Variance component estimation in animal breeding: a review†

Estimation of the genetic parameters of sheep growth traits based on machine vision acquisition

In the realm of animal phenotyping, manual measurements are frequently utilised. While machine-generated data show potential for enhancing high-throughput breeding, additional research and validation are imperative before incorporating them into genetic evaluation processes. This research presents a method for managing meat sheep and collecting data, utilising the Sheep Data Recorder system for data input and the Sheep Body Size Collector system for image capture. The study aimed to investigate the genetic parameter changes of growth traits in Ujumqin sheep by comparing machine-generated measurements with manual measurements. The dataset consisted of 552 data points from the offspring of 75 breeding rams and 399 breeding ewes. Six distinct random regression models were assessed to pinpoint the most suitable model for estimating genetic parameters linked to growth traits. These models were distinguished based on the inclusion or exclusion of maternal genetic effects, maternal permanent environmental effects, and covariance between maternal and direct genetic effects. Fixed factors such as individual age, individual sex, and ewe age were taken into account in the analysis. The genetic parameters for the yearling growth traits of Ujumqin sheep were calculated using ASReml software. The Akaike information criterion, the Bayesian information criterion, and fivefold cross-validation were employed to identify the optimal model. Research findings indicate that the most accurate models for manually measured data revealed heritability estimates of 0.12 ± 0.15 for BW, 0.05 ± 0.07 for body slanting length, 0.03 ± 0.07 for withers height, 0.15 ± 0.12 for hip height, 0.11 ± 0.11 for chest depth, 0.13 ± 0.13 for shoulder width, and 0.53 ± 0.15 for chest circumference. The optimal models for machine-predicted data showed heritability estimates of 0.1 ± 0.09 for body slanting length, 0.14 ± 0.12 for withers height, 0.55 ± 0.15 for hip height, 0.34 ± 0.15 for chest depth, 0.26 ± 0.15 for shoulder width, and 0.47 ± 0.16 for chest circumference. In manually measured data, genetic correlations ranged from 0.35 to 0.99, while phenotypic correlations ranged from 0.07 to 0.90. In machine data, genetic correlations ranged from -0.05 to 0.99, while phenotypic correlations ranged from 0.03 to 0.84. The results suggest that machine-based estimations may lead to an overestimation of heritability, but this discrepancy does not impact the selection of breeding models.

Genetic parameters for milk yield and reproductive traits in Honduran Holstein cattle

The aim of this study was to estimate the (co)variance components and genetic parameters for milk yield adjusted to 305d (MY305), calving-to-conception interval (CCI), number of services per conception (NSC) and calving interval (CI) of Honduran Holstein cows, by fitting a bivariate animal model using Maximum Restricted Likelihood procedures. Model included the fixed effects of calving number, the contemporary calving group (farm-season-year of calving and the cow age as covariate). The estimated means and standard deviations for MY, CCI, NSC and CI were, 5098.60 ± 1564.32 kg, 168.27 ± 104.71 days, 2.46 ± 1.69 services, and 448.73 ± 109.16 days, respectively; and their estimated heritabilities were 0.21 ± 0.05, 0.03 ± 0.028, 0.02 ± 0.024 and 0.06 ± 0.04, respectively. The genetic correlations between MY305 and CCI, NSC and CI were positive and antagonist, with values of 0.64 ± 0.52, 0.99 ± 0.56, and 0.32 ± 0.24 respectively. Even though moderate to low heritability was estimated for MY305, systematic selection for milk yield, with a reduction in reproductive efficiency, if considered as the only selection criterion is important to be considered. By including reproductive traits and considering permanent environment effects into the breeding program, might yield a slow, but constant and permanent improvement over time.

