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.