Mixed Model Equations Research Articles

Comparison of fixed effects and mixed model growth functions in modelling and predicting live weight in pigs

The objective of the present study was to compare alternative growth functions fitted to pig live weight data, with particular emphasis on the function׳s ability to predict future animal live weight. The final dataset consisted of 51,893 live weight records from 10,201 pigs aged between 61 and 200 days. Fixed effects models and mixed models were applied to the three different growth functions: von Bertalanffy, Gompertz, and Richards; fixed and mixed model polynomial equations were also considered. The growth function׳s ability to predict future live weight was determined by excluding a selection of animal live weight records post 160 days of age and comparing the predicted live weight to actual live weight. Irrespective of whether a fixed or mixed model framework was used, the Gompertz function best modelled the full dataset, with an accuracy squared for the full dataset (rw2) of 0.997 and root mean square error (RMSE) of 1.60kg for the fixed effects model and rw2 of 0.995 and RMSE of 2.25kg for the mixed model equation. The Gompertz mixed model also achieved the greatest accuracy squared of predicting (rww^2) future live weight records, with an rww^2 of 0.846 and RMSE of 5.35kg. A strong positive correlation was estimated between asymptotic mature weight (A; r=0.83 to 0.96) across the three growth functions for all considered equations. A strong negative correlation was estimated between parameters A and k (rate of maturation) for the Gompertz fixed effects model (−0.88) and mixed model (−0.70). Results from this study could be used to implement a decision support tool for pork producers, offering extra information when they are making important feeding, slaughter and breeding decisions.

The effect of overgrown claws on behaviour and claw abnormalities of sows in farrowing crates

The objective of this study was to evaluate the effect of overgrowth of the weight bearing claws on the behaviour of sows in farrowing crates. The study used 24 multiparous lactating sows, 13 with overgrown (OG) rear claws and 11 controls. Sows were video recorded continuously from approximately 12h before farrowing in order to capture postural behaviour for 6h prior to the birth of the first piglet. An index of the proportion of time spent in different postures was calculated by sampling sow postural behaviour every 10min. Lying down behaviour and sow behaviour while standing at feeding were directly observed during three feeding events within a week of farrowing, commencing approximately 10min prior to feed delivery and terminating once the sows lay down. Data on time spent “only” standing, time spent feeding, number of slips and weight shifts per minute and latency, time and number of attempts to lie down, among others, were recorded during the direct observations. Additionally, all front and hind weight bearing claws were examined for claw abnormalities which were scored according to severity using a 4-point scale (0=normal to 3=severe) on the day of transfer to the farrowing crate (d110 of gestation) and after farrowing while the sows were lying down. Data were analysed using generalised linear mixed model equation methods in PROC GLIMMIX of SAS v9.3. Sows with overgrown claws (OG) had a higher score for erosion (P<0.05) and corkscrew dew claws (P<0.05) than control sows. Furthermore, OG sows had higher erosion scores in the rear claws (P<0.05) compared to the control sows. There was no difference between control and OG sows in the time spent in the different postures prior to farrowing. On the first week after farrowing, OG sows spent less time feeding (P<0.05), slipped (P<0.05) and shifted weight (P<0.05) between their hind feet more frequently while feeding than control sows. OG sows required more attempts to stand up to feed (P<0.05) and had a shorter latency to lie down (P<0.01) after feeding compared with control sows. Overgrowth of the rear claws was associated with increased scores for other types of claw abnormalities and more frequent slips while in the farrowing crate; suggesting that overgrown claws could have negative implications for sow welfare and piglet mortality.