Temporal dynamics of genetic parameters and SNP effects for performance and disorder traits in poultry undergoing genomic selection

Accurate genetic parameters are crucial for predicting breeding values and selection responses in breeding programs. Genetic parameters change with selection, reducing additive genetic variance and changing genetic correlations. This study investigates the dynamic changes in genetic parameters for residual feed intake (RFI), gain (GAIN), breast percentage (BP), and femoral head necrosis (FHN) in a broiler population that undergoes selection, both with and without the use of genomic information. Changes in single nucleotide polymorphism (SNP) effects were also investigated when including genomic information. The dataset containing 200,093 phenotypes for RFI, 42,895 for BP, 203,060 for GAIN, and 63,349 for FHN was obtained from 55 mating groups. The pedigree included 1,252,619 purebred broilers, of which 154,318 were genotyped with a 60K Illumina Chicken SNP BeadChip. A Bayesian approach within the GIBBSF90 + software was applied to estimate the genetic parameters for single-, two-, and four-trait models with sliding time intervals. For all models, we used genomic-based (GEN) and pedigree-based approaches (PED), meaning with or without genotypes. For GEN (PED), heritability varied from 0.19 to 0.2 (0.31 to 0.21) for RFI, 0.18 to 0.11 (0.25 to 0.14) for GAIN, 0.45 to 0.38 (0.61 to 0.47) for BP, and 0.35 to 0.24 (0.53 to 0.28) for FHN, across the intervals. Changes in genetic correlations estimated by GEN (PED) were 0.32 to 0.33 (0.12 to 0.25) for RFI-GAIN, -0.04 to -0.27 (-0.18 to -0.27) for RFI-BP, -0.04 to -0.07 (-0.02 to -0.08) for RFI-FHN, -0.04 to 0.04 (0.06 to 0.2) for GAIN-BP, -0.17 to -0.06 (-0.02 to -0.01) for GAIN-FHN, and 0.02 to 0.07 (0.06 to 0.07) for BP-FHN. Heritabilities tended to decrease over time while genetic correlations showed both increases and decreases depending on the traits. Similar to heritabilities, correlations between SNP effects declined from 0.78 to 0.2 for RFI, 0.8 to 0.2 for GAIN, 0.73 to 0.16 for BP, and 0.71 to 0.14 for FHN over the eight intervals with genomic information, suggesting potential epistatic interactions affecting genetic trait architecture. Given rapid genetic architecture changes and differing estimates between genomic and pedigree-based approaches, using more recent data and genomic information to estimate variance components is recommended for populations undergoing genomic selection to avoid potential biases in genetic parameters.

Host genetic control on rumen microbiota and its impact on dairy traits in sheep

BACKGROUND

Milk yield and fine composition in sheep depend on the volatile and long-chain fatty acids, microbial proteins, vitamins produced through feedstuff digestion by the rumen microbiota. In cattle, the host genome has been shown to have a low to moderate genetic control on rumen microbiota abundance but a high control on dairy traits with heritabilities higher than 0.30. There is little information on the genetic correlations and quantitative trait loci (QTL) that simultaneously affect rumen microbiota abundance and dairy traits in ruminants, especially in sheep. Thus, our aim was to quantify the effect of the host genetics on rumen bacterial abundance and the genetic correlations between rumen bacterial abundance and several dairy traits, and to identify QTL that are associated with both rumen bacterial abundance and milk traits.

RESULTS

Our results in Lacaune sheep show that the heritability of rumen bacterial abundance ranges from 0 to 0.29 and that the heritability of 306 operational taxonomic units (OTU) is significantly different from 0. Of these 306 OTU, 96 that belong mainly to the Prevotellaceae, Lachnospiraceae and Ruminococcaceae bacterial families show strong genetic correlations with milk fatty acids and proteins (absolute values ranging from 0.33 to 0.99). Genome-wide association studies revealed a QTL for alpha-lactalbumin concentration in milk on Ovis aries chromosome (OAR) 11, and six QTL for rumen bacterial abundances i.e., for two OTU belonging to the genera Prevotella (OAR3 and 5), Rikeneleaceae_RC9_gut_group (OAR5), Ruminococcus (OAR5), an unknown genus of order Clostridia UCG-014 (OAR10), and CAG-352 (OAR11). None of these detected regions are simultaneously associated with rumen bacterial abundance and dairy traits, but the bacterial families Prevotellaceae, Lachnospiraceae and F082 show colocalized signals on OAR3, 5, 15 and 26.

