SNPs) with a total of 2,613 genotyped animals with BBSE records ranging from 616 to 826 animals depending on the trait. The heritabilities of the 27 traits recorded during a BBSE ranged from 0.02 to 0.49. Seven of the male fertility traits were recommended to be included in a breeding program based on their heritability and their phenotypic and genetic correlations. These traits are scrotal circumference, percent normal sperm, proximal droplets, distal midpiece reflex, knobbed acrosomes, vacuoles/teratoids, and sheath score. Using these seven traits in a breeding program would result in higher calving rates, increasing production and profitability.

Partitioning variance in reproductive success, within years and across lifetimes

Variance in reproductive success (s k 2 , with k = number of offspring) plays a large role in determining the rate of genetic drift and the scope within which selection acts. Various frameworks have been proposed to parse factors that contribute to s k 2 , but none has focused on age-specific values of ϕ = s k 2 / k ¯ , which indicate the degree to which reproductive skew is overdispersed (compared to the random Poisson expectation) among individuals of the same age and sex. Instead, within-age effects are generally lumped with residual variance and treated as "noise." Here, an ANOVA sums-of-squares framework is used to partition variance in annual and lifetime reproductive success into between-group and within-group components. For annual reproduction, the between-age effect depends on age-specific fecundity (b x), but relatively few empirical data are available on the within-age effect, which depends on ϕ x. By defining groups by age-at-death rather than age, the same ANOVA framework can be used to partition variance in lifetime reproductive success (LRS) into between-group and within-group components. Analytical methods are used to develop null-model expectations for random contributions to within-group and between-group components. For analysis of LRS, random variation in longevity appears as part of the between-group variance, and effects (if any) of skip breeding and persistent individual differences contribute to the within-group variance. Simulations are used to show that the methods for variance partitioning are asymptotically unbiased. Practical application is illustrated with empirical data for annual reproduction in American black bears and lifetime reproduction in Dutch great tits. Results show that overdispersed within-age variance (1) dominates annual s k 2 in both male and female black bears, (2) is the primary factor that reduces annual effective size to a fraction of the number of adults, and (3) represents most of the opportunity for selection. In contrast, about a quarter of the variance in LRS in great tits can be attributed to random variation in longevity, and most of the rest is due to modest differences in fecundity with age estimated for a single cohort of females. R code is provided that reads generic input files for annual and lifetime reproductive success and allows users to conduct variance partitioning with their own data.

Genetic Variance Estimation over Time in Broiler Breeding Programmes for Growth and Reproductive Traits

Monitoring the genetic variance of traits is a key priority to ensure the sustainability of breeding programmes in populations under directional selection, since directional selection can decrease genetic variation over time. Studies monitoring changes in genetic variation have typically used long-term data from small experimental populations selected for a handful of traits. Here, we used a large dataset from a commercial breeding line spread over a period of twenty-three years. A total of 2,059,869 records and 2,062,112 animals in the pedigree were used for the estimations of variance components for the traits: body weight (BWT; 2,059,869 records) and hen-housed egg production (HHP; 45,939 records). Data were analysed with three estimation approaches: sliding overlapping windows, under frequentist (restricted maximum likelihood (REML)) and Bayesian (Gibbs sampling) methods; expected variances using coefficients of the full relationship matrix; and a "double trait covariances" analysis by computing correlations and covariances between the same trait in two distinct consecutive windows. The genetic variance showed marginal fluctuations in its estimation over time. Whereas genetic, maternal permanent environmental, and residual variances were similar for BWT in both the REML and Gibbs methods, variance components when using the Gibbs method for HHP were smaller than the variances estimated when using REML. Large data amounts were needed to estimate variance components and detect their changes. For Gibbs (REML), the changes in genetic variance from 1999-2001 to 2020-2022 were 82.29 to 93.75 (82.84 to 93.68) for BWT and 76.68 to 95.67 (98.42 to 109.04) for HHP. Heritability presented a similar pattern as the genetic variance estimation, changing from 0.32 to 0.36 (0.32 to 0.36) for BWT and 0.16 to 0.15 (0.21 to 0.18) for HHP. On the whole, genetic parameters tended slightly to increase over time. The expected variance estimates were lower than the estimates when using overlapping windows. That indicates the low effect of the drift-selection process on the genetic variance, or likely, the presence of genetic variation sources compensating for the loss. Double trait covariance analysis confirmed the maintenance of variances over time, presenting genetic correlations >0.86 for BWT and >0.82 for HHP. Monitoring genetic variance in broiler breeding programmes is important to sustain genetic progress. Although the genetic variances of both traits fluctuated over time, in some windows, particularly between 2003 and 2020, increasing trends were observed, which warrants further research on the impact of other factors, such as novel mutations, operating on the dynamics of genetic variance.

Separating Measurement Error and Signal in Environmental Data: Use of Replicates to Address Uncertainty

Measurement uncertainty has long been a concern in the characterizing and interpreting environmental and toxicological measurements. We compared statistical analysis approaches when there are replicates: a Naı̈ve approach that omits replicates, a Hybrid approach that inappropriately treats replicates as independent samples, and a Measurement Error Model (MEM) approach in a random effects analysis of variance (ANOVA) model that appropriately incorporates replicates. A simulation study assessed the effects of sample size and levels of replication, signal variance, and measurement error on estimates from the three statistical approaches. MEM results were superior overall with confidence intervals for the observed mean narrower on average than those from the Naı̈ve approach, giving improved characterization. The MEM approach also featured an unparalleled advantage in estimating signal and measurement error variance separately, directly addressing measurement uncertainty. These MEM estimates were approximately unbiased on average with more replication and larger sample sizes. Case studies illustrated analyzing normally distributed arsenic and log-normally distributed chromium concentrations in tap water and calculating MEM confidence intervals for the true, latent signal mean and latent signal geometric mean (i.e., with measurement error removed). MEM estimates are valuable for study planning; we used simulation to compare various sample sizes and levels of replication.

Variance of age-specific log incidence decomposition (VALID): a unifying model of measured and unmeasured genetic and non-genetic risks

BACKGROUND

The extent to which known and unknown factors explain how much people of the same age differ in disease risk is fundamental to epidemiology. Risk factors can be correlated in relatives, so familial aspects of risk (genetic and non-genetic) must be considered.

DEVELOPMENT

We present a unifying model (VALID) for variance in risk, with risk defined as log(incidence) or logit(cumulative incidence). Consider a normally distributed risk score with incidence increasing exponentially as the risk increases. VALID's building block is variance in risk, Δ2, where Δ = log(OPERA) is the difference in mean between cases and controls and OPERA is the odds ratio per standard deviation. A risk score correlated r between a pair of relatives generates a familial odds ratio of exp(rΔ2). Familial risk ratios, therefore, can be converted into variance components of risk, extending Fisher's classic decomposition of familial variation to binary traits. Under VALID, there is a natural upper limit to variance in risk caused by genetic factors, determined by the familial odds ratio for genetically identical twin pairs, but not to variation caused by non-genetic factors.

APPLICATION

For female breast cancer, VALID quantified how much variance in risk is explained-at different ages-by known and unknown major genes and polygenes, non-genomic risk factors correlated in relatives, and known individual-specific factors.

CONCLUSION

VALID has shown that, while substantial genetic risk factors have been discovered, much is unknown about genetic and familial aspects of breast cancer risk especially for young women, and little is known about individual-specific variance in risk.

