Effects of dietary chromium supplementation on performance, carcass characteristics, and meat quality of growing-finishing swine: a meta-analysis

Dietary Cr supplementation has potential to decrease fat and increase lean in carcasses of growing-finishing swine. However, effects of Cr supplementation on performance and economically important carcass and meat quality characteristics varied considerably among studies. Therefore, a meta-analysis was designed to quantitatively describe effects obtained in several independent studies. To accommodate differences in methodology among studies, standardized effect sizes (Hedges's g) were calculated for results from 31 studies, in which Cr was supplemented as complexes of Cr Met chelate, Cr nanocomposite, Cr nicotinate, Cr propionate, Cr tripicolinate, or Cr yeast in diets for growing-finishing swine. Summary statistics were calculated by frequentist fixed and random effects, and hierarchical Bayesian models. With characteristics related to carcass quality, observed heterogeneity (P < 0.10) could not adequately be explained in a meta-regression by differences in initial BW and amount of Cr supplemented. Random effects and Bayesian models to summarize effect sizes for these characteristics showed similar results. According to random effects models, dietary Cr supplementation decreased (P < 0.05) 10th-rib fat thickness (mean effect size = -0.479; 95% confidence intervals = -0.680 to -0.279; 24 studies; 59 comparisons), whereas percentage carcass lean (mean effect size = 0.614; 95% confidence intervals = 0.366 to 0.863; 22 studies; 52 comparisons) and LM area (mean effect size = 0.571; 95% confidence intervals = 0.364 to 0.778; 29 studies; 72 comparisons) increased. Average daily gain and G:F, which did not present heterogeneity, were improved by Cr supplementation, whereas no effects were detected in characteristics (CIE color, drip loss, cook loss, shear force) related to meat quality. Some publication, or other small-study bias, was evident in results on growth and feed efficiency. However, directions of mean effect sizes were not changed by application of the trim-and-fill method to correct for bias.     

Frequentist and Bayesian approaches to prevalence estimation using examples from Johne's disease

Although frequentist approaches to prevalence estimation are simple to apply, there are circumstances where it is difficult to satisfy assumptions of asymptotic normality and nonsensical point estimates (greater than 1 or less than 0) may result. This is particularly true when sample sizes are small, test prevalences are low and imperfect sensitivity and specificity of diagnostic tests need to be incorporated into calculations of true prevalence. Bayesian approaches offer several advantages including direct computation of range-respecting interval estimates (e.g. intervals between 0 and 1 for prevalence) without the requirement of transformations or large-sample approximations, direct probabilistic interpretation, and the flexibility to model in a straightforward manner the probability of zero prevalence. In this review, we present frequentist and Bayesian methods for animal- and herd-level true prevalence estimation based on individual and pooled samples. We provide statistical methods for detecting differences between population prevalence and frequentist methods for sample size and power calculations. All examples are motivated using Mycobacterium avium subspecies paratuberculosis infection and we provide WinBUGS code for all examples of Bayesian estimation.     

The empirical bias of estimates by restricted maximum likelihood, Bayesian method, and method R under selection for additive, maternal, and dominance models.

Bayesian analysis via Gibbs sampling, restricted maximum likelihood (REML), and Method R were used to estimate variance components for several models of simulated data. Four simulated data sets that included direct genetic effects and different combinations of maternal, permanent environmental, and dominance effects were used. Parents were selected randomly, on phenotype across or within contemporary groups, or on BLUP of genetic value. Estimates by Bayesian analysis and REML were always empirically unbiased in large data sets. Estimates by Method R were biased only with phenotypic selection across contemporary groups; estimates of the additive variance were biased upward, and all the other estimates were biased downward. No empirical bias was observed for Method R under selection within contemporary groups or in data without contemporary group effects. The bias of Method R estimates in small data sets was evaluated using a simple direct additive model. Method R gave biased estimates in small data sets in all types of selection except BLUP. In populations where the selection is based on BLUP of genetic value or where phenotypic selection is practiced mostly within contemporary groups, estimates by Method R are likely to be unbiased. In this case, Method R is an alternative to single-trait REML and Bayesian analysis for analyses of large data sets when the other methods are too expensive to apply.     