CONCLUSIONS

In Lacaune dairy sheep, rumen microbiota abundance is partially controlled by the host genetics and is poorly genetically linked with milk protein and fatty acid compositions, and three main bacterial families, Prevotellaceae, Lachnospiraceae and F082, show specific associations with OAR3, 5, 15 and 26.

Influence of model selection and data structure on the estimation of genetic parameters in honeybee populations

Estimating genetic parameters of quantitative traits is a prerequisite for animal breeding. In honeybees, the genetic variance separates into queen and worker effects. However, under data paucity, parameter estimations that account for this peculiarity often yield implausible results. Consequently, simplified models that attribute all genetic contributions to either the queen (queen model) or the workers (worker model) are often used to estimate variance components in honeybees. However, the causes for estimations with the complete model (colony model) to fail and the consequences of simplified models for variance estimates are little understood. We newly developed the necessary theory to compare parameter estimates that were achieved by the colony model with those of the queen and worker models. Furthermore, we performed computer simulations to quantify the influence of model choice, estimation algorithm, true genetic parameters, rates of controlled mating, apiary sizes, and phenotype data completeness on the success of genetic parameter estimations. We found that successful estimations with the colony model were only possible if at least some of the queens mated controlled on mating stations. In that case, estimates were largely unbiased if more than 20% of the colonies had phenotype records. The simplified queen and worker models proved more stable and yielded plausible parameter estimates for almost all settings. Results obtained from these models were unbiased when mating was uncontrolled, but with controlled mating, the simplified models consistently overestimated heritabilities. This study elucidates the requirements for variance component estimation in honeybees and provides the theoretical groundwork for simplified honeybee models.

Influence of maternal and additive genetic effects on offspring growth traits in Beetal goat

The purpose of the present study was to obtain estimates of variance components and genetic parameters for direct and maternal effects on various growth traits in Beetal goat by fitting four animal models, attempting to separate direct genetic, maternal genetic and maternal permanent environmental effects under restricted maximum likelihood procedure. The data of 3,308 growth trait records of Beetal kids born during the period from 2004 to 2019 were used in the present study. Based on best fitted models, the direct additive h² estimates were 0.06, 0.27, 0.37, 0.17 and 0.10 for birth weight (BWT), weight at 3 (WT3), 6 (WT6), 9 (WT9) and 12 (WT12) months of age, respectively. Maternal permanent environmental effects significantly contributed for 10% and 7% of total variance for BWT and WWT, respectively, which reduced direct heritability by 40 and 10% for respective traits from the models without these effects. For average daily gain (ADG1) and Kleiber ratios (KR1) up to weaning period (3 months) traits, maternal permanent environmental effects accounted for 7% and 8% of phenotypic variance, respectively, and resulted in a reduction of 6.6% and 5.4% in direct h² of respective traits. For post-weaning traits, the maternal effects were non-significant (p > .05) which indicates diminishing influence of mothering ability for these traits. High and positive genetic correlations were obtained among WT3-WT6, WT6-WT9 and WT9-WT12 with correlations of 0.96 ± 0.25, 0.84 ± 0.23 and 0.90 ± 0.13, respectively. Thus, early selection at weaning age can be practised taking into consideration maternal variation for effective response to selection in Beetal goat.