Variance component estimates, phenotypic characterization, and genetic evaluation of bovine congestive heart failure in commercial feeder cattle

The increasing incidence of bovine congestive heart failure (BCHF) in feedlot cattle poses a significant challenge to the beef industry from economic loss, reduced performance, and reduced animal welfare attributed to cardiac insufficiency. Changes to cardiac morphology as well as abnormal pulmonary arterial pressure (PAP) in cattle of mostly Angus ancestry have been recently characterized. However, congestive heart failure affecting cattle late in the feeding period has been an increasing problem and tools are needed for the industry to address the rate of mortality in the feedlot for multiple breeds. At harvest, a population of 32,763 commercial fed cattle were phenotyped for cardiac morphology with associated production data collected from feedlot processing to harvest at a single feedlot and packing plant in the Pacific Northwest. A sub-population of 5,001 individuals were selected for low-pass genotyping to estimate variance components and genetic correlations between heart score and the production traits observed during the feeding period. At harvest, the incidence of a heart score of 4 or 5 in this population was approximately 4.14%, indicating a significant proportion of feeder cattle are at risk of cardiac mortality before harvest. Heart scores were also significantly and positively correlated with the percentage Angus ancestry observed by genomic breed percentage analysis. The heritability of heart score measured as a binary (scores 1 and 2 = 0, scores 4 and 5 = 1) trait was 0.356 in this population, which indicates development of a selection tool to reduce the risk of congestive heart failure as an EPD (expected progeny difference) is feasible. Genetic correlations of heart score with growth traits and feed intake were moderate and positive (0.289-0.460). Genetic correlations between heart score and backfat and marbling score were -0.120 and -0.108, respectively. Significant genetic correlation to traits of high economic importance in existing selection indexes explain the increased rate of congestive heart failure observed over time. These results indicate potential to implement heart score observed at harvest as a phenotype under selection in genetic evaluation in order to reduce feedlot mortality due to cardiac insufficiency and improve overall cardiopulmonary health in feeder cattle.

Analysis of the Genetic Parameters for Dairy Linear Appraisal and Zoometric Traits: A Tool to Enhance the Applicability of Murciano-Granadina Goats Major Areas Evaluation System

Selection for zoometrics defines individuals' productive longevity, endurance, enhanced productive abilities and consequently, their long-term profitability. When zoometric analysis is aimed at large highly selected populations or in those at different levels of selection, linear appraisal systems (LAS) provide a timely response. This study estimates genetic and phenotypic parameters for zoometric/LAS traits in Murciano-Granadina goats, estimating genetic and phenotypic correlations among all traits, and determining whether major area selection would be appropriate or if adaptability strategies may need to be followed. Heritability estimates for the zoometric/LAS traits were low to high, ranging from 0.09 to 0.43, and the accuracy of estimation has improved after decades, rendering standard errors negligible. Scale inversion of specific traits may need to be performed before major areas selection strategies are implemented. Genetic and phenotypic correlations suggests that negative selection against thicker bones and higher rear insertion heights indirectly results in the optimization of selection practices in the rest of the traits, especially those in the structure, capacity and mammary system major areas. The integration and implementation of the strategies proposed within the Murciano-Granadina breeding program maximizes selection opportunities and the sustainable international competitiveness of the Murciano-Granadina goat in the dairy goat breed panorama.

Temporal Trends in Variability of Respirable Dust and Respirable Quartz Concentrations in the European Industrial Minerals Sector

While between- and within-worker variability have been studied quite extensively, hardly any research is available that examines long-term trends in the variability of occupational exposure. In this first study on trends in occupational exposure variability temporal changes in the variability of respirable dust and respirable quartz concentrations within the European industrial minerals sector were demonstrated. Since 2000 the European Industrial Minerals Association's Dust Monitoring Program (IMA-DMP) has systematically collected respirable dust and respirable quartz measurements. The resulting IMA-DMP occupational exposure database contains at present approximately 40 000 personal full-shift measurements, collected at 177 sites owned by 39 companies, located in 23 European countries. Repeated measurements of workers performing their duties within a specific site-job-campaign combination allowed estimation of within- and between-worker variability in exposure concentrations. Overall day-to-day variability predominated the between-worker variability for both respirable dust concentrations and quartz concentrations. The within-worker variability in concentrations by job was two to three times higher for respirable quartz than for respirable dust. The median between-worker variability in respirable dust concentrations was low and further reduced over time. For quartz concentrations the same phenomenon albeit somewhat less strong was observed. In contrast, for the within-worker variability in concentrations downward and upward temporal trends were apparent for both respirable dust and respirable quartz. The study shows that the (relative) size of temporal variability is large and unpredictable and therefore regular measurement campaigns are needed to ascertain compliance to occupational exposure limit values.

Phenotypic Analysis of Fourier-Transform Infrared Milk Spectra in Dairy Goats

The infrared spectrum of bovine milk is used to predict many interesting traits, whereas there have been few studies on goat milk in this regard. The objective of this study was to characterize the major sources of variation in the absorbance of the infrared spectrum in caprine milk samples. A total of 657 goats belonging to 6 breeds and reared on 20 farms under traditional and modern dairy systems were milk-sampled once. Fourier-transform infrared (FTIR) spectra were taken (2 replicates per sample, 1314 spectra), and each spectrum contained absorbance values at 1060 different wavenumbers (5000 to 930 × cm^-1), which were treated as a response variable and analyzed one at a time (i.e., 1060 runs). A mixed model, including the random effects of sample/goat, breed, flock, parity, stage of lactation, and the residual, was used. The pattern and variability of the FTIR spectrum of caprine milk was similar to those of bovine milk. The major sources of variation in the entire spectrum were as follows: sample/goat (33% of the total variance); flock (21%); breed (15%); lactation stage (11%); parity (9%); and the residual unexplained variation (10%). The entire spectrum was segmented into five relatively homogeneous regions. Two of them exhibited very large variations, especially the residual variation. These regions are known to be affected by the absorbance of water, although they also exhibited wide variations in the other sources of variation. The average repeatability of these two regions were 45% and 75%, whereas for the other three regions it was about 99%. The FTIR spectrum of caprine milk could probably be used to predict several traits and to authenticate the origin of goat milk.

Study of genetic parameters for pre-weaning growth traits in inner Mongolia white Arbas cashmere goats

Inner Mongolia Arbas white cashmere goats is a dual-purpose breed for producing cashmere and meat. In recent years, its meat has become more and more popular among consumers because of rich nutrients and delicious flavor. Therefore, it is particularly important to study the genetic and non-genetic factors affecting the early growth traits and estimate variance components of pre-weaning growth traits of Inner Mongolia Albas white cashmere goats. A total of 37487 kidding records such as birth weight (BWT), weaning weight (WWT), average daily gain from birth to weaning (ADG) and Kleiber ratio (KR) from 343 sires and 7296 dams were used in this study. The most appropriate model was chosen on the basis of likelihood ratio test by fitting six models which excluding or including maternal genetic, maternal permanent environmental effects. The parameters were estimated under the most appropriate model using AIREML method by WOMBAT software. With the best model (Model 6), heritability estimates were 0.0435, 0.0911, 0.0932 and 0.2339 for BWT, WWT, ADG and KR traits, respectively. Maternal heritability estimates were 0.0143, 0.0246, 0.0220 and 0.0186 for BWT, WWT, ADG, and KR traits respectively. The correlation between different traits was estimated with the most suitable model by using bivariate analysis method. The direct additive genetic correlation among the traits ranged from -0.026 (BWT~KR) to 0.772 (ADG~KR). The maternal permanent environment correlation is between -0.289 (BWT-KR) ~0.900 (WWT-ADG). Results indicated that maternal effects and direct-maternal genetic covariance should be considered in any program aimed at improving pre-weaning growth traits to have an accurate genetic evaluation. In addition, positive and medium to high genetic correlations generally exist among WWT, ADG and KR due to the existence of genetic variation for early growth traits. The results showed that the genetic progress of these traits could be slowly through selection except for KR.

Genetic parameters of immune traits for Landrace and Large White pig breeds

Improving the immunocompetence towards pathogens represents a desirable objective of breeding strategies to increase resilience. However, the immune system is complex and the genetic foundation of the underlying components is not yet clarified. In the present study, we focused on 22 blood parameters of 1,144 Landrace (LR) and Large White (LW) piglets at the age of 6-7 weeks. The immune profiles covered immune cells, red blood cell characteristics and cytokines. Genetic parameters based on pedigree information along with possible environmental effects were estimated. Litter effects play an important role in the expression of immune parameters of their young progenies. Hence, litter impacts on the piglet's immune profile including the immune parameters of the dam itself were investigated by different models. To incorporate the complexity of the immune network, the data were further investigated with a principal component analysis. Immune traits showed low to high breed-specific heritabilities (h² ). Strong positive r_g were estimated among red blood cell characteristics (0.77-0.99) and among cytokines (0.48-0.99). Neutrophils and lymphocytes illustrated a high negative r_g (-0.96 to -0.98). The litter impact on piglet's immunity was examined and strengthened already observed breed differences. In LR, h² (0.22-0.15) and litter effect (c² ) (0.52-0.44) for IFN-γ decreased after statistical consideration of maternal impact. In LW, a decrease in h² (0.32-0.18) for IFN-γ and an increase in c² (0.54-0.56) were observed. Here, sufficient correlations were detected within various immune traits and functional biological networks of principal components. Most immune traits are heritable and are promising to cover global breed-specific immunocompetence in pigs. The analysis of immune traits has to be extended in order to find an optimal range and to characterize relationships between immunity and performance to gain an improved immune system without accidental losses in productivity.