206 GENOME-WIDE ASSOCIATIONS FOR REPRODUCTIVE TRAITS IN RUSSIAN HOLSTEIN POPULATION

Reproductive health is an important trait in selection of dairy cattle. A genome-wide association study (GWAS) is a powerful tool for annotating phenotypic effects on the genome and to get knowledge of genes and chromosomal regions associated with reproductive performance (Cole et al. 2011). Combining GWAS and genetic profiling of embryos before implantation enables to develop new strategies to select elite breeding genotypes before transfer (Humblot et al. 2010; Ponsart et al. 2013). The aim of the current study was to evaluate the association between single nucleotide polymorphisms (SNP) and estimated breeding values (EBV) for reproductive traits [interval to insemination (EBVII) and interval between calving (EBVIC)] for Russian Holstein cattle and to evaluate the effect of the biopsy procedure on the viability of bovine embryos produced in vitro as a basis for pre-implantation genetic diagnosis (PGD). Ninty-six progeny-tested sires of artificial insemination station Moscowskoe were selected based on the reliability for EBVII and EBVIC. Estimations of breeding values of sires were performed by best linear unbiased prediction (BLUP) mixed model equations. DNA was extracted from sire semen samples. SNP genotyping was performed using the Illumina BovineSNP50 BeadChip (Illumina Inc., San Diego, CA, USA) containing 54609 SNPs. Quality control information was carried out in PLINK (v. 1.07; Purcell et al. 2007 Am. J. Hum. Genet. 81). Based on the quality control information, 41442 SNPs were selected for subsequent GWAS. We have identified 3270 SNPs having significant effect (P &lt; 0.05) on studied traits. The most significant associations with EBVII were found for SNPs Hapmap38548-BTA-97184 and ARS-BFGL-BAC-11821 with coefficient of determination (R2) of 0.2189 and 0.1937, and P-values 2.27 × 10–6 and 1.01 × 10–6, respectively. The most significant effect on EBVIC was detected for SNPs ARS-BFGL-NGS-59769 and ARS-BFGL-NGS-38020 with coefficient of determination (R2) of 0.236 and 0.2421, and P-values 1.49 × 10–8 and 7.24 × 10–8, respectively. The highest number of significant associations was found on BTA5, BTA12, BTA19, and BTA14. Bovine embryos were produced in vitro using a standard procedure. Six to 8 cell biopsies were carried out at Day 6.5 after fertilization. The viability of biopsied embryos was evaluated comparing the hatching rates to non-manipulated embryos. The study of embryos viability after biopsy showed that the hatching rate of biopsied embryos (the number of hatched embryos from the number of embryos in stages of late morula and early blastocyte) was 48% comparing to 67% for non-manipulated embryos. Embryo biopsy is not dramatically decreasing embryo viability. Combining our results of association studies, performed on Russian Holstein population, and technique of embryo biopsy will provide us a powerful tool for selection progress.This research was supported by the Russian Ministry of Education and Science, project No. 2014-14-576-0057-175.

Assessment of Boeremia exigua var. rhapontica, as a biological control agent of Russian knapweed (Rhaponticum repens)

Russian knapweed (Rhaponticum repens (L.) Hidalgo) is an herbaceous perennial weed that was introduced and has become invasive in the United States, particularly in the semi-arid west. It is characterized by its extensive root system, low seed production, and persistence. The weed has caused serious reductions in yields and crop value and may significantly devalue the land itself. Conventional control strategies have been inadequate because of the size of infestations and economic and environmental costs of control. Biological control has been a sought-after potential solution to this weed problem. In the summer of 2002, diseased R. repens plants were collected near Cankiri, Turkey, and the facultative saprophytic fungus Boeremia exigua isolate FDWSRU 02-059 was isolated from diseased plants. Bayesian analysis of the actin, beta-tubulin, calmodulin, elongation factor, and ITS genes, of 66 isolates, representing the ten species of Boeremia and the 11 varieties of B. exigua, including FDWSRU 02-059, showed that the isolate is a unique genetic entity and was named B. exigua var. rhapontica Berner, Woudenberg & Tunali, var. nov. MycoBank MB809363. Disease incidence and severity data from host-range determination tests conducted at 25°C, the optimum temperature for growth and sporulation of B. ex. rhapontica, with adequate dew periods, were combined with a genetic distance matrix based on ITS sequences of 66 plant species related to R. repens. The combined disease and genetic data were analyzed by mixed model equations to produce best linear unbiased predictors (BLUPs), standard errors, and P>|t| values, in t-tests against zero, for disease incidence and severity for each species. BLUPs of disease incidence were significantly different from zero only for three Rhaponticum spp. while BLUPs of disease severity rankings were significantly different from zero only for R. repens, Rhaponticumcarthamoides, Rhaponticumuniflorum, and Leuzea berardioides. Best linear unbiased predictors for differences in above-ground dry weights between control and inoculated plants of a subset of the species evaluated were not significant. However, above-ground damage by B. ex. rhapontica to R. repens was nearly twice that for any other species, except Rhaponticum species.

Genetic variances of SNP loci for milk yield in dairy cattle.