A Bayesian meta-analysis of the effects of administering an intra-vaginal (CIDR) device in combination with other hormones on the reproductive performance of cycling,anoestrous and inseminated cows

AIMS: To evaluate the effectiveness of treatment programmes that included controlled internal drug-releasing (CIDR) devices containing progesterone (P4) in improving synchrony of oe- strus, and conception and pregnancy rates in cycling, anoestrous and inseminated dairy cows, using meta-analysis. To describe the difference in response between cycling and anoestrous cows to CIDR-based synchrony programmes.

METHODS: Scientific papers written in the English language between 1989 and 2002 that investigated the effects of treat- ment programmes including CIDR devices on reproductive per- formance in dairy heifers or lactating dairy cows were identified using a computerised literature search. The criteria for inclusion incorporated evidence that treatment allocation was completely randomised; the population studied was lactating dairy cows; and that data were available on submission, conception and pregnancy rates and their associated measures of variability. Re- productive outcomes from 25 synchrony trials (total n= 11,058 cows) were analysed. Summary measures of the effect of treat- ment on reproductive outcome were assessed using fixed- and random-effects Bayesian meta-analysis models.

RESULTS: Treatment programmes including a CIDR device increased the risk of submission in cycling cows (predicted Bayesian RR=2.86, 95% credible interval 1.46–5.67). Compared with controls, synchrony programmes including CIDR devices in cycling dairy cows had no effect on the risk of conception to first service post-treatment (predicted Bayesian RR=1.00, 95% credible interval=0.80-1.24). Compared with controls, synchrony programmes including CIDR devices had no effect on the risk of pregnancy throughout the mating period (pre- dicted Bayesian RR=1.02, 95% credible interval=0.89-1.17). In anoestrous cows, CIDR treatment had no effect on the risk of conception to first service post-treatment and no effect on the risk of pregnancy throughout the mating period, compared with anoestrous, untreated controls (predicted Bayesian RR=0.91 and 0.97, respectively; 95% credible interval=0.68–1.26 and 0.59-1.60, respectively).

CONCLUSION: The results of this meta-analysis showed that synchrony programmes using CIDR devices combined with other hormones reliably enhanced submission rates in lactat- ing dairy cows. The relatively small number of trials with data suitable for analysis and the heterogeneity of results at the indi- vidual trial level limited our ability to confirm either a beneficial or deleterious effect of treatment on conception or pregnancy rates. Further randomised, controlled trials to evaluate the ef- fectiveness of this form of reproductive therapy in commercial dairy farms are needed.     

A simulation study to assess statistical methods for binary repeated measures data

Binary repeated measures data are commonly encountered in both experimental and observational veterinary studies. Among the wide range of statistical methods and software applicable to such data one major distinction is between marginal and random effects procedures. The objective of the study was to review and assess the performance of marginal and random effects estimation procedures for the analysis of binary repeated measures data. Two simulation studies were carried out, using relatively small, balanced, two-level (time within subjects) datasets. The first study was based on data generated from a marginal model with first order autocorrelation, the second on a random effects model with autocorrelated random effects within subjects. Three versions of the models were considered in which a dichotomous treatment was modelled additively, either between or within subjects, or modelled by a time interaction. Among the studied statistical procedures were: generalized estimating equations (GEE), Marginal Quasi Likelihood, likelihood based on numerical integration, penalized quasi-likelihood, restricted pseudo likelihood and Bayesian Markov Chain Monte Carlo. Results for data generated by the marginal model showed autoregressive GEE to be highly efficient when treatment was within subjects, even with strongly correlated responses. For treatment between subjects, random effects procedures also performed well in some situations; however, a relatively small number of subjects with a short time series proved a challenge for both marginal and random effects procedures. Results for data generated by the random effects model showed bias in estimates from random effects procedures when autocorrelation was present in the data, while the marginal procedures generally gave estimates close to the marginal parameters.     