Is single-step genomic REML with the algorithm for proven and young more computationally efficient when less generations of data are present?

Efficient computing techniques allow the estimation of variance components for virtually any traditional dataset. When genomic information is available, variance components can be estimated using genomic REML (GREML). If only a portion of the animals have genotypes, single-step GREML (ssGREML) is the method of choice. The genomic relationship matrix (G) used in both cases is dense, limiting computations depending on the number of genotyped animals. The algorithm for proven and young (APY) can be used to create a sparse inverse of G (GAPY~-1) with close to linear memory and computing requirements. In ssGREML, the inverse of the realized relationship matrix (H-1) also includes the inverse of the pedigree relationship matrix, which can be dense with a long pedigree, but sparser with short. The main purpose of this study was to investigate whether costs of ssGREML can be reduced using APY with truncated pedigree and phenotypes. We also investigated the impact of truncation on variance components estimation when different numbers of core animals are used in APY. Simulations included 150K animals from 10 generations, with selection. Phenotypes (h2 = 0.3) were available for all animals in generations 1-9. A total of 30K animals in generations 8 and 9, and 15K validation animals in generation 10 were genotyped for 52,890 SNP. Average information REML and ssGREML with G-1 and GAPY~-1 using 1K, 5K, 9K, and 14K core animals were compared. Variance components are impacted when the core group in APY represents the number of eigenvalues explaining a small fraction of the total variation in G. The most time-consuming operation was the inversion of G, with more than 50% of the total time. Next, numerical factorization consumed nearly 30% of the total computing time. On average, a 7% decrease in the computing time for ordering was observed by removing each generation of data. APY can be successfully applied to create the inverse of the genomic relationship matrix used in ssGREML for estimating variance components. To ensure reliable variance component estimation, it is important to use a core size that corresponds to the number of largest eigenvalues explaining around 98% of total variation in G. When APY is used, pedigrees can be truncated to increase the sparsity of H and slightly reduce computing time for ordering and symbolic factorization, with no impact on the estimates.

Concordance correlation coefficients estimated by modified variance components and generalized estimating equations for longitudinal overdispersed Poisson data

For longitudinal overdispersed Poisson data sets, estimators of the intra-, inter-, and total concordance correlation coefficient through variance components have been proposed. However, biased estimators of quadratic forms are used in concordance correlation coefficient estimation. In addition, the generalized estimating equations approach has been used in estimating agreement for longitudinal normal data and not for longitudinal overdispersed Poisson data. Therefore, this paper proposes a modified variance component approach to develop the unbiased estimators of the concordance correlation coefficient for longitudinal overdispersed Poisson data. Further, the indices of intra-, inter-, and total agreement through generalized estimating equations are also developed considering the correlation structure of longitudinal count repeated measurements. Simulation studies are conducted to compare the performance of the modified variance component and generalized estimating equation approaches for longitudinal Poisson and overdispersed Poisson data sets. An application of corticospinal diffusion tensor tractography study is used for illustration. In conclusion, the modified variance component approach performs outstandingly well with small mean square errors and nominal 95% coverage rates. The generalized estimating equation approach provides in model assumption flexibility of correlation structures for repeated measurements to produce satisfactory concordance correlation coefficient estimation results.

Estimation of Genetic Parameters of Type Traits in First Parity Cows of the Autochthonous Cika Cattle in Slovenia

The aim of this study was to estimate genetic parameters of 26 individual and four composite type traits in first parity Cika cows. An analysis of variance was performed with the generalized linear model procedure of the SAS/STAT statistical package, where the fixed effects of year of recording, cow's age at recording and days after calving as a linear regression were included in the model. The variance components for the direct additive genetic effect and the herd effect in all type traits were estimated using the REML method in the VCE-6 software package. The estimated heritabilities ranged from 0.42 to 0.67 for the measured body frame traits, from 0.36 to 0.80 for the scored autochthonous traits, from 0.11 to 0.61 for the scored body frame traits, and from 0.20 to 0.47 for the scored udder traits. The estimated heritabilities for the composite traits called "autochthonous characteristics", "muscularity", "body frame" and "udder" were 0.55, 0.19, 0.19, and 0.26, respectively. The estimated genetic correlations among the measured body frame traits were positive and high, while the majority of them among the scored body frame traits were low to moderate. The estimated proportions of variance explained by the herd effect for the composite traits "autochthonous characteristics," "muscularity," "body frame" and "udder" were 0.09, 0.28, 0.14, and 0.10, respectively. The estimated heritabilities for the type traits of first parity Cika cows were similar to those reported for other breeds where breeding values have been routinely predicted for a long time. All estimated genetic parameters are already used for breeding value prediction in the Cika cattle population.

Using population crossover trials to improve the decision process regarding treatment individualization in N-of-1 trials

Healthcare researchers are showing renewed interest in the utilization of N-of-1 clinical trials for the individualization of pharmacological treatments. Here, we propose a frequentist approach to conducting treatment individualization in N-of-1 trials that we call "partial empirical Bayes." We infer the most beneficial treatment for the patient from combining the information provided by a previously conducted population crossover trial with individual patient data. We propose a method for estimating an optimal number of treatment cycles and investigate the statistical conditions under which N-of-1 trials are more beneficial than traditional clinical approaches. We represent the patient population with a random-coefficients linear model and calculate estimators of posttreatment individual disease severities. We show the estimators' consistency under the most common N-of-1 designs and examine their prediction errors and performance with small numbers of patient's responses. We demonstrate by simulating new patients that our approach is equivalent or superior to both the common clinical practice of recommending the on-average best treatment for all patients and the common individualization method that simply compares average responses to the tested treatments. We conclude that some situations exist in which individualization with N-of-1 trials is highly beneficial while other situations exist in which individualization may be unfruitful.

Genetic selection indices for growth traits in Blanco-Orejinegro cattle

Selection indices are used in genetic improvement programs, with the purpose of selectins simultaneous for several economically important traits. The objective of this study was to construct equations for selection indices in the Blanco-Orejinegro (BON) breed and to determine the index that would generate the greatest genetic progress. The information used included birth weight (BW), body weights adjusted to 120, 240, 480, and 720 days old (W120, W240, W240, 480 and W720, respectively), age at first calving (AFC) and interval between first and second calving (IBC) estimated breeding values. Two Smith and Hazel indices were calculated using variances (I1) and literature (I2), with a part two indices designed using information from experts and breeders (I3 and I4). All the indices favored the reduction of weight at birth. The I1 focused mainly on W120 and I2, I3 and I4 focused on 720. In general, the estimated indices obtained similar reliability and expected genetic differences I1 generated a decrease in direct BW. I2 generated the largest increases in BW and AFC. I3 and I4 generated positive changes in growth and reproductive traits, with I3 generating the greatest genetic gains in the population, especially for W240.

GPS Coordinates for Modelling Correlated Herd Effects in Genomic Prediction Models Applied to Hanwoo Beef Cattle

Simple Summary

It is widely known that the environment influences phenotypic expression and that its effects must be accounted for in genetic evaluation programs. The most used method to account for environmental effects is to add herd and the contemporary group to the model. Although generally informative, the herd effect treats different farms as independent units. However, if two farms are located physically close to each other, they potentially share correlated environmental factors. We introduce a method to model herd effects using physical distances between farms based on GPS coordinates as a proxy for the correlation matrix of these effects, aiming to account for similarities and differences between farms due to environmental factors. A population of beef cattle was used to evaluate the impact on the variance components and on the genomic prediction, of modelling herd effects as correlated, in comparison to assuming the farms as completely independent units. The main result was an increase in the reliabilities of the predicted genomic breeding values compared to reliabilities obtained with traditional models, a finding of practical relevance for genetic evaluation programs.