Regression coefficients and genetic variances for 40,890 single nucleotide polymorphisms (SNPs) for milk yield were calculated using mixed model equations, with deregressed proof (DRP) as the dependent variable. Bulls were genotyped using the Illumina BovineSNP50 v2 BeadChip and SNPs were edited according the minor allele frequency (MAF) and high incidence of missing genotype. Evaluation was conducted in two rounds. In the preliminary round, the direct genetic values (DGVs) of all genotyped bulls (2,904) were computed and the absolute difference between the DGV and the input DRP of each bull was investigated. Bulls with an absolute difference greater than the mean absolute difference plus two standard deviations were eliminated from the data set prior to the final analysis (2,766 bulls remaining). SNP regression coefficients from the final analysis had a mean absolute value of 0.506 kg and a standard deviation of 0.409 kg. The SNP with the highest regression coefficient and genetic variance was ARSBFGLNGS4939 on chromosome 14. This SNP is located within the gene DGAT1 (diacylglycerol O-acyltransferase 1). Other SNPs with high regression coefficients and genetic variance are localised in proximity to DGAT1. The mean genetic variance of an individual SNP was 0.170, with a standard deviation of 0.384 and a mean heterozygosity of 0.372. The sum of genetic variances of all SNPs was only 6,968.8, probably because of the existence of genetic covariances between loci. The largest sum of genetic variances was on chromosome 14 (498.4, 7.15 % of the total). After the final analysis, the correlation between the DGV and the input DRP was 0.951 for all bulls. The variance of the predicted DGV was 98.11 % of the variance of the input estimated breeding value (EBV) and 63.65 % of the variance of the DRP.

Further remarks on the connection between fixed linear model and mixed linear model

The linear mixed model \(\mathbf {y}= \mathbf {X}\varvec{\beta }+ \mathbf {Z}\mathbf {u}+ \varvec{\varepsilon }\), where \(\varvec{\beta }\) is the vector of fixed effects and \(\mathbf {u}\) the vector of random effects, has strong links with a particular augmented linear model including only fixed effects. This goes back to Henderson’s mixed model equations and was recently exploited by Haslett and Puntanen (Stat Papers 51:465–475, 2010), who restated Henderson’s result in a model with possibly singular covariance matrices. In this paper we point out that the connection between the two models is actually very straightforward: a mixed linear model can be obtained from the augmented model by a simple linear transformation. This, for example, immediately opens up a new viewpoint for studying the relationship between the BLUEs and BLUPs in the two models. In doing so we discuss a modification of the Frisch–Waugh–Lovell theorem as well as some not so well established theorems about the BLUPs of random errors.

Genetic parameter estimates and principal component analysis on performance and carcass traits of a terminal pig sire line

This study aimed to estimate genetic parameters for five traits related to performance and carcass in a terminal pig sire line using multitrait (MUV) and reduced rank animal models, and to analyze the relationship between the breeding values (EBVs) of the traits using genetic principal component analysis (PCA) applied directly on the mixed model equations (one-step PCA) and on the EBVs obtained using the MUV (two-step PCA). The heritabilities were very similar using both procedures ranged from 0.032 ± 0.014 for feed conversion to 0.102 ± 0.029 for lean meat. Except for some differences in the heritability for feed conversion ratio, the heritability estimates were remarkably similar using One-step PCA or MUV. The genetic correlations obtained using One-Step PCA were more reliable due to their lower standard errors compared to those obtained using MUV. The one-step PCA had better fit than MUV and could reduce the time computing due to the reduction of the additive genetic matrix.

Assigning unknown parent groups to reduce bias in genomic evaluations of final score in US Holsteins

Assigning unknown parent groups (UPG) in mixed-model equations using single-step genomic BLUP was investigated to reduce bias and to increase accuracy in genomic estimated breeding values (GEBV). The original UPG were defined based on the animal's birth year and the sex of the animal's unknown parents. Combining the last 2 UPG for the animals’ birth years and separating the UPG for US and non-US Holsteins were considered in the redefinition. A full data set in the 2011 national genetic evaluation of final score in US Holsteins was used to calculate estimated breeding values (EBV) for validation, and a subset of the 2011 data, which excluded phenotypes recorded after 2007, was used to calculate GEBV for all animals, including 34,500 genotyped bulls. The EBV and GEBV in 2007 were compared with EBV in the 2011 full data. The last group effects for unknown sires and dams were overestimated with the GEBV model using the reduced 2007 data. The genetic trends from EBV in 2011 and GEBV in 2007 with the original UPG in the last few years demonstrated inflation, whereas GEBV with the redefined UPG by combining the last 2 groups showed deflation. On the other hand, the redefined UPG by separating for US and non-US Holsteins reduced the bias in GEBV. Regression coefficients smaller than unity for GEBV for young genotyped bulls with no daughters in 2007 on progeny deviations in 2011 also indicated inflation. The redefining of UPG reduced bias and slightly increased accuracy in GEBV for both US and non-US genotyped bulls. Rank correlations between GEBV in 2007 and in 2011 with the redefined UPG were higher than those with no UPG and the original UPG, especially for non-US bulls. Redefining of UPG in genomic evaluation could improve reliability of GEBV and provide correct genetic trends.