Effectiveness of adjusting for heterogeneity of variance in genetic evaluation of Japanese Black cattle

Heterogeneity of variance among subclasses of an effect is a potential source of bias in genetic evaluation. The objectives of this study were to quantify the heterogeneity of variance in carcass weight in Japanese Black cattle, to develop an adjustment method to account for the heterogeneity, and to evaluate the effectiveness of the method. A total of 96,950 records were collected from steers and heifers slaughtered from 1997 to 2005. These records were grouped into 2,767 farm-market-year-sex subclasses. Fourteen log-linear models for the variances were set up to estimate the heterogeneous phenotypic variances within subclasses. Schwarz's Bayesian information criterion was used for model selection. The preadjustment of records to a baseline variance was based on maximum likelihood estimates obtained from the selected model. As a result of adjustment, the SD, the CV, and the Gini coefficient for the phenotypic variance decreased by 68.6, 69.8, and 70.1%, respectively. When the top 5% of sires and top 1% of dams were selected, Spearman's rank correlation coefficients between the adjusted and unadjusted data were 0.95 for the selected sires and 0.78 for the selected dams. The effectiveness of the adjustment was evaluated in terms of the ability to predict breeding values, using the results of the successive genetic evaluations. Mean squared error between the parent averages and actual predicted values of the genetic merit for the sires whose progeny had a carcass record only from 2003 to 2005 was significantly reduced by the adjustment (P < 0.05). The results suggest that the genetic evaluation becomes more accurate by adjusting the data using the procedure developed in this study.     

Elusive cats in our backyards: persistence of the North Chinese leopard (Panthera pardus japonensis) in a human-dominated landscape in central China

The North Chinese leopard (Panthera pardus japonensis), the least-known big cat, disappeared in most historical range for decades, following the development of modern civilization. Unfortunately, we have scarce knowledge about the status of this big cat so far, apart from anecdotal reports. In this study, we investigated density, distribution, and habitat use of the leopard, the apex predator, in a complex forest landscape in the Loess Plateau. We used a camera-trapping network to obtain population estimates for leopards over 2 years through spatially explicit capture–recapture models. Our results, based on maximum likelihood and Bayesian/MCMC methods, reveal that the largest wild population of the leopard was found widely distributed in remnant forests in central Loess plateau. The population is increasing in our study area, and the density of leopards (1.70 (SE = 0.48) − 2.40 (SE = 0.67)/100 km²) is higher than other areas of China. According to the analysis of 2 seasonal occupancy models, prey species drive partially the leopard habitat use, predicting that the big cat thrives from the recovery of prey community. However, human disturbances, especially oil wells, seem to have negative impacts on the habitat use of leopards. Specifically, it is necessary to have joint efforts by the government and researchers to improve human disturbances management and prey species population density, as well as strengthen the investment in research on the North Chinese leopard, which could all further strengthen protection ability and ensure the long-term survival of this species.     

A Bayesian meta-analysis of the effects of administering an intra-vaginal (CIDR) device in combination with other hormones on the reproductive performance of cycling, anoestrous and inseminated cows

AIMS: To evaluate the effectiveness of treatment programmes that included controlled internal drug-releasing (CIDR) devices containing progesterone (P4) in improving synchrony of oestrus, and conception and pregnancy rates in cycling, anoestrous and inseminated dairy cows, using meta-analysis. To describe the difference in response between cycling and anoestrous cows to CIDR-based synchrony programmes. METHODS: Scientific papers written in the English language between 1989 and 2002 that investigated the effects of treatment programmes including CIDR devices on reproductive performance in dairy heifers or lactating dairy cows were identified using a computerised literature search. The criteria for inclusion incorporated evidence that treatment allocation was completely randomised; the population studied was lactating dairy cows; and that data were available on submission, conception and pregnancy rates and their associated measures of variability. Reproductive outcomes from 25 synchrony trials (total n=11,058 cows) were analysed. Summary measures of the effect of treatment on reproductive outcome were assessed using fixed- and random-effects Bayesian meta-analysis models. RESULTS: Treatment programmes including a CIDR device increased the risk of submission in cycling cows (predicted Bayesian RR=2.86, 95% credible interval=1.46-5.67). Compared with controls, synchrony programmes including CIDR devices in cycling dairy cows had no effect on the risk of conception to first service post-treatment (predicted Bayesian RR=1.00, 95% credible interval=0.80-1.24). Compared with controls, synchrony programmes including CIDR devices had no effect on the risk of pregnancy throughout the mating period (predicted Bayesian RR=1.02, 95% credible interval=0.89-1.17). In anoestrous cows, CIDR treatment had no effect on the risk of conception to first service post-treatment and no effect on the risk of pregnancy throughout the mating period, compared with anoestrous, untreated controls (predicted Bayesian RR=0.91 and 0.97, respectively; 95% credible interval=0.68-1.26 and 0.59-1.60, respectively). CONCLUSION: The results of this meta-analysis showed that synchrony programmes using CIDR devices combined with other hormones reliably enhanced submission rates in lactating dairy cows. The relatively small number of trials with data suitable for analysis and the heterogeneity of results at the individual trial level limited our ability to confirm either a beneficial or deleterious effect of treatment on conception or pregnancy rates. Further randomised, controlled trials to evaluate the effectiveness of this form of reproductive therapy in commercial dairy farms are needed.     