Abstract

It is widely known that the environment influences phenotypic expression and that its effects must be accounted for in genetic evaluation programs. The most used method to account for environmental effects is to add herd and contemporary group to the model. Although generally informative, the herd effect treats different farms as independent units. However, if two farms are located physically close to each other, they potentially share correlated environmental factors. We introduce a method to model herd effects that uses the physical distances between farms based on the Global Positioning System (GPS) coordinates as a proxy for the correlation matrix of these effects that aims to account for similarities and differences between farms due to environmental factors. A population of Hanwoo Korean cattle was used to evaluate the impact of modelling herd effects as correlated, in comparison to assuming the farms as completely independent units, on the variance components and genomic prediction. The main result was an increase in the reliabilities of the predicted genomic breeding values compared to reliabilities obtained with traditional models (across four traits evaluated, reliabilities of prediction presented increases that ranged from 0.05 ± 0.01 to 0.33 ± 0.03), suggesting that these models may overestimate heritabilities. Although little to no significant gain was obtained in phenotypic prediction, the increased reliability of the predicted genomic breeding values is of practical relevance for genetic evaluation programs.

Quantifying the contribution of dominance deviation effects to complex trait variation in biobank-scale data

The proportion of variation in complex traits that can be attributed to non-additive genetic effects has been a topic of intense debate. The availability of biobank-scale datasets of genotype and trait data from unrelated individuals opens up the possibility of obtaining precise estimates of the contribution of non-additive genetic effects. We present an efficient method to estimate the variation in a complex trait that can be attributed to additive (additive heritability) and dominance deviation (dominance heritability) effects across all genotyped SNPs in a large collection of unrelated individuals. Over a wide range of genetic architectures, our method yields unbiased estimates of additive and dominance heritability. We applied our method, in turn, to array genotypes as well as imputed genotypes (at common SNPs with minor allele frequency [MAF] > 1%) and 50 quantitative traits measured in 291,273 unrelated white British individuals in the UK Biobank. Averaged across these 50 traits, we find that additive heritability on array SNPs is 21.86% while dominance heritability is 0.13% (about 0.48% of the additive heritability) with qualitatively similar results for imputed genotypes. We find no statistically significant evidence for dominance heritability (p<0.05/50 accounting for the number of traits tested) and estimate that dominance heritability is unlikely to exceed 1% for the traits analyzed. Our analyses indicate a limited contribution of dominance heritability to complex trait variation.

Inference for high-dimensional linear mixed-effects models: A quasi-likelihood approach

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional fixed effects. The proposed method is applicable to general settings where the dimension of the random effects and the cluster sizes are possibly large. Regarding the fixed effects, we provide rate optimal estimators and valid inference procedures that do not rely on the structural information of the variance components. We also study the estimation of variance components with high-dimensional fixed effects in general settings. The algorithms are easy to implement and computationally fast. The proposed methods are assessed in various simulation settings and are applied to a real study regarding the associations between body mass index and genetic polymorphic markers in a heterogeneous stock mice population.

Beef trait genetic parameters based on old and recent data and its implications for genomic predictions in Italian Simmental cattle

This study aimed to evaluate the changes in variance components over time to identify a subset of data from the Italian Simmental (IS) population that would yield the most appropriate estimates of genetic parameters and breeding values for beef traits to select young bulls. Data from bulls raised between 1986 and 2017 were used to estimate genetic parameters and breeding values for four beef traits (average daily gain [ADG], body size [BS], muscularity [MUS], and feet and legs [FL]). The phenotypic mean increased during the years of the study for ADG, but it decreased for BS, MUS, and FL. The complete dataset (ALL) was divided into four generational subsets (Gen1, Gen2, Gen3, and Gen4). Additionally, ALL was divided into two larger subsets: the first one (OLD) combined data from Gen1 and Gen2 to represent the starting population, and the second one (CUR) combined data from Gen3 and Gen4 to represent a subpopulation with stronger ties to the current population. Genetic parameters were estimated with a four-trait genomic animal model using a single-step genomic average information restricted maximum likelihood algorithm. Heritability estimates from ALL were 0.26 ± 0.03 for ADG, 0.33 ± 0.04 for BS, 0.55 ± 0.03 for MUS, and 0.23 ± 0.03 for FL. Higher heritability estimates were obtained with OLD and ALL than with CUR. Considerable changes in heritability existed between Gen1 and Gen4 due to fluctuations in both additive genetic and residual variances. Genetic correlations also changed over time, with some values moving from positive to negative or even to zero. Genetic correlations from OLD were stronger than those from CUR. Changes in genetic parameters over time indicated that they should be updated regularly to avoid biases in genomic estimated breeding values (GEBV) and low selection accuracies. GEBV estimated using CUR variance components were less biased and more consistent than those estimated with OLD and ALL variance components. Validation results indicated that data from recent generations produced genetic parameters that more appropriately represent the structure of the current population, yielding accurate GEBV to select young animals and increasing the likelihood of higher genetic gains.

Mean comparisons and power calculations to ensure reproducibility in preclinical drug discovery

In the pharmaceutical industry, in vivo animal experiments are conducted to test the effects of novel preclinical drug compounds. Well-planned animal studies involve a sample size and statistical power analysis to provide a basis for the number of animals allocated into comparator arms of a future study. These calculations require approximate values for the parameters of a statistical model that will be applied to the future data and used to test for differences via statistical hypotheses. If the prestudy parameter estimates are nearly correct, the power analysis guarantees that a difference will be detected from the study data, up to a prespecified probability. Traditional power computations, however, are not calculated with reproducibility in mind. In this work, the issue of reproducibility in drug discovery is tackled from the point of view that study-to-study variability is not included in a typical sample size and power analysis. Three proposed methods that yield a reproducible mean-comparison analysis are derived and compared.

A unified linear mixed model for familial relatedness and population structure in genetic association studies

Familial relatedness (FR) and population structure (PS) are two major sources for genetic correlation. In the human population, both FR and PS can further break down into additive and dominant components to account for potential additive and dominant genetic effects. In this study, besides the classical additive genomic relationship matrix, a dominant genomic relationship matrix is introduced. A link between the additive/dominant genomic relationship matrices and the coancestry (or kinship)/double coancestry coefficients is also established. In addition, a way to separate the FR and PS correlations based on the estimates of coancestry and double coancestry coefficients from the genomic relationship matrices is proposed. A unified linear mixed model is also developed, which can account for both the additive and dominance effects of FR and PS correlations as well as their possible random interactions. Finally, this unified linear mixed model is applied to analyze two study cohorts from UK Biobank.

Within-Person Variation in Nutrient Intakes across Populations and Settings: Implications for the Use of External Estimates in Modeling Usual Nutrient Intake Distributions

Determining the proportion of a population at risk of inadequate or excessive nutrient intake is a crucial step in planning and managing nutrition intervention programs. Multiple days of 24-h dietary intake data per subject allow for adjustment of modeled usual nutrient intake distributions for the proportion of total variance in intake attributable to within-individual variation (WIV:total). When only single-day dietary data are available, an external adjustment factor can be used; however, WIV:total may vary by population, and use of incorrect WIV:total ratios may influence the accuracy of prevalence estimates and subsequent program impacts. WIV:total values were compiled from publications and from reanalyses of existing datasets to describe variation in WIV:total across populations and settings. The potential impact of variation in external WIV:total on estimates of prevalence of inadequacy was assessed through simulation analyses using the National Cancer Institute 1-d method. WIV:total values were extracted from 40 publications from 24 countries, and additional values were calculated from 15 datasets from 12 nations. Wide variation in WIV:total (from 0.02 to 1.00) was observed in publications and reanalyses. Few patterns by population characteristics were apparent, but WIV:total varied by age in children (< vs. >1 y) and between rural and urban settings. Simulation analyses indicated that estimates of the prevalence of inadequate intake are sensitive to the selected ratio in some cases. Selection of an external WIV:total estimate should consider comparability between the reference and primary studies with regard to population characteristics, study design, and statistical methods. Given wide variation in observed ratios with few discernible patterns, the collection of ≥2 days of intake data in at least a representative subsample in population dietary studies is strongly encouraged. In the case of single-day dietary studies, sensitivity analyses are recommended to determine the robustness of prevalence estimates to changes in the variance ratio.

