Genetic analysis of ventricular arrhythmia in young German Shepherd Dogs.

BACKGROUND: Ventricular arrhythmias (VA) and sudden death are inherited in German Shepherd Dogs (GSDs). OBJECTIVES: To estimate the genetic parameters (heritabilities and correlations) of 3 traits of VA (single premature ventricular complexes (PVCs), 2 consecutive PVCs (couplets), and 3 or more consecutive PVCs-ventricular tachycardia [VT]). ANIMALS: Three hundred and ninety-eight GSDs. METHODS: Prospective, observational, case control study. Dogs were phenotyped by 24-hour ambulatory ECG from 6 to 45 weeks of age. Edited ECG records included the number of incidents of (1) single PVCs, (2) couplets, and (3) VT. RESULTS: A data set of 1,239 Holter records from 398 GSDs was used to estimate genetic variables. Phenotypic correlations for affectedness (binarily coded 0/1) of the 3 traits ranged from 0.55 to 0.74, whereas correlations for severity (continuous values of 24-hour VA counts) ranged from 0.26 to 0.39. Estimates of genetic correlation among the severity traits were 0.06 to 0.27. Estimated heritabilities were 0.54, 0.54, and 0.46 for affectedness and 0.33, 0.69, and 0.69 for severity of PVCs, couplets, and VT, respectively. Month and year of birth and age at ECG recording had significant effects on all 3 traits. Season of ECG recording had a significant effect on the number of single PVCs, but not couplets or incidents of VT. Age of onset differed, with single PVCs appearing an average of 4 days earlier than couplets and VT. CONCLUSION: These results imply a strong genetic component for this disease but suggest that differences in the 3 traits should be taken into consideration in studies to identify the underlying genes.

Describing interactions in dystocia scores with a threshold model.

Field data on calving difficulty scores provided by the American Simmental Association were subjected to two methods of analysis: ordinary least-squares analysis and maximum likelihood with an assumed threshold model. In each analysis, the model included the interaction of sex of calf X age of dam. This interaction was readily apparent in the data (observed scale): within the youngest dams 58% of the heifer calves and 37% of the bull calves were born unassisted vs 96% and 92%, respectively, in the oldest dams. The objective was to determine if this interaction would be greatly reduced or would disappear on the underlying scale of a threshold model. The least-squares estimate of the sex difference was greatest within the youngest age-of-dam group (18 to 24 mo) and steadily declined with increasing age of dam, approaching zero for dams 6 yr and older. In contrast, the estimates of the sex difference from the threshold analysis were remarkably similar across ages of dam. It was concluded that observed interactions in calving ease data could be adequately described by a threshold model in which the effects of age of dam and sex of calf act additively on the underlying variable.

Analysis of gestation length in American Simmental cattle.

Records of gestation length (71,461) for Simmental cattle were distributed with mean 284.3 d and standard deviation 5.52 d. Gestation length was found to increase with percent Simmental and was 1.9 d longer for calves born to mature dams than for those born to heifer dams. Bull calves experienced gestation lengths 1.5 d longer than heifer calves. Sire, maternal grandsire, residual and total variances were estimated to be 2.42, .58, 22.78 and 25.78 d2, respectively, by Henderson's Method III. Heritability of gestation length was calculated to be .374 from the sire variance and .09 from the maternal grandsire variance. Direct additive genetic variance was considered to be of greater importance than maternal additive genetic variance. Correlations between the evaluations of sires for gestation length and heifer calving ease, birth weight and weaning weight were .26, .26 and .13, respectively.

Estimation of variance and covariance components to determine heritabilities and repeatability of weaning weight in American Simmental cattle.

Components of (co)variance for weaning weight were estimated from field data provided by the American Simmental Association. These components were obtained for the observational components of variance corresponding to a sire, maternal grandsire, and dam within maternal grandsire model. From these estimates, direct additive genetic variance (Sigma2A), maternal additive genetic variance (Sigma2M), covariance between direct and maternal additive genetic effects (SigmaAM), variance of permanent environment(Sigma2pe) and temporary environment variance(Sigma2te) were determined. A procedure to approximate restricted maximum likelihood (REML) estimates of the observational components of variance based on the expectation-maximization (EM) algorithm is described. From these results, phenotypic variance ( ) of weaning weight was 667.88 kg2. Values forSigma2A, Sigma2M, Sigma2pe and Sigma2te were 79,30,58,38,49.45, and 469.97 kg2, respectively. Genetic correlation between direct and maternal additive genetic effects was .16.