“Bending” and beyond: Better estimates of quantitative genetic parameters?

Multivariate estimation of genetic parameters involving more than a handful of traits can be afflicted by problems arising through substantial sampling variation. We present a review of underlying causes and proposals to improve estimates, focusing on linear mixed model‐based estimation via restricted maximum likelihood (REML). Both full multivariate analyses and pooling of results from overlapping subsets of traits are considered. It is suggested to impose a penalty on the likelihood designed to reduce sampling variances at the expense of a little additional bias. Simulation results are discussed which demonstrate that this can yield REML estimates that are on average closer to the population values than their unpenalized counterparts. Suitable penalties can be obtained based on assumed prior distributions of selected parameters. Necessary choices of penalty functions and of the stringency of penalization are examined. We argue that scale‐free penalty functions lend themselves to a simple scheme imposing a mild, default penalty which can yield “better” estimates without being likely to incur detrimental effects.     

The effect of ignoring individual heterogeneity in Weibull log-normal sire frailty models

The objective of this study was, by means of simulation, to quantify the effect of ignoring individual heterogeneity in Weibull sire frailty models on parameter estimates and to address the consequences for genetic inferences. Three simulation studies were evaluated, which included 3 levels of individual heterogeneity combined with 4 levels of censoring (0, 25, 50, or 75%). Data were simulated according to balanced half-sib designs using Weibull log-normal animal frailty models with a normally distributed residual effect on the log-frailty scale. The 12 data sets were analyzed with 2 models: the sire model, equivalent to the animal model used to generate the data (complete sire model), and a corresponding model in which individual heterogeneity in log-frailty was neglected (incomplete sire model). Parameter estimates were obtained from a Bayesian analysis using Gibbs sampling, and also from the software Survival Kit for the incomplete sire model. For the incomplete sire model, the Monte Carlo and Survival Kit parameter estimates were similar. This study established that when unobserved individual heterogeneity was ignored, the parameter estimates that included sire effects were biased toward zero by an amount that depended in magnitude on the level of censoring and the size of the ignored individual heterogeneity. Despite the biased parameter estimates, the ranking of sires, measured by the rank correlations between true and estimated sire effects, was unaffected. In comparison, parameter estimates obtained using complete sire models were consistent with the true values used to simulate the data. Thus, in this study, several issues of concern were demonstrated for the incomplete sire model.     

Comparison of methods for estimation of individual-level prevalence based on pooled samples.

We review frequentist and Bayesian approaches for estimating animal-level disease prevalence using pooled samples obtained by simple random sampling. We determine the preferred approach for different prevalence scenarios and with varying knowledge about sensitivity and specificity values. When sensitivity and specificity are perfect or known, we can choose between the large-sample theory estimates and the one-to-one relationship exact estimates. When sensitivity and specificity are unknown, we must use large-sample theory estimates or Bayesian methodology (which gives exact estimates). However, when the large-sample theory produces a negative lower confidence limit, we must use one of the exact methods. We compare estimates from each approach using culture results from pools of 20 eggs from three flocks on a California ranch that were producing eggs that were contaminated with Salmonella enteritidis phage type 4.     