Parametric Statistical Inference for Comparing Means and Variances

Purpose

The purpose of this tutorial is to provide visual scientists with various approaches for comparing two or more groups of data using parametric statistical tests, which require that the distribution of data within each group is normal (Gaussian). Non-parametric tests are used for inference when the sample data are not normally distributed or the sample is too small to assess its true distribution.

Methods

Methods are reviewed using retinal thickness, as measured by optical coherence tomography (OCT), as an example for comparing two or more group means. The following parametric statistical approaches are presented for different situations: two-sample t-test, Analysis of Variance (ANOVA), paired t-test, and the analysis of repeated measures data using a linear mixed-effects model approach.

Results

Analyzing differences between means using various approaches is demonstrated, and follow-up procedures to analyze pairwise differences between means when there are more than two comparison groups are discussed. The assumption of equal variance between groups and methods to test for equal variances are examined. Examples of repeated measures analysis for right and left eyes on subjects, across spatial segments within the same eye (e.g. quadrants of each retina), and over time are given.

Conclusions

This tutorial outlines parametric inference tests for comparing means of two or more groups and discusses how to interpret the output from statistical software packages. Critical assumptions made by the tests and ways of checking these assumptions are discussed. Efficient study designs increase the likelihood of detecting differences between groups if such differences exist. Situations commonly encountered by vision scientists involve repeated measures from the same subject over time, measurements on both right and left eyes from the same subject, and measurements from different locations within the same eye. Repeated measurements are usually correlated, and the statistical analysis needs to account for the correlation. Doing this the right way helps to ensure rigor so that the results can be repeated and validated.

Variance estimates are similar using pedigree or genomic relationships with or without the use of metafounders or the algorithm for proven and young animals1

With an increase in the number of animals genotyped there has been a shift from using pedigree relationship matrices (A) to genomic ones. As the use of genomic relationship matrices (G) has increased, new methods to build or approximate G have developed. We investigated whether the way variance components are estimated should reflect these changes. We estimated variance components for maternal sow traits by solving with restricted maximum likelihood, with four methods of calculating the inverse of the relationship matrix. These methods included using just the inverse of A (A−1), combining A−1 and the direct inverse of G (HDIRECT−1), including metafounders (HMETA−1), or combining A−1 with an approximated inverse of G using the algorithm for proven and young animals (HAPY−1). There was a tendency for higher additive genetic variances and lower permanent environmental variances estimated with A−1 compared with the three H−1 methods, which supports that G−1 is better than A−1 at separating genetic and permanent environmental components, due to a better definition of the actual relationships between animals. There were limited or no differences in variance estimates between HDIRECT−1, HMETA−1, and HAPY−1. Importantly, there was limited differences in variance components, repeatability or heritability estimates between methods. Heritabilities ranged between <0.01 to 0.04 for stayability after second cycle, and farrowing rate, between 0.08 and 0.15 for litter weight variation, maximum cycle number, total number born, total number still born, and prolonged interval between weaning and first insemination, and between 0.39 and 0.44 for litter birth weight and gestation length. The limited differences in heritabilities suggest that there would be very limited changes to estimated breeding values or ranking of animals across models using the different sets of variance components. It is suggested that variance estimates continue to be made using A−1, however including G−1 is possibly more appropriate if refining the model, for traits that fit a permanent environmental effect.

Multiple QTL Mapping in Autopolyploids: A Random-Effect Model Approach with Application in a Hexaploid Sweetpotato Full-Sib Population

In developing countries, the sweetpotato, Ipomoea batatas (L.) Lam. [Formula: see text], is an important autopolyploid species, both socially and economically. However, quantitative trait loci (QTL) mapping has remained limited due to its genetic complexity. Current fixed-effect models can fit only a single QTL and are generally hard to interpret. Here, we report the use of a random-effect model approach to map multiple QTL based on score statistics in a sweetpotato biparental population ('Beauregard' × 'Tanzania') with 315 full-sibs. Phenotypic data were collected for eight yield component traits in six environments in Peru, and jointly adjusted means were obtained using mixed-effect models. An integrated linkage map consisting of 30,684 markers distributed along 15 linkage groups (LGs) was used to obtain the genotype conditional probabilities of putative QTL at every centiMorgan position. Multiple interval mapping was performed using our R package QTLpoly and detected a total of 13 QTL, ranging from none to four QTL per trait, which explained up to 55% of the total variance. Some regions, such as those on LGs 3 and 15, were consistently detected among root number and yield traits, and provided a basis for candidate gene search. In addition, some QTL were found to affect commercial and noncommercial root traits distinctly. Further best linear unbiased predictions were decomposed into additive allele effects and were used to compute multiple QTL-based breeding values for selection. Together with quantitative genotyping and its appropriate usage in linkage analyses, this QTL mapping methodology will facilitate the use of genomic tools in sweetpotato breeding as well as in other autopolyploids.

An experimental study of methods for the analysis of variance components in the inference of laboratory information

Measurement uncertainty (MU) can be estimated and calculated by different procedures, representing different aspects and intended use. It is appropriate to distinguish between uncertainty determined under repeatability and reproducibility conditions, and to distinguish causes of variation using analysis of variance components. The intra-laboratory MU is frequently determined by repeated measurements of control material(s) of one or several concentrations during a prolonged period of time. We demonstrate, based on experimental results, how such results can be used to identify the repeatability, 'pure' reproducibility and intra-laboratory variance as the sum of the two. Native patient material was used to establish repeatability using the Dahlberg formula for random differences between measurements and an expanded Dahlberg formula if a non-random difference, e.g. bias, was expected. Repeatability and reproducibility have different clinical relevance in intensive care compared to monitoring treatment of chronic diseases, comparison with reference intervals or screening.

Genomic Prediction and Association Analysis with Models Including Dominance Effects for Important Traits in Chinese Simmental Beef Cattle

Simple Summary

Dominance effects play important roles in determining genetic changes with regard to complex traits. We conducted genomic predictions and genome-wide association studies in order to investigate the effects of dominance on carcass weight, dressing percentage, meat percentage, average daily gain, and chuck roll in 1233 Simmental beef cattle. Using dominance models, we improved the predictive abilities and found several candidate single-nucleotide polymorphisms (SNPs) and genes associated with these traits. Our studies helped us to understand causal mutation mapping and genomic selection models with dominance effects in Chinese Simmental beef cattle.

Abstract

Non-additive effects play important roles in determining genetic changes with regard to complex traits; however, such effects are usually ignored in genetic evaluation and quantitative trait locus (QTL) mapping analysis. In this study, a two-component genome-based restricted maximum likelihood (GREML) was applied to obtain the additive genetic variance and dominance variance for carcass weight (CW), dressing percentage (DP), meat percentage (MP), average daily gain (ADG), and chuck roll (CR) in 1233 Simmental beef cattle. We estimated predictive abilities using additive models (genomic best linear unbiased prediction (GBLUP) and BayesA) and dominance models (GBLUP-D and BayesAD). Moreover, genome-wide association studies (GWAS) considering both additive and dominance effects were performed using a multi-locus mixed-model (MLMM) approach. We found that the estimated dominance variances accounted for 15.8%, 16.1%, 5.1%, 4.2%, and 9.7% of the total phenotypic variance for CW, DP, MP, ADG, and CR, respectively. Compared with BayesA and GBLUP, we observed 0.5–1.1% increases in predictive abilities of BayesAD and 0.5–0.9% increases in predictive abilities of GBLUP-D, respectively. Notably, we identified a dominance association signal for carcass weight within RIMS2, a candidate gene that has been associated with carcass weight in beef cattle. Our results suggest that dominance effects yield variable degrees of contribution to the total genetic variance of the studied traits in Simmental beef cattle. BayesAD and GBLUP-D are convenient models for the improvement of genomic prediction, and the detection of QTLs using a dominance model shows promise for use in GWAS in cattle.