Evaluation of Simmental carcass EPD estimated using live and carcass data.

This study was conducted to compare carcass EPD predicted using yearling live animal data and/or progeny carcass data, and to quantify the association between the carcass phenotype of progeny and the sire EPD. The live data model (L) included scan weight, ultrasound fat thickness, longissimus muscle area, and percentage of intramuscular fat from yearling (369 d of age) Simmental bulls and heifers. The carcass data model (C) included hot carcass weight, fat thickness, longissimus muscle area, and marbling score from Simmental-sired steers and cull heifers (453 d of age). The combined data model (F) included live animal and carcass data as separate but correlated traits. All data and pedigree information on 39,566 animals were obtained from the American Simmental Association, and all EPD were predicted using animal model procedures. The genetic model included fixed effects of contemporary group and a linear covariate for age at measurement, and a random animal genetic effect. The EPD from L had smaller variance and range than those from either C or F. Further, EPD from F had highest average accuracy. Correlations indicated that evaluations from C and F were most similar, and L would significantly (P < 0.05) re-rank sires compared with models including carcass data. Progeny (n = 824) with carcass data collected subsequent to evaluation were used to quantify the association between progeny phenotype and sire EPD using a model including contemporary group, and linear regressions for age at slaughter and the appropriate sire EPD. The regression coefficient was generally improved for sire EPD from L when genetic regression was used to scale EPD to the appropriate carcass trait basis. The EPD from C and F had similar linear associations with progeny phenotype, although EPD from F may be considered optimal because of increased accuracy. These data suggest that carcass EPD based on a combination of live and carcass data predict differences in progeny phenotype at or near theoretical expectation.

Lambing performance of Morlam and Dorset ewes under accelerated lambing systems.

Two accelerated lambing systems, Morlam using Morlam sheep (USDA, Beltsville 1966 to 1975) and Camal using Dorset ewes (Cornell 1978 to 1981), were evaluated for first lambing ages, interlambing intervals and conception probabilities. Morlam ewes were continuously exposed to rams over the year, while Camal Dorset ewes were exposed every other month. Morlam lambs were mated as early as 367 d of age and Camal Dorset lambs as early as 340 d. Early lambing was associated with higher rates of perinatal mortality (P greater than .05) and smaller litter size (P less than .01). Lambing years among Morlam ewes and season of birth of Camal Dorset ewes influenced (P less than .01) their first lambing ages. Lambing intervals averaged 293 and 303 d among Morlam and Camal Dorset ewes, respectively. Age at first lambing and season in which the previous lambing occurred with influential factors (P less than .01) on lambing intervals of Morlam ewes; longer intervals resulted when ewe lambs were mated at early ages (less than 12 mo), and when the previous lambing occurred in winter. Estimates of conditional probabilities of conception by month given the occurrence of estrus, reflected seasonal changes in both systems. The overall probability of conception for the Morlam system (P = .16) was relatively higher than that for the Camal Dorset system (P = .14); numbers of lambings per ewe per yr were 1.28 and 1.21, respectively. Estimates of heritability for age at first lambing, lambing interval and conception probability were .31, .06 and .30, respectively.

Parameter estimation for carcass traits including growth information of Simmental beef cattle using restricted maximum likelihood with a multiple-trait model.

(Co)variance component estimates were computed for retail cuts per day of age (kilograms per day), cutability (percentage of carcass weight), and marbling score (1 through 11) using a multiple-trait sire model. Restricted maximum likelihood estimates of (co)variance components were obtained via an expectation-maximization algorithm. Carcass data consisted of 8,265 progeny records collected by U.S. Simmental producers. Growth trait information (birth weight, weaning weight, and[or] postweaning gain) for those progeny with carcass data and an additional 5,405 contemporaries formed the complete data set for analysis. A total of 420 sires were represented. Three models differing in number of traits were investigated: 1) carcass traits with growth traits, 2) carcass traits only, and 3) single trait. The final models did not include postweaning gain because of convergence problems. Parameter estimates for all three models were essentially the same. Heritability estimates were .30, .18, and .23 for retail cuts per day, cutability, and marbling score, respectively. Correlations between growth and carcass traits were low except for those with retail cuts per day, which were moderate and positive. The additional information gained by adding growth traits to the carcass-traits-only evaluation lowered prediction error variances most for retail cuts per day. Little change in prediction error variances was found for cutability and marbling score. Inclusion of growth traits in future sire evaluations for carcass traits will benefit the evaluation of retail cuts per day but have considerably less effect on cutability and marbling score.