Evaluation of estimated genetic values and their application to genome-wide investigation of systolic blood pressure.

The concept of breeding values, an individual's phenotypic deviation from the population mean as a result of the sum of the average effects of the genes they carry, is of great importance in livestock, aquaculture, and cash crop industries where emphasis is placed on an individual's potential to pass desirable phenotypes on to the next generation. As breeding or genetic values (as referred to here) cannot be measured directly, estimated genetic values (EGVs) are based on an individual's own phenotype, phenotype information from relatives, and, increasingly, genetic data. Because EGVs represent additive genetic variation, calculating EGVs in an extended human pedigree is expected to provide a more refined phenotype for genetic analyses. To test the utility of EGVs in genome-wide association, EGVs were calculated for 847 members of 20 extended Mexican American families based on 100 replicates of simulated systolic blood pressure. Calculations were performed in GAUSS to solve a variation on the standard Best Linear Unbiased Predictor (BLUP) mixed model equation with age, sex, and the first 3 principal components of sample-wide genetic variability as fixed effects and the EGV as a random effect distributed around the relationship matrix. Three methods of calculating kinship were considered: expected kinship from pedigree relationships, empirical kinship from common variants, and empirical kinship from both rare and common variants. Genome-wide association analysis was conducted on simulated phenotypes and EGVs using the additive measured genotype approach in the SOLAR software package. The EGV-based approach showed only minimal improvement in power to detect causative loci.

Using recursion to compute the inverse of the genomic relationship matrix

Computing the inverse of the genomic relationship matrix using recursion was investigated. A traditional algorithm to invert the numerator relationship matrix is based on the observation that the conditional expectation for an additive effect of 1 animal given the effects of all other animals depends on the effects of its sire and dam only, each with a coefficient of 0.5. With genomic relationships, such an expectation depends on all other genotyped animals, and the coefficients do not have any set value. For each animal, the coefficients plus the conditional variance can be called a genomic recursion. If such recursions are known, the mixed model equations can be solved without explicitly creating the inverse of the genomic relationship matrix. Several algorithms were developed to create genomic recursions. In an algorithm with sequential updates, genomic recursions are created animal by animal. That algorithm can also be used to update a known inverse of a genomic relationship matrix for additional genotypes. In an algorithm with forward updates, a newly computed recursion is immediately applied to update recursions for remaining animals. The computing costs for both algorithms depend on the sparsity pattern of the genomic recursions, but are lower or equal than for regular inversion. An algorithm for proven and young animals assumes that the genomic recursions for young animals contain coefficients only for proven animals. Such an algorithm generates exact genomic EBV in genomic BLUP and is an approximation in single-step genomic BLUP. That algorithm has a cubic cost for the number of proven animals and a linear cost for the number of young animals. The genomic recursions can provide new insight into genomic evaluation and possibly reduce costs of genetic predictions with extremely large numbers of genotypes.

Parámetros genéticos para caracteres productivos y reproductivos en Holstein y Jersey Colombiano

El objetivo de este estudio fue estimar parámetros genéticos y fenotípicos en características productivas y reproductivas en ganado Holstein y Jersey de Antioquia, Colombia. La información fue obtenida de 85 hatos lecheros de raza Holstein y 7 hatos de raza Jersey, ubicados en 18 municipios del Departamento de Antioquia. Las características productivas evaluadas fueron: producción de leche (PL), porcentaje de proteína (PP), porcentaje de grasa (PG) y puntaje de células somáticas (SCS) y las características reproductivas evaluadas fueron: intervalo entre partos (IEP), días abiertos (DA), número de servicios por concepción (NSC) y tasa de concepción (TC). Los componentes de (co)varianza, los parámetros genéticos y fenotípicos fueron estimados empleando modelos mixtos univariados y bivariados y las soluciones de las ecuaciones de los modelos mixtos fueron obtenidas mediante el método de máxima verosimilitud restricta libre de derivadas. Las heredabilidades obtenidas para características productivas oscilaron entre 0,22 y 0,35, excepto para SCS que fueron bajas (h2