Dissecting total genetic variance into additive and dominance components of purebred and crossbred pig traits

The partition of the total genetic variance into its additive and non-additive components can differ from trait to trait, and between purebred and crossbred populations. A quantification of these genetic variance components will determine the extent to which it would be of interest to account for dominance in genomic evaluations or to establish mate allocation strategies along different populations and traits. This study aims at assessing the contribution of the additive and dominance genomic variances to the phenotype expression of several purebred Piétrain and crossbred (Piétrain × Large White) pig performances. A total of 636 purebred and 720 crossbred male piglets were phenotyped for 22 traits that can be classified into six groups of traits: growth rate and feed efficiency, carcass composition, meat quality, behaviour, boar taint and puberty. Additive and dominance variances estimated in univariate genotypic models, including additive and dominance genotypic effects, and a genomic inbreeding covariate allowed to retrieve the additive and dominance single nucleotide polymorphism variances for purebred and crossbred performances. These estimated variances were used, together with the allelic frequencies of the parental populations, to obtain additive and dominance variances in terms of genetic breeding values and dominance deviations. Estimates of the Piétrain and Large White allelic contributions to the crossbred variance were of about the same magnitude in all the traits. Estimates of additive genetic variances were similar regardless of the inclusion of dominance. Some traits showed relevant amount of dominance genetic variance with respect to phenotypic variance in both populations (i.e. growth rate 8%, feed conversion ratio 9% to 12%, backfat thickness 14% to 12%, purebreds-crossbreds). Other traits showed higher amount in crossbreds (i.e. ham cut 8% to 13%, loin 7% to 16%, pH semimembranosus 13% to 18%, pH longissimus dorsi 9% to 14%, androstenone 5% to 13% and estradiol 6% to 11%, purebreds-crossbreds). It was not encountered a clear common pattern of dominance expression between groups of analysed traits and between populations. These estimates give initial hints regarding which traits could benefit from accounting for dominance for example to improve genomic estimated breeding value accuracy in genetic evaluations or to boost the total genetic value of progeny by means of assortative mating.

Seed local adaptation and seedling plasticity account for Gleditsia triacanthos tree invasion across biomes

BACKGROUND AND AIMS

Phenotypic plasticity and local adaption can contribute to the success of invasive species. While the former is an environmentally induced trait, the latter involves a selection process to filter the best genotype for a location. We examined the evidence for phenotypic plasticity and local adaptation for seed and seedling traits of the invasive tree Gleditsia triacanthos, with three origins distributed along an approx. 10° latitude gradient across three biomes.

METHODS

In sub-tropical forests, dry woodlands and secondary temperate grasslands in Argentina, we harvested seeds from clusters of neighbouring trees (i.e. families) distributed within 15-20 km in each origin (biome). We manipulated the environmental conditions relevant to each biome, assuming that propagule availability did not represent an ecological barrier. In growth chambers, we evaluated seed imbibition and seed germination under different light, temperature and water potential. In a 2 year common garden, we evaluated the impact of resident vegetation removal on seedling survival and growth.

KEY RESULTS

Mean time to complete seed imbibition differed among origins; seeds from temperate grasslands reached full imbibition before seeds from dry woodlands and sub-tropical forests. Germination was always >70 %, but was differentially affected by water potential, and light quantity (dark-light) and quality (red-far red) among origins, suggesting local adaptation. In the common garden, vegetation removal rather than origin negatively affected seedling survival and enhanced seedling growth. Vegetation removal increased basal diameter, leaves per plant and spine number, and reduced the height:basal diameter ratio.

CONCLUSIONS

We conclude that local adaptation in seed germination traits and plastic changes in seedling allometry (e.g. height:diameter) may allow this tree to respond over the short and long term to changes in environmental conditions, and to contribute to shape G. triacanthos as a successful woody invader. Overall, our study revealed how local adaptation and plasticity can explain different aspects of tree invasion capacity across biomes.

Selection for temperament has no negative consequences on important production traits in farmed mink1

Danish and European legislation recommend mink breeding programs that include selection for "confidence," defined as exploratory activity in a standardized behavioral test. Although this recommendation may improve mink welfare, farmers may consider this criterion risky due to possible negative consequences on other traits. The overall objectives of this study were to estimate the heritability of exploratory/fearful behavior and to identify genetic correlations with other traits of major economic importance in mink fur production. Various aspects of social influence on exploratory/fearful behavior, such as effects of the mother and litter siblings before weaning, the mother's age, and cage mates after weaning, were analyzed. In total, 26,371 1-yr-old Brown mink (Neovison vison) individuals born during the period of 2013 to2016 were included in the study. Exploratory/fearful behavior was the main trait analyzed. The production traits analyzed were live pelt quality and body weight. Both of these traits were assessed during live grading in November. Pelt length and quality were determined using the dried pelts of nonbreeders. Fertility data were obtained from the Fur Farm database. Linear mixed models were run using the restricted maximum-likelihood method. The genetic correlation between female and male behavior was 0.95 (SE = 0.06), indicating similar genetic backgrounds for both sexes (P = 0.40). For both sexes, the estimated heritability of behavior was 0.19 (SE = 0.03). We found no significant genetic correlation between behavior and production/fertility traits (P > 0.05). Common litter variance indicated a preweaning effect of litter mates and/or dam on postweaning temperament. There was a tendency for offspring from older mothers to explore more than offspring from 1-yr-old mothers. This trend was especially pronounced for males of 2-yr-old mothers (P = 0.05) and females of 4-yr-old mothers (P = 0.06). We conclude that confidence may be selected for among farm mink without detrimental effects on economically important production traits, such as pelt quality and fertility.

Permutation and Bayesian tests for testing random effects in linear mixed-effects models

In many applications of linear mixed-effects models to longitudinal and multilevel data especially from medical studies, it is of interest to test for the need of random effects in the model. It is known that classical tests such as the likelihood ratio, Wald, and score tests are not suitable for testing random effects because they suffer from testing on the boundary of the parameter space. Instead, permutation and bootstrap tests as well as Bayesian tests, which do not rely on the asymptotic distributions, avoid issues with the boundary of the parameter space. In this paper, we first develop a permutation test based on the likelihood ratio test statistic, which can be easily used for testing multiple random effects and any subset of them in linear mixed-effects models. The proposed permutation test would be an extension to two existing permutation tests. We then aim to compare permutation tests and Bayesian tests for random effects to find out which test is more powerful under which situation. Nothing is known about this in the literature, although this is an important practical problem due to the usefulness of both methods in tackling the challenges with testing random effects. For this, we consider a Bayesian test developed using Bayes factors, where we also propose a new alternative computation for this Bayesian test to avoid some computational issue it encounters in testing multiple random effects. Extensive simulations and a real data analysis are used for evaluation of the proposed permutation test and its comparison with the Bayesian test. We find that both tests perform well, albeit the permutation test with the likelihood ratio statistic tends to provide a relatively higher power when testing multiple random effects.

Genetic parameters for semen production traits in Swiss dairy bulls

Variance components (VC) were estimated for the semen production trait ejaculate volume, sperm concentration and sperm motility in the Swiss cattle breeds Brown Swiss (BS), Original Braunvieh (OB), Holstein (HO), Red-Factor-Carrier (RF), Red Holstein (RH), Swiss Fleckvieh (SF) and Simmental (SI). For this purpose, semen production traits from 2,617 bulls with 124,492 records were used. The data were collected in the years 2000-2012. The model for genetic parameter estimation across all breeds included the fixed effects age of bull at collection, year of collection, month of collection, number of collection per bull and day, interval between consecutive collections, semen collector, bull breed as well as a random additive genetic component and a permanent environmental effect. The same model without a fixed breed effect was used to estimate VC and repeatabilities separately for each of the breeds BS, HO, RH, SF and SI. Estimated heritabilities across all breeds were 0.42, 0.25 and 0.09 for ejaculate volume, sperm concentration and sperm motility, respectively. Different heritabilities were estimated for ejaculate volume (0.42; 0.45; 0.49; 0.40; 0.10), sperm concentration (0.34; 0.30; 0.20; 0.07; 0.23) and number of semen portions (0.18; 0.30; 0.04; 0.14; 0.04) in BS, HO, RH, SF and SI breed, respectively. The phenotypic and genetic correlations across all breeds between ejaculate volume and sperm concentration were negative (-0.28; -0.56). The other correlations across all breeds were positive. The phenotypic and genetic correlations were 0.01 and 0.19 between sperm motility and ejaculate volume, respectively. Between sperm motility and sperm concentration, the phenotypic and genetic correlations were 0.20 and 0.36, respectively. The results are consistent with other analyses and show that genetic improvement through selection is possible in bull semen production traits.