Multiple trait prediction for a type of model with heterogeneous genetic and residual covariance structures.

A restricted set of models is defined that allows for heterogeneous genetic and residual covariance structures. Multiple trait models and models with multiple random factors are included. The restriction on the model is that the correlations among genetic effects in different classes are the same. Equivalently, the genetic covariance matrices are assumed to differ between classes due to scaling. This assumption greatly reduces the number of parameters that must be specified and does not adversely affect the computational burden of a mixed model analysis. An application of the model for genetic evaluation of beef cattle is described and illustrated numerically.

Variance heterogeneity in direct and maternal weight traits by sex and percent purebred for Simmental-sired calves.

Phenotypic variances for linear and transformed weight traits were partitioned into residual, direct genetic (D) and maternal genetic (M) components using REML techniques with American Simmental Association data from calves born 1969 to 1985. Variance components were estimated separately from subclasses defined by sex (male, female) and percent Simmental (50, greater than or equal to 75). The model included fixed effects of contemporary group and age-of-dam (less than 3, 3 to 5, greater than 5 yr). Additive relationships among sires and maternal grandsires were included. Results follow for a sire-maternal grandsire model for greater than or equal to 75% Simmental untransformed data based on 143,280 male and 281,805 female weaning weights (WW) representing 4,763 and 7,406 sires, respectively. Female results are bracketed. For computational simplification, 47,650 [30,909] postweaning gain (PW) records were included in the analysis only for 114,404 [182,255] calves with birth weight (BW). Phenotypic standard deviations (kg) were: BW, 4.5 [4.1]; WW, 26.9 [23.2]; and PW, 25.9 [19.9]. Heritabilities were: BWD, .40 [.45]; WWD, .32 [.39]; PWD, .26 [.32]; BWM, .13 [.15]; WWM, .20 [.16]; and PWM, .01 [.01]. These heritabilities are higher than previously used for genetic evaluations in this breed. Moderate and positive correlations .26 to .50, existed between direct effects and were similar for both sexes. Direct and maternal effects on the same trait were correlated negatively: BW, -.45 [-.31]; and WW, -.27 [-.34]. Genetic correlation between BWM and WWM was .53 [.49]. First-cross progeny exhibited less genetic and residual variation and had lower heritabilities than Simmental calves of higher percent. Correlations between sire evaluations on the subsets were consistent with those expected given a perfect genetic correlation between traits for each sex and percent Simmental. Logarithmic transformed records were no more homogeneous than untransformed records.

Genetic parameters for carcass traits and their live animal indicators in Simmental cattle.

The objective of this study was to estimate parameters required for genetic evaluation of Simmental carcass merit using carcass and live animal data. Carcass weight, fat thickness, longissimus muscle area, and marbling score were available from 5,750 steers and 1,504 heifers sired by Simmental bulls. Additionally, yearling ultrasound measurements of fat thickness, longissimus muscle area, and estimated percentage of intramuscular fat were available on Simmental bulls (n = 3,409) and heifers (n = 1,503). An extended pedigree was used to construct the relationship matrix (n = 23,968) linking bulls and heifers with ultrasound data to steers and heifers with carcass data. All data were obtained from the American Simmental Association. No animal had both ultrasound and carcass data. Using an animal model and treating corresponding ultrasound and carcass traits separately, genetic parameters were estimated using restricted maximum likelihood. Heritability estimates for carcass traits were 0.48 +/- 0.06, 0.35 +/- 0.05, 0.46 +/- 0.05, and 0.54 +/- 0.05 for carcass weight, fat thickness, longissimus muscle area, and marbling score, respectively. Heritability estimates for bull (heifer) ultrasound traits were 0.53 +/- 0.07 (0.69 +/- 0.09), 0.37 +/- 0.06 (0.51 +/- 0.09), and 0.47 +/- 0.06 (0.52 +/- 0.09) for fat thickness, longissimus muscle area, and intramuscular fat percentage, respectively. Heritability of weight at scan was 0.47 +/- 0.05. Using a bivariate weight model including scan weight of bulls and heifers with carcass weight of slaughter animals, a genetic correlation of 0.77 +/- 0.10 was obtained. Models for fat thickness, longissimus muscle area, and marbling score were each trivariate, including ultrasound measurements on yearling bulls and heifers, and corresponding carcass traits of slaughter animals. Genetic correlations of carcass fat thickness with bull and heifer ultrasound fat were 0.79 +/- 0.13 and 0.83 +/- 0.12, respectively. Genetic correlations of carcass longissimus muscle area with bull and heifer ultrasound longissimus muscle area were 0.80 +/- 0.11 and 0.54 +/- 0.12, respectively. Genetic correlations of carcass marbling score with bull and heifer ultrasound intramuscular fat percentage were 0.74 +/- 0.11 and 0.69 +/- 0.13, respectively. These results provide the parameter estimates necessary for genetic evaluation of Simmental carcass merit using both data from steer and heifer carcasses, and their ultrasound indicators on yearling bulls and heifers.