Total Hip Arthroplasty for Hip Fractures

This study aimed to determine the dislocation and reoperation rate, functional outcomes, and the survival rate of the unique subset of very old but lucid and independent patients with hip fractures following a total hip arthroplasty (THA) and geriatric team-coordinated perioperative care. Between 2000 and 2006, previously independent ambulatory patients ≥80 years old presenting with an intracapsular hip fracture were given THAs under the care of an integrated orthopedic surgery-geriatric service. Their fracture-related complications, ambulation, mental status, and survival were followed for 5 to 11 years postinjury. Five years postinjury, 57 (61.3%) patients of the original study group were living. In all, 3 (3.2%) patients had postoperative hip dislocations (and 2 patients had dislocation twice) and 2 reoperations were needed within the first postoperative month. There were no hip dislocations or reoperations after the first year. Radiographs obtained on 88% of the surviving patients at 5 years postoperatively showed that all remained unchanged from their immediate postoperative images. Nearly half of the patients were still able to ambulate as they did preoperatively and their mixed-model equation was statistically unchanged. This study of patients >80 years old with previously good functional status demonstrates that with appropriate surgical (best prosthesis, good operating technique, and regional anesthesia) and geriatric (pre- and postoperative assessments, close follow-up, medication adjustments, and fall-prevention instruction) care, they have few hip dislocations and reoperations, survive postfracture at least as long as their noninjured contemporaries, and continue to function and ambulate as they did prior to their injury.

Haplotype-assisted genomic evaluations in Nordic Red Dairy Cattle

In admixed populations originating from different base breeds, such as the Nordic Red Dairy Cattle, identity by state of haplotypes instead of single nucleotide polymorphisms (SNP) is a better surrogate for identity by descent. Therefore, haplotypes are expected to be more useful in recovering genetic relationships among animals and linkage disequilibrium between markers and quantitative trait loci (QTL). The objective of this study was to improve the prediction accuracy in genomic evaluations by the use of haplotypes of short chromosomal segments. In the first step, around 38,000 SNPs from a 50K chip were simultaneously scanned for QTL signals with BayesB. Based on these results, the SNPs with the strongest QTL signals were then pre-selected and haplotype blocks were constructed around these. In the second step, we estimated the relative variances for the pre-selected haplotypes with BayesA. In the final step, mixed model equations of the evaluation model were solved to estimate haplotype effects. Here, a pre-defined proportion of the genetic variance was assigned to a pedigree-based animal effect and the rest to haplotypes. The accuracies of several combinations for the number and the length of haplotype blocks were assessed by calculation of genome-enhanced breeding values and validation test reliabilities (R2). For three production traits (milk, protein, fat) and fertility, the highest R2 observed were 0.48, 0.41, 0.42 and 0.33, respectively. For milk and protein, we observed an improvement over G-BLUP of 3 and 1 percentage points, respectively. For fat and fertility, the highest R2 were the same as for GBLUP. Further analysis using only single SNPs instead of haplotype blocks yielded similar results. This may indicate a need to choose an alternative approach to pre-select haplotype blocks.

Phyllosphere Bacteria Improve Animal Contribution to Plant Nutrition

AbstractMany plant species have evolved special adaptations for acquiring nitrogen in nutrient‐poor soils. In Brazilian savannas, the bromeliad Bromelia balansae (Bromeliaceae) is inhabited by mutualistic spiders (Psecas chapoda, Salticidae), which provide nutrients to the plant through their debris (feces, prey carcasses). In this study, we tested if bacteria present on the B. balansae phyllosphere improves plant nutrition and growth by mineralizing complex organic N compounds from spider debris that accumulate on the phyllosphere into simple compounds that may be absorbed easily by leaves. We conducted a greenhouse experiment by manipulating bacteria abundance on the bromeliad phyllosphere using antibiotics. Using isotopic mixed model equations, we demonstrated that debris from spiders contributed 10.7 ± 1.9 percent (mean ± standard error) of the N in bromeliads that had their bacterial abundance reduced. In contrast, spider feces contributed 27.1 ± 4.4 percent of bromeliad N in the presence of the entire bacterial assemblage. These bromeliads accumulated 57 percent more soluble protein and grew 13 percent more than bromeliads that were grown under reduced bacterial density. These results highlight the importance of mineralizing bacteria on phyllosphere as a mechanism of N uptake by bromeliads.