Breed-adjusted genomic relationship matrices as a method to account for population stratification in multibreed populations of tropically adapted beef heifers

Context Beef cattle breeds in Australia can broadly be broken up into two subspecies, namely, Bos indicus and Bos taurus. Due to the time since divergence between the subspecies, it is likely that mutations affecting quantitative traits have developed independently in each. Aims We hypothesise that this will affect the prediction accuracy of genomic selection of admixed and composite populations that include both ancestral subspecies. Our study investigates methods to quantify population stratification in a multibreed population of tropically adapted heifers, with the aim of improving prediction accuracy of genomic selection for reproductive maturity score. Methods We used genotypes and reproductive maturity phenotypes from 3695 tropically adapted heifers from three purebred populations, namely, Brahman, Santa Gertrudis and Droughtmaster. Two of these breeds, Santa Gertrudis and Droughtmaster, are stabilised composites of varying B. indicus × B. taurus ancestry, and the third breed, Brahman, has predominately B. indicus ancestry. Genotypes were imputed to three marker-panel densities and population stratification was accounted for in genomic relationship matrices by using breed-specific allele frequencies when calculating the genomic relationships among animals. Prediction accuracy and bias were determined using a five-fold cross validation of randomly selected multibreed cohorts. Key Results Our results showed that the use of breed-adjusted genomic relationship matrices did not improve either prediction accuracy or bias for a lowly heritable trait such as reproductive maturity score. However, using breed-adjusted genomic relationship matrices allowed the capture of a higher proportion of additive genetic effects when estimating variance components. Conclusions These findings suggest that, despite seeing no improvement in prediction accuracy, it may still be beneficial to use breed-adjusted genomic relationship matrices in multibreed populations to improve the estimation of variance components. Implications As such, genomic evaluations using breed-adjusted genomic relationship matrices may be beneficial in multibreed populations.

Bias in estimates of variance components in populations undergoing genomic selection: a simulation study

Background

After the extensive implementation of genomic selection (GS), the choice of the statistical model and data used to estimate variance components (VCs) remains unclear. A primary concern is that VCs estimated from a traditional pedigree-based animal model (P-AM) will be biased due to ignoring the impact of GS. The objectives of this study were to examine the effects of GS on estimates of VC in the analysis of different sets of phenotypes and to investigate VC estimation using different methods. Data were simulated to resemble the Danish Jersey population. The simulation included three phases: (1) a historical phase; (2) 20 years of conventional breeding; and (3) 15 years of GS. The three scenarios based on different sets of phenotypes for VC estimation were as follows: (1) Pheno₁: phenotypes from only the conventional phase (1–20 years); (2) Pheno_1 + 2: phenotypes from both the conventional phase and GS phase (1–35 years); (3) Pheno₂: phenotypes from only the GS phase (21–35 years). Single-step genomic BLUP (ssGBLUP), a single-step Bayesian regression model (ssBR), and P-AM were applied. Two base populations were defined: the first was the founder population referred to by the pedigree-based relationship (P-base); the second was the base population referred to by the current genotyped population (G-base).

Results

In general, both the ssGBLUP and ssBR models with all the phenotypic and genotypic information (Pheno_1 + 2) yielded biased estimates of additive genetic variance compared to the P-base model. When the phenotypes from the conventional breeding phase were excluded (Pheno₂), P-AM led to underestimation of the genetic variance of P-base. Compared to the VCs of G-base, when phenotypes from the conventional breeding phase (Pheno₂) were ignored, the ssBR model yielded unbiased estimates of the total genetic variance and marker-based genetic variance, whereas the residual variance was overestimated.

Conclusions

The results show that neither of the single-step models (ssGBLUP and ssBR) can precisely estimate the VCs for populations undergoing GS. Overall, the best solution for obtaining unbiased estimates of VCs is to use P-AM with phenotypes from the conventional phase or phenotypes from both the conventional and GS phases.

Average information residual maximum likelihood in practice

Gilmour, Thompson, and Cullis (Biometrics, 1995, 51, 1440) presented the average information residual maximum likelihood (REML) algorithm for efficient variance parameter estimation in the linear mixed model. That paper dealt specifically with traditional variance component models, but the algorithm was quickly applied to more general models and implemented in several REML packages including ASReml (Gilmour et al., Biometrics, 2015, 51, 1440). This paper outlines the theory with respect to these more general models, describes the main issues encountered in fitting these models and how they have been addressed in the ASReml software. The issues covered are the basics steps in the implementation of the algorithm, keeping parameters within the parameter space, maximizing sparsity, avoiding issues associated with unstructured variance matrices by using the factor-analytic structure and handling singularities in marker-based relationship matrices and current work.