Efficient Monte Carlo algorithm for restricted maximum likelihood estimation of genetic parameters

Monte Carlo (MC) methods have been found useful in estimation of variance parameters for large data and complex models with many variance components (VC), with respect to both computer memory and computing time. A disadvantage has been a fluctuation in round-to-round values of estimates that makes the estimation of convergence challenging. Furthermore, with Newton-type algorithms, the approximate Hessian matrix might have sufficient accuracy, but the inaccuracy in the gradient vector exaggerates the round-to-round fluctuation to intolerable. In this study, the reuse of the same random numbers within each MC sample was used to remove the MC fluctuation. Simulated data with six VC parameters were analysed by four different MC REML methods: expectation-maximization (EM), Newton-Raphson (NR), average information (AI) and Broyden's method (BM). In addition, field data with 96 VC parameters were analysed by MC EM REML. In all the analyses with reused samples, the MC fluctuations disappeared, but the final estimates by the MC REML methods differed from the analytically calculated values more than expected especially when the number of MC samples was small. The difference depended on the random numbers generated, and based on repeated MC AI REML analyses, the VC estimates were on average non-biased. The advantage of reusing MC samples is more apparent in the NR-type algorithms. Smooth convergence opens the possibility to use the fast converging Newton-type algorithms. However, a disadvantage from reusing MC samples is a possible "bias" in the estimates. To attain acceptable accuracy, sufficient number of MC samples need to be generated.

Does trait variation within broadly distributed species mirror patterns across species? A case study in Puerto Rico

Although populations are phenotypically diverse, the majority of trait-based studies have focused on examining differences among species. The justification for this broadly applied approach is based on the assumption that differences among species are always greater than within species. This is likely true for local communities, but species are often broadly distributed across a wide range of environments and patterns of intraspecific variation might surpass differences among species. Therefore, an appropriate interpretation of the functional diversity requires an assessment of patterns of trait variation across different ecological scales. In this study, we examine and characterize patterns of leaf trait variation for species that are broadly distributed along an elevational gradient. We focus on seven leaf traits that represent a main axis of functional differentiation in plants reflecting the balance between photosynthetic efficiency, display, and stomatal conductance. We evaluated patterns of trait variance across ecological scales (elevation, species, populations, and individuals) and examined trait covariance at both within species and across species levels, along the elevation gradient. Our results show three key patterns: (1) intraspecific leaf trait variation for broadly distributed species is comparable to the interspecific trait variation, (2) the trait variance structure is highly variable across species, and (3) trait coordination between pairs of leaf traits is evident across species along the gradient, but not always within species. Combined, our results show that trait coordination and covariance are highly idiosyncratic across broadly distributed and co-occurring species, indicating that species may achieve similar functional roles even when exhibiting different phenotypes. This result challenges the traditional paradigm of functional ecology that assumes single trait values as optimal solutions for environments. In conclusion, patterns of trait variation both across and within species should be considered in future studies that assess trade-offs among traits over environmental gradients.

Estimation of genetic parameters for BW and body measurements in Brahman cattle

Body weight and body measurements are commonly used to represent growth and measured at several growth stages in beef cattle. Those economically important traits should be genetically improved. To achieve breeding programs, genetic parameters are prerequisite, as they are needed for designing and predicting outcomes of breeding programs, as well as estimating of breeding values. (Co)variance components were estimated for BW and body measurements on Brahman cattle born between 1990 and 2016 from 17 research herds across Thailand. The traits measured were BW, heart girth (GR), hip height (HH) and body length (BL) and were measured at birth, 200 days, 400 days and 600 days of age. The number of records varied between traits from 18 890 for birth BW to 876 for GR at 600 days. Estimation of variance components was performed using restricted maximum likelihood using univariate and multivariate animal models. Pre-weaning traits were influenced by genetic and/or permanent environmental effects of the dam, except for BL. Heritability estimates from birth to 600 days of age ranged from 0.28±0.01 to 0.50±0.06 for BW, 0.27±0.01 to 0.43±0.09 for GR, 0.28±0.01 to 0.58±0.08 for HH and 0.34±0.01 to 0.51±0.08 for BL using univariate analysis. Heritability estimates for the traits studied increased with age. A similar trend was observed for the phenotypic and genetic correlations between subsequent BW and body measurements. A positive correlation was observed between different traits measured at a similar age, ranging from 0.22±0.01 to 0.72±0.01 for the phenotypic correlation and 0.25±0.04 to 0.97±0.11 for the genetic correlation. Also, a positive correlation was observed for similar traits across different age classes ranging from 0.07±0.03 to 0.76±0.02 for the phenotypic correlation and 0.24±0.11 to 0.92±0.05 for the genetic correlation. Therefore, all correlations between body measurements at the same age and across age classes were positive. The results show the potential improvement of growth traits in Brahman cattle, and those traits can be improved simultaneously under the same breeding program.

An alternative derivation of Harville's restricted log likelihood function for variance component estimation

Estimation of variance components in linear mixed models is important in clinical trial and longitudinal data analysis. It is also important in animal and plant breeding for accurately partitioning total phenotypic variance into genetic and environmental variances. Restricted maximum likelihood (REML) method is often preferred over the maximum likelihood (ML) method for variance component estimation because REML takes into account the lost degree of freedom resulting from estimating the fixed effects. The original restricted likelihood function involves a linear transformation of the original response variable (a collection of error contrasts). Harville's final form of the restricted likelihood function does not involve the transformation and thus is much easier to manipulate than the original restricted likelihood function. There are several different ways to show that the two forms of the restricted likelihood are equivalent. In this study, I present a much simpler way to derive Harville's restricted likelihood function. I first treat the fixed effects as random effects and call such a mixed model a pseudo random model (PDRM). I then construct a likelihood function for the PDRM. Finally, I let the variance of the pseudo random effects be infinity and show that the limit of the likelihood function of the PDRM is the restricted likelihood function.

Biodiversity and ecosystem function: making sense of numerous species interactions in multi-species communities

Understanding the biodiversity and ecosystem function relationship can be challenging in species-rich ecosystems. Traditionally, species richness has been relied on heavily to explain changes in ecosystem function across diversity gradients. Diversity-Interactions models can test how ecosystem function is affected by species identity, species interactions, and evenness, in addition to richness. However, in a species-rich system, there may be too many species interactions to allow estimation of each coefficient, and if all interaction coefficients are estimable, they may be devoid of any sensible biological meaning. Parsimonious descriptions using constraints among interaction coefficients have been developed but important variability may still remain unexplained. Here, we extend Diversity-Interactions models to describe the effects of diversity on ecosystem function using a combination of fixed coefficients and random effects. Our approach provides improved standard errors for testing fixed coefficients and incorporates lack-of-fit tests for diversity effects. We illustrate our methods using data from a grassland and a microbial experiment. Our framework considerably reduces the complexities associated with understanding how species interactions contribute to ecosystem function in species-rich ecosystems.