Estimation of Genetic Correlations and Selection Responses for Carcass Traits between Ultrasound and Real Carcass Measurements in Hanwoo Cows

This study was conducted to determine genetic correlations among carcass traits measured by ultrasound and real carcass measurements and to estimate indirect selection responses for real carcass traits based on ultrasound measurements in Hanwoo cows. To accomplish this, 22,080 ultrasound measurement records from 17,926 cows collected from 2001 to 2012 and 11,907 carcass records obtained from fattened cattle from 2008 to 2012 were used. Genetic parameters were estimated based on eye muscle area (EMA), backfat thickness (BF) and marbling score (MS) measured by ultrasound-scanning of live cows and using the official technique on chilled bovine half-carcasses after slaughtering. Heritability and genetic correlation for carcass traits were estimated using a mixed model equation that consisted of environmental effects as fixed parameters and additive genetic effects and residual effects as random parameters, assuming that traits were different between ultrasound and carcass measurements. This statistical method was applied to the average information restricted maximum likelihood method. The heritability of EMA, BF and MS measured by ultrasound were 0.33, 0.61 and 0.46, respectively, while the heritability estimates of the corresponding traits based on carcass measurements were 0.29, 0.40 and 0.38, respectively and the genetic correlation between ultrasound and carcass traits for EMA, BF and MS were 0.41, 0.78 and 0.67, respectively. The genetic correlation between ultrasound and carcass traits was highly positive. Additionally, the selection response for marbling score was estimated to be 0.42 per generation if the cows were selected based on the ultrasound scan marbling score with an assumed selection intensity of 0.8. Overall, these results indicate that the ultrasound scan technique would be applicable to judging cow selection for genetically improved meat quality.

Employing a Monte Carlo Algorithm in Newton-Type Methods for Restricted Maximum Likelihood Estimation of Genetic Parameters

Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR), where the information matrix was generated via sampling; MC average information(AI), where the information was computed as an average of observed and expected information; and MC Broyden's method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden's method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.

Effect of rubber slat mats on the behaviour and welfare of group housed pregnant sows

This study evaluated the effect of flooring, lameness, body and limb lesion scores on postural and spatial behaviour of gestating sows. Sixty-four sows were kept in groups of four in pens with four solid concrete floored feeding stalls and a concrete fully slatted group area from 4 weeks after service. The slats were either left uncovered (CON; n=8 groups) or 10mm thick rubber slat mats were affixed (RUB; n=8 groups). Lameness (0=normal to 5=severe), limb (environmentally induced lesions, e.g. callus, wounds, swellings; scored according to severity—0=normal to 6=severe) and body (aggression induced lesions; scored according to severity—0=normal to 5=severe) lesions were scored on days 1, 8, 25, 50 and 75 relative to entering the experiment. Additionally video recordings were made of the groups for 24h on the same days which were sampled instantaneously every 10min. An index of the proportion of time spent in (1) different postures (standing, ventral [VL] and lateral lying [LL] and total lying [VL+LL]); (2) locations (stalls or group area), (3) posture by location and (4) number of postural changes was calculated. Sows were categorized as non-lame (score ≤1) or lame (score ≥2). Median scores were calculated for body and limb lesions and were classified as ≤median or >median. Lameness, limb and body lesions were analysed using logistic binomial regression. Behavioural variables were tested for normality and analysed using mixed model equations. Flooring did not affect lameness, body lesion scores, time spent in each posture or the index of postural changes (P>0.05). RUB sows spent more time in the group area (76.3 vs. 53.3±5.8%; P<0.01) and lay more there (80.0 vs. 62.4±5.3%; P<0.05) compared with CON sows. Sows with scores >median for wounds on the limbs spent more time LL (41.2 vs. 48.3±3.6%; P<0.05) and less time VL (36.3 vs. 29.9±2.9%; P<0.05). On the other hand, sows with body lesion scores >median spent more time VL (29.9 vs. 36.3±2.9%; P<0.05). Lame sows stood less and lay more (P<0.05) in the feeding stalls. When sows had access to rubber flooring they spent more time in the covered area and lay more there compared with sows in pens where the concrete slats were bare. This reflects the preference of group housed sows for a comfortable surface for lying during pregnancy. Other sow factors such as body and limb lesions and lameness status are also related with lying behaviour.