Estimating variance components in population scale family trees

The rapid digitization of genealogical and medical records enables the assembly of extremely large pedigree records spanning millions of individuals and trillions of pairs of relatives. Such pedigrees provide the opportunity to investigate the sociological and epidemiological history of human populations in scales much larger than previously possible. Linear mixed models (LMMs) are routinely used to analyze extremely large animal and plant pedigrees for the purposes of selective breeding. However, LMMs have not been previously applied to analyze population-scale human family trees. Here, we present Sparse Cholesky factorIzation LMM (Sci-LMM), a modeling framework for studying population-scale family trees that combines techniques from the animal and plant breeding literature and from human genetics literature. The proposed framework can construct a matrix of relationships between trillions of pairs of individuals and fit the corresponding LMM in several hours. We demonstrate the capabilities of Sci-LMM via simulation studies and by estimating the heritability of longevity and of reproductive fitness (quantified via number of children) in a large pedigree spanning millions of individuals and over five centuries of human history. Sci-LMM provides a unified framework for investigating the epidemiological history of human populations via genealogical records.

A UNIFIED FRAMEWORK FOR VARIANCE COMPONENT ESTIMATION WITH SUMMARY STATISTICS IN GENOME-WIDE ASSOCIATION STUDIES

Linear mixed models (LMMs) are among the most commonly used tools for genetic association studies. However, the standard method for estimating variance components in LMMs-the restricted maximum likelihood estimation method (REML)-suffers from several important drawbacks: REML requires individual-level genotypes and phenotypes from all samples in the study, is computationally slow, and produces downward-biased estimates in case control studies. To remedy these drawbacks, we present an alternative framework for variance component estimation, which we refer to as MQS. MQS is based on the method of moments (MoM) and the minimal norm quadratic unbiased estimation (MINQUE) criterion, and brings two seemingly unrelated methods-the renowned Haseman-Elston (HE) regression and the recent LD score regression (LDSC)-into the same unified statistical framework. With this new framework, we provide an alternative but mathematically equivalent form of HE that allows for the use of summary statistics. We provide an exact estimation form of LDSC to yield unbiased and statistically more efficient estimates. A key feature of our method is its ability to pair marginal z-scores computed using all samples with SNP correlation information computed using a small random subset of individuals (or individuals from a proper reference panel), while capable of producing estimates that can be almost as accurate as if both quantities are computed using the full data. As a result, our method produces unbiased and statistically efficient estimates, and makes use of summary statistics, while it is computationally efficient for large data sets. Using simulations and applications to 37 phenotypes from 8 real data sets, we illustrate the benefits of our method for estimating and partitioning SNP heritability in population studies as well as for heritability estimation in family studies. Our method is implemented in the GEMMA software package, freely available at www.xzlab.org/software.html.

Walking through the statistical black boxes of plant breeding

The main statistical procedures in plant breeding are based on Gaussian process and can be computed through mixed linear models. Intelligent decision making relies on our ability to extract useful information from data to help us achieve our goals more efficiently. Many plant breeders and geneticists perform statistical analyses without understanding the underlying assumptions of the methods or their strengths and pitfalls. In other words, they treat these statistical methods (software and programs) like black boxes. Black boxes represent complex pieces of machinery with contents that are not fully understood by the user. The user sees the inputs and outputs without knowing how the outputs are generated. By providing a general background on statistical methodologies, this review aims (1) to introduce basic concepts of machine learning and its applications to plant breeding; (2) to link classical selection theory to current statistical approaches; (3) to show how to solve mixed models and extend their application to pedigree-based and genomic-based prediction; and (4) to clarify how the algorithms of genome-wide association studies work, including their assumptions and limitations.