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.

Genetic evaluation of beef carcass data using different endpoint adjustments.

Carcass data from 6,795 Simmental-sired animals born from 1992 to 2001 were used to determine whether adjustment to a constant age, back-fat, HCW, or marbling score would result in differences in heritability of the carcass traits and, correspondingly, if EPD calculated using those variance components and adjustments would result in sire reranking. The endpoints were age (EPA), backfat (EPF), HCW (EPC), or marbling (EPM). The traits analyzed were 12th-rib backfat (FAT), HCW, marbling (MRB), LM area (LMA), and percentage retail cuts (PRC). The data were analyzed using an animal model, where contemporary group was included as a fixed effect and was composed of slaughter date, sex, and herd. Random effects included in the model were direct genetic and residual. Estimates of heritability ranged from 0.12 to 0.14, 0.32 to 0.34, and 0.26 to 0.27 for FAT, HCW, and LMA, respectively, for the corresponding endpoints. Heritability for MRB was estimated to be 0.27 at all endpoints. For PRC, estimates of heritability were more variable, with estimates of 0.23 +/- 0.05, 0.32 +/- 0.05, 0.21 +/- 0.05, and 0.20 +/- 0.04 for EPA, EPF, EPC, and EPM, respectively. However, because the EPF and EPC adjustments adjust for a component trait of PRC (FAT and HCW, respectively), they may be altering the trait to one different from PRC. Spearman rank correlations between EPD within a trait using EPA compared with the other endpoints were >0.90 (P < 0.01) for FAT, HCW, MRB, and LMA. For PRC, Spearman rank correlations with EPA EPD were 0.73 (P < 0.01), 0.93 (P < 0.01), and 0.95 (P < 0.01) for EPF, EPC, and EPM, respectively. For most traits and endpoints, there was little reranking among sires when alternative endpoints were used. However, adjusting PRC to EPF appears to result in a greater heritability and substantial re-ranking of sires, potentially due to the adjustment changing the trait to one other than PRC.

Validation of commercial DNA tests for quantitative beef quality traits.

Associations between 3 commercially available genetic marker panels (GeneSTAR Quality Grade, GeneSTAR Tenderness, and Igenity Tender-GENE) and quantitative beef traits were validated by the US National Beef Cattle Evaluation Consortium. Validation was interpreted to be the independent confirmation of the associations between genetic tests and phenotypes, as claimed by the commercial genotyping companies. Validation of the quality grade test (GeneSTAR Quality Grade) was carried out on 400 Charolais x Angus crossbred cattle, and validation of the tenderness tests (GeneSTAR Tenderness and Igenity Tender-GENE) was carried out on over 1,000 Bos taurus and Bos indicus cattle. The GeneSTAR Quality Grade marker panel is composed of 2 markers (TG5, a SNP upstream from the start of the first exon of thyroglobulin, and QG2, an anonymous SNP) and is being marketed as a test associated with marbling and quality grade. In this validation study, the genotype results from this test were not associated with marbling score; however, the association of substituting favorable alleles of the marker panel with increased quality grade (percentage of cattle grading Choice or Prime) approached significance (P < or = 0.06), mainly due to the effect of 1 of the 2 markers. The GeneSTAR Tenderness and Igenity TenderGENE marker panels are being marketed as tests associated with meat tenderness, as assessed by Warner-Bratzler shear force. These marker panels share 2 common mu-calpain SNP, but each has a different calpastatin SNP. In both panels, there were highly significant (P < 0.001) associations of the calpastatin marker and the mu-calpain haplotype with tenderness. The genotypic effects of the 2 tenderness panels were similar to each other, with a 1 kg difference in Warner-Bratzler shear force being observed between the most and least tender genotypes. Unbiased and independent validation studies are important to help build confidence in marker technology and also as a potential source of data required to enable the integration of marker data into genetic evaluations. As DNA tests associated with more beef production traits enter the marketplace, it will become increasingly important, and likely more difficult, to find independent populations with suitable phenotypes for validation studies.