Exploring the potential of hierarchical generalized linear models in animal breeding and genetics

Exploring the potential of hierarchical generalized linear models in animal breeding and genetics

단형질 개체모형을 이용한 한우 육종가 추정프로그램 개발

단형질 개체모형을 이용한 육종가 추정프로그램의 해를 구하는 컴퓨터 프로그램을 포트란 언어를 이용하여 자체개발하였고, 프로그램은 자료기반으로 반복적으로 계산을 해 나가는 간접법을 이용한 것으로 일반적인 알고리즘으로 프로그램을 개발하고 이의 효율을 개선한 개선알고리즘으로 프로그램을 개발하여, 두 프로그램 간 효율을 비교하였다. 기존의 전통적인 알고리즘은 순차적인 반복문을 이용하여 자료를 읽고 기록하는 방법이며, 새로운 알고리즘은 효과별로 LHS를 직접 작성하여 추정하는 방법을 사용하였다. 개발된 두 가지 프로그램으로 육종가를 추정하고, 그 추정 값이 정확하게 평가되었는지 알아보기 위하여 기존에 개발되어 사용되고 있는 BLUPF90 (Misztal, 2007)과 MTDFREML (Boldman 등, 1999)과 비교하여 보았다. 서로 다른 프로그램으로 추정된 육종가간의 상관은 전체 항목에서 99% 이상 고도의 상관이 나타났으며, 프로그램 추정치 간의 높은 상관으로 볼 때 Model I, Model II는 정확하게 개발되었고 평가된 것을 확인할 수 있었다. Solution이 수렴 될 때까지의 반복횟수는 Model I은 2,568 round, Model II는 1,038 round로 수렴되어 Model II가 Model I보다 작은 반복횟수에서 수렴이 된 것을 확인할 수 있었으며, 수렴속도는 Model I은 256.008초, Model II는 235.729초로 Model II가 Model I 보다 약 10% 정도 개선된 것을 확인할 수 있었다. 개발된 프로그램을 기존 D/B와 연계한다면 농가 및 지자체 등에 지속적인 개량 정보를 제공할 수 있으며, 농가 단위 암소 유전능력평가로 암소개량을 도모할 수 있을 것이라 사료된다. Estimate breeding value can be used as single trait animal model was developed directly using the Fortran language program. The program is based on data computed by using the indirect method repeatedly. The program develops a common algorithm and imprves efficiency. Algorithm efficiency was compared between the two programs. Estimated using the solution is easy to farm and brand the service, pedigree data base was associated with the development of an improved system. The existing program that uses the single trait animal model and the comparative analysis of efficiency is weak because the estimation of the solution and the conventional algorithm programmed through regular formulation involve many repetition; therefore, the newly developed algorithm was conducted to improve speed by reducing the repetition. Single trait animal model was used to analyze Gauss-Seidel iteration method, and the aforesaid two algorithms were compared thorough the mixed model equation which is used the most commonly in estimating the current breeding value by applying the procedures such as the preparation of information necessary for modelling, removal of duplicative data, verifying the parent information of based population in the pedigree data, and assigning sequential numbers, etc. The existing conventional algorithm is the method for reading and recording the data by utilizing the successive repetitive sentences, while new algorithm is the method for directly generating the left hand side for estimation based on effect. Two programs were developed to ensure the accurate evaluation. BLUPF90 and MTDFREML were compared using the estimated solution. In relation to the pearson and spearman correlation, the estimated breeding value correlation coefficients were highest among all traits over 99.5%. Depending on the breeding value of the high correlation in Model I and Model II, accurate evaluation can be found. The number of iteration to convergence was 2,568 in Model I and 1,038 in Model II. The speed of solving was 256.008 seconds in Model I and 235.729 seconds in Model II. Model II had a speed of approximately 10% more than Model I. Therefore, it is considered to be much more effective to analyze large data through the improved algorithm than the existing method. If the corresponding program is systemized and utilized for the consulting of farm and industrial services, it would make contribution to the early selection of individual, shorten the generation, and cultivation of superior groups, and help develop the Hanwoo industry further through the improvement of breeding value based enhancement, ultimately paving the way for the country to evolve into an advanced livestock country.

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.