One hundred years of statistical developments in animal breeding

Statistical methodology has played a key role in scientific animal breeding. Approximately one hundred years of statistical developments in animal breeding are reviewed. Some of the scientific foundations of the field are discussed, and many milestones are examined from historical and critical perspectives. The review concludes with a discussion of some future challenges and opportunities arising from the massive amount of data generated by livestock, plant, and human genome projects.

Application of supernodal sparse factorization and inversion to the estimation of (co)variance components by residual maximum likelihood

We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left-looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver (YAMS), was developed and compared with FSPAK with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire-maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32,840 to 1,048,872. The YAMS software factorized and inverted the matrices up to 13 and 10 times faster than FSPAK, respectively, when an appropriate ordering strategy was applied. The YAMS package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using YAMS. The YAMS package is freely available on request by contacting the corresponding author.

Correlated responses in sow appetite, residual feed intake, body composition, and reproduction after divergent selection for residual feed intake in the growing pig

Residual feed intake (RFI) has been explored as an alternative selection criterion to feed conversion ratio to capture the fraction of feed intake not explained by expected production and maintenance requirements. Selection experiments have found that low RFI in the growing pig is genetically correlated with reduced fatness and feed intake. Selection for feed conversion ratio also reduces sow appetite and fatness, which, together with increased prolificacy, has been seen as a hindrance for sow lifetime performance. The aims of our study were to derive equations for sow RFI during lactation (SRFI) and to evaluate the effect of selection for RFI during growth on sow traits during lactation. Data were obtained on 2 divergent lines selected for 7 generations for low and high RFI during growth in purebred Large Whites. The RFI was measured on candidates for selection (1,065 pigs), and sow performance data were available for 480 sows having from 1 to 3 parities (1,071 parities). Traits measured were sow daily feed intake (SDFI); sow BW and body composition before farrowing and at weaning (28.4 ± 1.7d); number of piglets born total, born alive, and surviving at weaning; and litter weight, average piglet BW, and within-litter SD of piglet BW at birth, 21 d of age (when creep feeding was available), and weaning. Sow RFI was defined as the difference between observed SDFI and SDFI predicted for sow maintenance and production. Daily production requirements were quantified by litter size and daily litter BW gain as well as daily changes in sow body reserves. The SRFI represented 24% of the phenotypic variability of SDFI. Heritability estimates for RFI and SRFI were both 0.14. The genetic correlation between RFI and SRFI was 0.29 ± 0.23. Genetic correlations of RFI with sow traits were low to moderate, consistent with responses to selection; selection for low RFI during growth reduced SDFI and increased number of piglets and litter growth, but also increased mobilization of body reserves. No effect on rebreeding performance was found. Metabolic changes previously observed during growth in response to selection might explain part of the better efficiency of the low-RFI sows, decreasing basal metabolism and favoring rapid allocation of resources to lactation. We propose to consider SRFI as an alternative to SDFI to select for efficient sows with reduced input demands during lactation.

The importance of sample size in the determination of a flock-level antimicrobial resistance profile for Escherichia coli in broilers

Determining herd- or flock-specific antimicrobial resistance profiles is important to guide therapeutic use of antimicrobials and to assess risk factors for the development and spread of antimicrobial resistance. As such, it is of utmost importance to optimize the sampling strategy for the determination of herd-specific antimicrobial resistance profiles. However, the multitude of prevalences measured at the same time as well as the presence of variation both at the level of the animal and the bacterial population of concern make it impossible to use conventional sample size determination methods. In this article, the use of bootstrapping techniques for sample size determination was explored. In particular, one-stage and two-stage bootstrap samplings were used to determine the optimal number of animals and the optimal number of isolates within one animal. Results show that focus should be on the number of animals sampled rather than on the number of isolates tested within one animal.