Influence of population structure on estimates of direct and maternal parameters.

The estimation of (co)variance components for multiple traits with maternal genetic effects was found to be influenced by population structure. Two traits in a closed breeding herd with random mating were simulated over nine generations. Population structures were simulated on the basis of different proportions of dams not having performance records (0, 0.1, 0.5, 0.8 and 0.9): three genetic correlations (-0.5, 0.0 and +0.5) between direct and maternal effects and three genetic correlations (0, 0.3 and 0.8) between two traits. Three ratios of direct to maternal genetic variances, (1:3, 1:1, 3:1), were also considered. Variance components were estimated by restricted maximum likelihood. The proportion of dams without records had an effect on the SE of direct-maternal covariance estimates when the proportion was 0.8 or 0.9 and the true correlation between direct and maternal effects was negative. The ratio of direct to maternal genetic variances influenced the SE of the (co)variance estimates more than the proportion of dams with missing records. The correlation between two traits did not have an effect on the SE of the estimates. The proportion of dams without records and the correlation between direct and maternal effects had the strongest effects on bias of estimates. The largest biases were obtained when the proportion of dams without records was high, the correlation between direct and maternal effects was positive, and the direct variance was greater than the maternal variance, as would be the situation for most growth traits in livestock. Total bias in all parameter estimates for two traits was large in the same situations. Poor population structure can affect both bias and SE of estimates of the direct-maternal genetic correlation, and can explain some of the large negative estimates often obtained.     

"Quasi-REML" correlation estimates between production and health traits in the presence of selection and confounding: a simulation study

Performance of the "quasi-REML" method for estimating correlations between a continuous trait and a categorical trait, and between two categorical traits, was studied with Monte Carlo simulations. Three continuous, correlated traits were simulated for identical populations and three scenarios with either no selection, selection for one moderately heritable trait (Trait 1, h2 = .25), and selection for the same trait plus confounding between sires and management groups. The "true" environmental correlations between Traits 2 (h2 = .10) and 3 (h2 = .05) were always of the same absolute size (.20), but further data scenarios were generated by setting the sign of environmental correlation to either positive or negative. Observations for Traits 2 and 3 were then reassigned to binomial categories to simulate health or reproductive traits with incidences of 15 and 5%, respectively. Genetic correlations (r(g12), r(g13), and r(g23) and environmental correlations (r(e12), r(e13), and r(e23)) were estimated for the underlying continuous scale (REML) and the visible categorical scales ("quasi-REML") with linear multiple-trait sire and animal models. Contrary to theory, practically all "quasi-REML" genetic correlations were underestimated to some extent with the sire and animal models. Selection inflated this negative bias for sire model estimates, and the sign of r(e23) noticeably affected r(g23) estimates for the animal model, with greater bias and SD for estimates when the "true" r(e23) was positive. Transformed "quasi-REML" environmental correlations between a continuous and a categorical trait were estimated with good efficiency and little bias, and corresponding correlations between two categorical traits were systematically overestimated. Confounding between sires and contemporary groups negatively affected all correlation estimates on the underlying and the visible scales, especially for sire model "quasi-REML" estimates of genetic correlation. Selection, data structure, and the (co)variance structure influences how well correlations involving categorical traits are estimated with "quasi-REML" methods.     

Scaling to account for heterogeneous variances in a Bayesian analysis of broiler quantitative trait loci