Bayesian modelling of lung function data from multiple-breath washout tests

Paediatric respiratory researchers have widely adopted the multiple-breath washout (MBW) test because it allows assessment of lung function in unsedated infants and is well suited to longitudinal studies of lung development and disease. However, a substantial proportion of MBW tests in infants fail current acceptability criteria. We hypothesised that a model-based approach to analysing the data, in place of traditional simple empirical summaries, would enable more efficient use of these tests. We therefore developed a novel statistical model for infant MBW data and applied it to 1197 tests from 432 individuals from a large birth cohort study. We focus on Bayesian estimation of the lung clearance index, the most commonly used summary of lung function from MBW tests. Our results show that the model provides an excellent fit to the data and shed further light on statistical properties of the standard empirical approach. Furthermore, the modelling approach enables the lung clearance index to be estimated by using tests with different degrees of completeness, something not possible with the standard approach. Our model therefore allows previously unused data to be used rather than discarded, as well as routine use of shorter tests without significant loss of precision. Beyond our specific application, our work illustrates a number of important aspects of Bayesian modelling in practice, such as the importance of hierarchical specifications to account for repeated measurements and the value of model checking via posterior predictive distributions.

Inference on phenotype-specific effects of genes using multivariate kernel machine regression

We consider the problem of assessing the joint effect of a set of genetic markers on multiple, possibly correlated phenotypes of interest. We develop a kernel machine based multivariate regression framework, where the joint effect of the marker set on each of the phenotypes is modeled using prespecified kernel functions with unknown variance components. Unlike most existing methods that mainly focus on the global association between the marker set and the phenotype set, we develop estimation and testing procedures to study phenotype-specific associations. Specifically, we develop an estimation method based on the penalized likelihood approach to estimate phenotype-specific effects and their corresponding standard errors while accounting for possible correlation among the phenotypes. We develop testing procedures for the association of the marker set with any subset of phenotypes using a score-based variance components testing method. We assess the performance of our proposed methodology via a simulation study and demonstrate the utility of the proposed method using the Clinical Antipsychotic Trials of Intervention Effectiveness (CATIE) data.

On the substructure controls in rare variant analysis: Principal components or variance components?

Recent studies showed that population substructure (PS) can have more complex impact on rare variant tests and that similarity-based collapsing tests (e.g., SKAT) may suffer more severely by PS than burden-based tests. In this work, we evaluate the performance of SKAT coupling with principal components (PC) or variance components (VC) based PS correction methods. We consider confounding effects caused by PS including stratified populations, admixed populations, and spatially distributed nongenetic risk; we investigate which types of variants (e.g., common, less frequent, rare, or all variants) should be used to effectively control for confounding effects. We found that (i) PC-based methods can account for confounding effects in most scenarios except for admixture, although the number of sufficient PCs depends on the PS complexity and the type of variants used. (ii) PCs based on all variants (i.e., common + less frequent + rare) tend to require equal or fewer sufficient PCs and often achieve higher power than PCs based on other variant types. (iii) VC-based methods can effectively adjust for confounding in all scenarios (even for admixture), though the type of variants should be used to construct VC may vary. (iv) VC based on all variants works consistently in all scenarios, though its power may be sometimes lower than VC based on other variant types. Given that the best-performed method and which variants to use depend on the underlying unknown confounding mechanisms, a robust strategy is to perform SKAT analyses using VC-based methods based on all variants.

Variance component analysis to assess protein quantification in biomarker discovery. Application to MALDI-TOF mass spectrometry

Controlling the technological variability on an analytical chain is critical for biomarker discovery. The sources of technological variability should be modeled, which calls for specific experimental design, signal processing, and statistical analysis. Furthermore, with unbalanced data, the various components of variability cannot be estimated with the sequential or adjusted sums of squares of usual software programs. We propose a novel approach to variance component analysis with application to the matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) technology and use this approach for protein quantification by a classical signal processing algorithm and two more recent ones (BHI-PRO 1 and 2). Given the high technological variability, the quantification failed to restitute the known quantities of five out of nine proteins present in a controlled solution. There was a linear relationship between protein quantities and peak intensities for four out of nine peaks with all algorithms. The biological component of the variance was higher with BHI-PRO than with the classical algorithm (80-95% with BHI-PRO 1, 79-95% with BHI-PRO 2 vs. 56-90%); thus, BHI-PRO were more efficient in protein quantification. The technological component of the variance was higher with the classical algorithm than with BHI-PRO (6-25% vs. 2.5-9.6% with BHI-PRO 1 and 3.5-11.9% with BHI-PRO 2). The chemical component was also higher with the classical algorithm (3.6-18.7% vs. < 3.5%). Thus, BHI-PRO were better in removing noise from signal when the expected peaks are detected. Overall, either BHI-PRO algorithm may reduce the technological variance from 25 to 10% and thus improve protein quantification and biomarker validation.

Confidence intervals for heritability via Haseman-Elston regression

Heritability is the proportion of phenotypic variance in a population that is attributable to individual genotypes. Heritability is considered an important measure in both evolutionary biology and in medicine, and is routinely estimated and reported in genetic epidemiology studies. In population-based genome-wide association studies (GWAS), mixed models are used to estimate variance components, from which a heritability estimate is obtained. The estimated heritability is the proportion of the model's total variance that is due to the genetic relatedness matrix (kinship measured from genotypes). Current practice is to use bootstrapping, which is slow, or normal asymptotic approximation to estimate the precision of the heritability estimate; however, this approximation fails to hold near the boundaries of the parameter space or when the sample size is small. In this paper we propose to estimate variance components via a Haseman-Elston regression, find the asymptotic distribution of the variance components and proportions of variance, and use them to construct confidence intervals (CIs). Our method is further developed to obtain unbiased variance components estimators and construct CIs by meta-analyzing information from multiple studies. We demonstrate our approach on data from the Hispanic Community Health Study/Study of Latinos (HCHS/SOL).

THE OCCURRENCE AND SIGNIFICANCE OF EPISTATIC VARIANCE FOR QUANTITATIVE CHARACTERS AND ITS MEASUREMENT IN HAPLOIDS

Epistatic genetic variance for quantitative traits may play an important role in evolution, but detecting epistasis in diploid organisms is difficult and requires complex breeding programs and very large sample sizes. We develop a model for detecting epistasis in organisms with a free-living haploid stage in their life cycles. We show that epistasis is indicated by greater variance among families of haploid progeny derived from individual diploids than among clonally replicated haploid sibs from the same sporophyte. Simulations show that the power to detect epistasis is linearly related to the number of sporophytes and the number of haploids per sporophyte in the dataset. We illustrate the model with data from growth variation among gametophytes of the moss, Ceratodon purpureus. The experiment failed to detect epistatic variance for biomass production, although there was evidence of additive variance.

A comprehensive assessment of exposures to respirable dust and silica in the taconite mining industry

This study assessed the present-day levels (year 2010-2011) of exposure to respirable dust (RD) and respirable silica (RS) in taconite mines and evaluated how the mining process influences exposure concentrations. Personal samples (n = 679) were collected to assess exposure levels of workers to RD and RS at six mines in the Mesabi Iron Range of Minnesota. The RD and RS concentrations were measured using the National Institute for Occupational Safety and Health (NIOSH) 0600 and NIOSH 7500, respectively. Between-mine, between-SEG (similar exposure groups), within-SEG, and within-worker components of variability for RD and RS exposures were estimated using a two- or three-way nested random-effects ANOVA model. The majority of RD concentrations across all mines were below the Mine Safety and Health Administration (MSHA) Permissible Exposure Limit (PEL). The highest concentrations of RD were often observed in either the Pelletizing or Crushing departments, which are inherently dusty operations. With a few exceptions, the concentrations of RS in the crushing and concentrating processes were higher than those in the other mining processes, as well as higher than the American Conference of Governmental Industrial Hygienists (ACGIH) Threshold Limit Value (TLV) for RS. The magnetic separation and flotation processes in the concentrating department reduced the levels of RS significantly, and lowered the percentage of quartz in RD in the pelletizing department. There was little variability among the six mines or between the two mineralogically distinct zones for either RD or RS exposures. The between-SEG variability for RS did not differ substantially across most of the mines and was a major component of exposure variance. The within-SEG (or between-worker) variance component was typically the smallest because in many instances one worker from a SEG within a mine was monitored multiple times. Some of these findings were affected by the degree of censoring in each SEG and mine, characteristics of the taconite rock, seasonal effects during sampling, or the tasks assigned to each job in that mine.