A Bayesian framework for comparative quantitative genetics

Bayesian approaches have been extensively used in animal breeding sciences, but similar approaches in the context of evolutionary quantitative genetics have been rare. We compared the performance of Bayesian and frequentist approaches in estimation of quantitative genetic parameters (viz. matrices of additive and dominance variances) in datasets typical of evolutionary studies and traits differing in their genetic architecture. Our results illustrate that it is difficult to disentangle the relative roles of different genetic components from small datasets, and that ignoring, e.g. dominance is likely to lead to biased estimates of additive variance. We suggest that a natural summary statistic for G-matrix comparisons can be obtained by examining how different the underlying multinormal probability distributions are, and illustrate our approach with data on the common frog (Rana temporaria). Furthermore, we derive a simple Monte Carlo method for computation of fraternity coefficients needed for the estimation of dominance variance, and use the pedigree of a natural Siberian jay (Perisoreus infaustus) population to illustrate that the commonly used approximate values can be substantially biased.

Genetic parameters for residual feed intake in growing pigs, with emphasis on genetic relationships with carcass and meat quality traits

Data were collected over the first 4 generations of a divergent selection experiment for residual feed intake of Large White pigs having ad libitum access to feed. This data set was used to obtain estimates of heritability for residual feed intake and genetic correlations (r(a)) between this trait and growth, carcass, and meat quality traits. Individual feed intake of group-housed animals was measured by single-space electronic feeders. Upward and downward selection lines were maintained contemporarily, with 6 boars and 35 to 40 sows per line and generation. Numbers of records were 793 for residual feed intake (RFI1) of boar candidates for selection issued from first-parity (P1) litters and tested over a fixed BW range (35 to 95 kg) and 657 for residual feed intake (RFI2) and growth, carcass, and meat quality traits of castrated males and females issued from second-parity (P2) litters and tested from 28 to 107 kg of BW. Variance and covariance components were estimated using REML methodology applied to a series of multitrait animal models, which always included the criterion for selection as 1 of the traits. Estimates of heritability for RFI1 and RFI2 were 0.14 +/- 0.03 and 0.24 +/- 0.03, respectively, whereas the estimate of r(a) between the 2 traits was 0.91 +/- 0.08. Estimates of r(a) indicated that selection for low residual feed intake has the potential to improve feed conversion ratio and reduce daily feed intake, with minimal correlated effect for ADG of P2 animals. Estimates of r(a) between RFI2 and body composition traits of P2 animals were positive for traits related to the amount of fat depots (r(a) = 0.44 +/- 0.16 for carcass backfat thickness) and negative for carcass lean meat content (r(a) = -0.55 +/- 0.14). There was a tendency for a negative genetic correlation between RFI2 and carcass dressing percent (r(a) = -0.36 +/- 0.21). Moreover, selection for low residual feed intake is expected, through lower ultimate pH and lighter color, to decrease pork quality (r(a) = 0.77 +/- 0.14 between RFI2 and a meat quality index intended to predict the ratio of the weight of ham after curing and cooking to the weight of defatted and boneless fresh ham).

Up hill, down dale: quantitative genetics of curvaceous traits

'Repeated' measurements for a trait and individual, taken along some continuous scale such as time, can be thought of as representing points on a curve, where both means and covariances along the trajectory can change, gradually and continually. Such traits are commonly referred to as 'function-valued' (FV) traits. This review shows that standard quantitative genetic concepts extend readily to FV traits, with individual statistics, such as estimated breeding values and selection response, replaced by corresponding curves, modelled by respective functions. Covariance functions are introduced as the FV equivalent to matrices of covariances. Considering the class of functions represented by a regression on the continuous covariable, FV traits can be analysed within the linear mixed model framework commonly employed in quantitative genetics, giving rise to the so-called random regression model. Estimation of covariance functions, either indirectly from estimated covariances or directly from the data using restricted maximum likelihood or Bayesian analysis, is considered. It is shown that direct estimation of the leading principal components of covariance functions is feasible and advantageous. Extensions to multi-dimensional analyses are discussed.