A Bayesian method for QTL analysis that is capable of accounting for heterogeneity of variance between sexes, is introduced. The Bayesian method uses a parsimonious model that includes scaling parameters for polygenic and QTL allelic effects per sex. Furthermore, the method employs a reduced animal model to increase computational efficiency. Markov Chain Monte Carlo techniques were applied to obtain estimates of genetic parameters. In comparison with previous regression analyses, the Bayesian method 1) estimates dispersion parameters and polygenic effects, 2) uses individual observations instead of offspring averages, and 3) estimates fixed effect levels and covariates and heterogeneity of variance between sexes simultaneously with other parameters, taking uncertainties fully into account. Broiler data collected in a feed efficiency and a carcass experiment were used to illustrate QTL analysis based on the Bayesian method. The experiments were conducted in a population consisting of 10 full-sib families of a cross between two broiler lines. Microsatellite genotypes were determined on generation 1 and 2 animals and phenotypes were collected on third-generation offspring from mating members from different families. Chromosomal regions that seemed to contain a QTL in previous regression analyses and showed heterogeneity of variance were chosen. Traits analyzed in the feed efficiency experiment were BW at 48 d and growth, feed intake, and feed intake corrected for BW between 23 and 48 d. In the carcass experiment, carcass percentage was analyzed. The Bayesian method was successful in finding QTL in all regions previously detected.     

Evaluation of diagnostic tests in the absence of a gold standard using an Anaplasma marginale field data set

The evaluation of newly developed diagnostic tests (tests) commonly involves the comparison of the test outcomes (pos/neg.) of a sample of animals to those of a reference test (gold standard) in order to derive sensitivity and specificity estimates. Often, however, new tests have to be evaluated against an imperfect reference test since a true gold standard test is either too expensive or too costly to apply. This results in bias in the test characteristic estimates. To solve this problem, latent class and Bayesian models can be used to estimate sensitivity and specificity when evaluating a diagnostic test in the absence of a gold standard. They require at least two imperfect reference tests applied to all individuals in the study. In our approach we used a two-test two-population scenario. Both the gold standard and these modelling approaches rely on various assumptions. When violated, biased results will be obtained. The analysis of field data from an Anaplasma marginale outbreak in cattle in Switzerland with four diagnostic procedures (detection of the agent, serology, PCR and hematocrit measurements) was used as a practical example to demonstrate and critically discuss the approaches taken. In this relatively small data set (n = 275) the estimates for the test characteristics obtained by the different methods were quite similar. Overall, the bias in the point estimates depended mainly on the chosen estimation approach. All tests showed a non-negligible correlation mainly in the test sensitivities. This emphasizes the importance of taking into account test dependence even if it seems not biologically plausible at first thought.     

Inferring source attribution from a multiyear multisource data set of Salmonella in Minnesota

Salmonella enterica is a global health concern because of its widespread association with foodborne illness. Bayesian models have been developed to attribute the burden of human salmonellosis to specific sources with the ultimate objective of prioritizing intervention strategies. Important considerations of source attribution models include the evaluation of the quality of input data, assessment of whether attribution results logically reflect the data trends and identification of patterns within the data that might explain the detailed contribution of different sources to the disease burden. Here, more than 12,000 non‐typhoidal Salmonella isolates from human, bovine, porcine, chicken and turkey sources that originated in Minnesota were analysed. A modified Bayesian source attribution model (available in a dedicated R package), accounting for non‐sampled sources of infection, attributed 4,672 human cases to sources assessed here. Most (60%) cases were attributed to chicken, although there was a spike in cases attributed to a non‐sampled source in the second half of the study period. Molecular epidemiological analysis methods were used to supplement risk modelling, and a visual attribution application was developed to facilitate data exploration and comprehension of the large multiyear data set assessed here. A large amount of within‐source diversity and low similarity between sources was observed, and visual exploration of data provided clues into variations driving the attribution modelling results. Results from this pillared approach provided first attribution estimates for Salmonella in Minnesota and offer an understanding of current data gaps as well as key pathogen population features, such as serotype frequency, similarity and diversity across the sources. Results here will be used to inform policy and management strategies ultimately intended to prevent and control Salmonella infection in the state.     