DNA-based paternity analysis and genetic evaluation in a large, commercial cattle ranch setting.

Deoxyribonucleic acid-based tests were used to assign paternity to 625 calves from a multiple-sire breeding pasture. There was a large variability in calf output and a large proportion of young bulls that did not sire any offspring. Five of 27 herd sires produced over 50% of the calves, whereas 10 sires produced no progeny and 9 of these were yearling bulls. A comparison was made between the paternity results obtained when using a DNA marker panel with a high (0.999), cumulative parentage exclusion probability (P(E)) and those obtained when using a marker panel with a lower P(E) (0.956). A large percentage (67%) of the calves had multiple qualifying sires when using the lower resolution panel. Assignment of the most probable sire using a likelihood-based method based on genotypic information resolved this problem in approximately 80% of the cases, resulting in 75% agreement between the 2 marker panels. The correlation between weaning weight, on-farm EPD based on pedigrees inferred from the 2 marker panels was 0.94 for the 24 bulls that sired progeny. Partial progeny assignments inferred from the lower resolution panel resulted in the generation of EPD for bulls that actually sired no progeny according to the high-P(E) panel, although the Beef Improvement Federation accuracies of EPD for these bulls were never greater than 0.14. Simulations were performed to model the effect of loci number, minor allele frequency, and the number of offspring per bull on the accuracy of genetic evaluations based on parentage determinations derived from SNP marker panels. The SNP marker panels of 36 and 40 loci produced EPD with accuracies nearly identical to those EPD resulting from use of the true pedigree. However, in field situations where factors including variable calf output per sire, large sire cohorts, relatedness among sires, low minor allele frequencies, and missing data can occur concurrently, the use of marker panels with a larger number of SNP loci will be required to obtain accurate on-farm EPD.

Bayesian reanalysis of a quantitative trait locus accounting for multiple environments by scaling in broilers.

A Bayesian method was developed to handle QTL analyses of multiple experimental data of outbred populations with heterogeneity of variance between sexes for all random effects. The method employed a scaled reduced animal model with random polygenic and QTL allelic effects. A parsimonious model specification was applied by choosing assumptions regarding the covariance structure to limit the number of parameters to estimate. Markov chain Monte Carlo algorithms were applied to obtain marginal posterior densities. Simulation demonstrated that joint analysis of multiple environments is more powerful than separate single trait analyses of each environment. Measurements on broiler BW obtained from 2 experiments concerning growth efficiency and carcass traits were used to illustrate the method. The population consisted of 10 full-sib families from a cross between 2 broiler lines. Microsatellite genotypes were determined on generations 1 and 2, and phenotypes were collected on groups of generation 3 animals. The model included a polygenic correlation, which had a posterior mean of 0.70 in the analyses. The reanalysis agreed on the presence of a QTL in marker bracket MCW0058-LEI0071 accounting for 34% of the genetic variation in males and 24% in females in the growth efficiency experiment. In the carcass experiment, this QTL accounted for 19% of the genetic variation in males and 6% in females.

Clinical ketosis: phenotypic and genetic correlations between occurrences and with milk yield.

The repeatability and heritability of ketosis were estimated using data from 28,277 Finnish Ayrshire cows. A four-trait linear model including community-year, calving age and month, genetic group, and random sire effects was used to describe first and second lactation milk yields and veterinary diagnoses of ketosis. Variance components were estimated using REML. The disease traits were also analyzed with a categorical model including the same effects except that community and year were separate factors. Variance components were estimated with marginal maximum likelihood. Genetic relationships between 339 sires analyzed were included in models. The phenotypic correlation between the first and second lactation was defined as a repeatability of trait. The lactational incidence risk of ketosis was .05 in both the first and the second lactation. Average milk production was 4956 and 5547 kg in the first and second lactations, respectively. Estimates of heritabilities were .09 and .07 for ketosis and .23 and .19 for milk in the first and second lactations, respectively. Genetic correlations between first and second lactation recordings were .64 for ketosis and .93 for milk. Repeatabilities between subsequent lactations were .36 (.13 in linear analysis) for ketosis and .68 for milk. In the first lactation, genetic relationship between milk yield and ketosis was unfavorable, but in the second lactation ketosis and milk yield were genetically and phenotypically unrelated.