Estimation of quantitative genetic parameters

This paper gives a short review of the development of genetic parameter estimation over the last 40 years. This shows the development of more statistically and computationally efficient methods that allow the fitting of more biologically appropriate models. Methods have evolved from direct methods based on covariances between relatives to methods based on individual animal models. Maximum-likelihood methods have a natural interpretation in terms of best linear unbiased predictors. Improvements in iterative schemes to give estimates are discussed. As an example, a recent estimation of genetic parameters for a British population of dairy cattle is discussed. The development makes a connection to relevant work by Bill Hill.

Genetic parameters for level and change of body condition score and body weight in dairy cows

(Co)variance components for body condition score (BCS), body weight (BW), BCS change, BW change, and milk yield traits were estimated. The data analyzed included 6646 multiparous Holstein-Friesian cows with records for BCS, BW, and(or) milk yield at different stages of lactation from 74 dairy herds throughout Southern Ireland. Heritability estimates for BCS ranged from 0.27 to 0.37, while those for BCS change ranged from 0.02 to 0.10. Heritability estimates for BW records varied from 0.39 to 0.50, while heritabilities for BW change were similar to those observed for BCS change (0.03 to 0.09). The genetic correlations between BCS and BW at the same days in milk deviated little from 0.50, and the genetic correlations between BCS change and BW change over the same period ranged from 0.42 to 0.55. BCS and BW directly postpartum were both phenotypically and genetically negatively correlated with both BW change and BCS change in early lactation. The genetic correlations between BCS and milk yield were negative. The results of the present study show that animals that lose most BCS in early lactation tend to gain most BCS in late lactation, a trend also exhibited by BW.

Application of a mixed normal mixture model for the estimation of Mastitis-related parameters

The current methodology for estimating genetic parameters for SCC (SCS) does not account for the difference in SCS between healthy cows and cows with an intramammary infection (IMI). We propose a two-component finite mixed normal mixture model to estimate IMI prevalence, separate SCS subpopulation means, individual posterior probabilities of IMI, and SCS variance components. The theory is presented and the expectation-conditional maximization algorithm is utilized to compute maximum likelihood estimates. The methodology is illustrated on two simulated data sets based on the current knowledge of SCS parameters. Maximum likelihood estimates of IMI prevalence and SCS subpopulation means were close to simulated values, except for the estimate of IMI prevalence when both subpopulations were almost confounded. Individual posterior probabilities of IMI were always higher among infected than among healthy cows. Error and additive variance components obtained under the mixture model were closer to simulated values than restricted maximum likelihood estimates obtained assuming a homogeneous SCS distribution, especially when subpopulations were completely separated and when mixing proportion was highest. Convergence was linear and rapid when priors were chosen with caution. The advantages of the methodology are demonstrated, and its feasibility for large data sets is discussed.

Estimation of variance components of quantitative traits in inbred populations

Use of variance-component estimation for mapping of quantitative-trait loci in humans is a subject of great current interest. When only trait values, not genotypic information, are considered, variance-component estimation can also be used to estimate heritability of a quantitative trait. Inbred pedigrees present special challenges for variance-component estimation. First, there are more variance components to be estimated in the inbred case, even for a relatively simple model including additive, dominance, and environmental effects. Second, more identity coefficients need to be calculated from an inbred pedigree in order to perform the estimation, and these are computationally more difficult to obtain in the inbred than in the outbred case. As a result, inbreeding effects have generally been ignored in practice. We describe here the calculation of identity coefficients and estimation of variance components of quantitative traits in large inbred pedigrees, using the example of HDL in the Hutterites. We use a multivariate normal model for the genetic effects, extending the central-limit theorem of Lange to allow for both inbreeding and dominance under the assumptions of our variance-component model. We use simulated examples to give an indication of under what conditions one has the power to detect the additional variance components and to examine their impact on variance-component estimation. We discuss the implications for mapping and heritability estimation by use of variance components in inbred populations.