Spatial distribution of Escherichia coli O157-positive farms in Scotland

Using a sample of 949 Scottish farms with finishing cattle, the spatial distribution of Escherichia coli O157-positive farms was investigated using disease mapping models. The overall prevalence of E. coli O157-positive farms was estimated as 22%. The regions used in this study were the 16 postcode areas of Scotland. For each region, the posterior relative risk (RR) was estimated as a model-based alternative to the saturated standardized morbidity ratio (SMR), i.e., the ratio between observed and expected cases in a region. Three Bayesian hierarchical models with generalized linear modeling of the area-specific risks were used to estimate the posterior relative risk of E. coli O157-positive farms in the postcode areas: a random-effects model incorporating only spatially uncorrelated heterogeneity; a model incorporating both spatially correlated and uncorrelated heterogeneity; and a pseudo-mixture model with unstructured correlation and a weighted mix of two variance components representing the spatial correlation and a jump structure. None of the models identified any areas with a significant increase or decrease in risk. The deviance information criteria slightly favored the simplest model (RR range: 0.92--1.09). However, this model appeared to smooth out more of the variation in the RR compared to the pseudo-mixture model, which gave a more informative pattern of the posterior relative risks (range: 0.81--1.22).     

Estimation of genetic parameters and response to selection for a continuous trait subject to culling before testing

The consequences of assuming a zero environmental covariance between a binary trait 'test-status' and a continuous trait on the estimates of genetic parameters by restricted maximum likelihood and Gibbs sampling and on response from genetic selection when the true environmental covariance deviates from zero were studied. Data were simulated for two traits (one that culling was based on and a continuous trait) using the following true parameters, on the underlying scale: h2 = 0.4; r(A) = 0.5; r(E) = 0.5, 0.0 or -0.5. The selection on the continuous trait was applied to five subsequent generations where 25 sires and 500 dams produced 1500 offspring per generation. Mass selection was applied in the analysis of the effect on estimation of genetic parameters. Estimated breeding values were used in the study of the effect of genetic selection on response and accuracy. The culling frequency was either 0.5 or 0.8 within each generation. Each of 10 replicates included 7500 records on 'test-status' and 9600 animals in the pedigree file. Results from bivariate analysis showed unbiased estimates of variance components and genetic parameters when true r(E) = 0.0. For r(E) = 0.5, variance components (13-19% bias) and especially (50-80%) were underestimated for the continuous trait, while heritability estimates were unbiased. For r(E) = -0.5, heritability estimates of test-status were unbiased, while genetic variance and heritability of the continuous trait together with were overestimated (25-50%). The bias was larger for the higher culling frequency. Culling always reduced genetic progress from selection, but the genetic progress was found to be robust to the use of wrong parameter values of the true environmental correlation between test-status and the continuous trait. Use of a bivariate linear-linear model reduced bias in genetic evaluations, when data were subject to culling.     

Variational bayesian method of estimating variance components

We developed a Bayesian analysis approach by using a variational inference method, a so‐called variational Bayesian method, to determine the posterior distributions of variance components. This variational Bayesian method and an alternative Bayesian method using Gibbs sampling were compared in estimating genetic and residual variance components from both simulated data and publically available real pig data. In the simulated data set, we observed strong bias toward overestimation of genetic variance for the variational Bayesian method in the case of low heritability and low population size, and less bias was detected with larger population sizes in both methods examined. The differences in the estimates of variance components between the variational Bayesian and the Gibbs sampling were not found in the real pig data. However, the posterior distributions of the variance components obtained with the variational Bayesian method had shorter tails than those obtained with the Gibbs sampling. Consequently, the posterior standard deviations of the genetic and residual variances of the variational Bayesian method were lower than those of the method using Gibbs sampling. The computing time required was much shorter with the variational Bayesian method than with the method using Gibbs sampling.     

Assessing Relationships Between Genetic Evaluations Using Robust Regression with an Application to Holsteins in Uruguay

Globalization of dairy cattle breeding has created a need for international sire proofs. Some early methods for converting proofs from one population to another are based on simple linear regression. An alternative robust regression method based on the t-distribution is presented, and maximum likelihood and Bayesian techniques for analysis are described, including the situation in which some proofs are missing. Procedures were used to investigate the relationship between Holstein sire proofs obtained by two Uruguayan genetic evaluation programs. The results suggest that conversion equations developed from data including only sires having proofs in both populations can lead to distorted results, relative to estimates obtained using techniques for incomplete data. There was evidence of non-normality of regression residuals, which constitutes an additional source of bias. A robust estimator may not solve all problems, but can provide simple conversion equations that are less sensitive to outlying proofs and to departures from assumptions.