Effects of clinical ketosis on test day milk yields in Finnish Ayrshire cattle.

A linear model for repeated measurements was used to estimate the effects of clinical ketosis on 722,198 test day milk yields collected from September 1, 1985 to January 31, 1988 on 60,851 Finnish Ayrshire cows of parity < 7. An index was created to differentiate among milk collected within 17 d following diagnosis of ketosis, milk collected before or > 17 d after diagnosis, and milk collected on nonketotic cows. For each parity separately, the statistical model included fixed effects (ketosis, calving season, year and season of milk sampling, and stage of lactation) and random effects (herd and permanent and temporary environments) on test day milk yields. The pattern underlying correlations between temporary environmental effects was accommodated in the statistical model. Compared with those for nonketotic cows, lactation curves of cows with ketosis showed a depression in early lactation; estimated milk loss was 44.3 kg for 17 d after diagnosis. The 305-d milk yield of cows diagnosed with ketosis was estimated to be 141.1 kg higher than that of cows free of ketosis. Although milk losses occurred after ketosis, ketotic cows yielded more milk over the entire lactation than did nonketotic cows; and yields would have been even higher if cows had not had ketosis.

Simulation study on covariance component estimation for two binary traits in an underlying continuous scale.

The usefulness of the variance and covariance component estimation methods based on a threshold model was studied in a multiple-trait situation with two binary traits. Estimation equations that yield marginal maximum likelihood estimates of variance components on the underlying continuous variable scale and point estimates of location parameters with empirical Bayesian properties are described. Methods were tested on simulated data sets that were generated to exhibit three different incidences, 25, 15, and 5%. Results were compared with analyses of the same data sets with a REML method based on normal distribution and a linear model. Heritabilities and residual correlations calculated from discrete observations were transformed to underlying parameters. In estimation of heritabilities, all methods performed equally well at all incidence levels and with no detectable bias. As suggested by threshold theory, the genetic correlation was accurately estimated directly from the observations without any need of correction for incidence. Marginal maximum likelihood estimates of genetic correlations were similar to linear model estimates; discrepancies from the true parameters were consistent with both methods. In estimation of residual correlations, the method with the linear model approach yielded satisfactory estimates only at the highest incidence level, 25%. For 5% incidence, the uncorrected estimate of residual correlation was 50% less than the true value, and after correction for incidence, the parameter was overestimated by 90%. The estimates of residual correlation from the threshold model were regarded fair, except at the lowest level of incidence, where the estimate was 27% higher than the true value. Results indicated that when an accurate estimate of residual correlation is needed, the marginal maximum likelihood estimates are superior to the estimates calculated with the linear model. Using correction for the incidence level for residual correlation did not work well except at the highest incidence level.

Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations.

A Bayesian approach is presented for mapping a quantitative trait locus (QTL) using the 'Fernando and Grossman' multivariate Normal approximation to QTL inheritance. For this model, a Bayesian implementation that includes QTL position is problematic because standard Markov chain Monte Carlo (MCMC) algorithms do not mix, i.e. the QTL position gets stuck in one marker interval. This is because of the dependence of the covariance structure for the QTL effects on the adjacent markers and may be typical of the 'Fernando and Grossman' model. A relatively new MCMC technique, simulated tempering, allows mixing and so makes possible inferences about QTL position based on marginal posterior probabilities. The model was implemented for estimating variance ratios and QTL position using a continuous grid of allowed positions and was applied to simulated data of a standard granddaughter design. The results showed a smooth mixing of QTL position after implementation of the simulated tempering sampler. In this implementation, map distance between QTL and its flanking markers was artificially stretched to reduce the dependence of markers and covariance. The method generalizes easily to more complicated applications and can ultimately contribute to QTL mapping in complex, heterogeneous, human, animal or plant populations.